Finite convolution associativity — exact evidence

Current Alpha v34 checked use; first admitted v31; not Stable. Original HA and the independently compiled Lean checker have freshly verified the complete bundle before this page was generated.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.

347 checked bundle nodes · 971 proof edges · 25115 body proof nodes.

Literal self-contained proof bundle · SHA-256 05cb102ae5fb423e325223589eb17b8f1dd0aa8d3cb8419425142f9be087d9f3

dirichlet_associativity_candidate.py · dirichlet_fubini_candidate.py

Unchanged historical local checkpoint record · Historical snapshot manifest. Those records retain their original non-admitting flags; current authority comes from the separate freshly verified v31 release.

Exact theorem nodes and inherited prerequisites

DF0001 dirichlet_grid_entry_omitted · actual bundle node 314
DF0002 dirichlet_grid_entry_from_factorization · actual bundle node 315
DF0003 dirichlet_grid_entry_omitted_value · actual bundle node 316
DF0004 dirichlet_grid_entry_factor_product · actual bundle node 317
DF0005 dirichlet_grid_entry_functional · actual bundle node 318
DF0006 dirichlet_grid_entry_exists · actual bundle node 319
DF0007 dirichlet_grid_entry_transpose · actual bundle node 320
DF0008 dirichlet_grid_flat_entry_exists · actual bundle node 321
DF0009 dirichlet_grid_flat_entry_coordinates · actual bundle node 322
DF000A dirichlet_grid_flat_prefix_zero · actual bundle node 323
DF000B dirichlet_grid_flat_prefix_append · actual bundle node 324
DF000C dirichlet_grid_flat_prefix_exists · actual bundle node 325
DF000D dirichlet_grid_from_flat_prefix · actual bundle node 326
DF000E dirichlet_grid_table_exists · actual bundle node 327
DF000F dirichlet_grid_table_lookup · actual bundle node 328
DF0010 dirichlet_grid_middle_factor_equation · actual bundle node 329
DF0011 dirichlet_grid_entry_from_convolution_entry · actual bundle node 330
DF0012 dirichlet_grid_entry_convolution_product · actual bundle node 331
DF0013 dirichlet_grid_nondivisor_row_value_zero · actual bundle node 332
DF0014 dirichlet_factor_row_scalar · actual bundle node 333
DF0015 dirichlet_grid_row_slice · actual bundle node 334
DF0016 dirichlet_grid_column_slice · actual bundle node 335
DF0017 dirichlet_grid_fubini_exists · actual bundle node 336
DF0018 dirichlet_factor_row_zero_sum · actual bundle node 337
DF0019 dirichlet_factor_row_sum_product · actual bundle node 338
DF001A dirichlet_factor_row_nested_entry · actual bundle node 339
DF001B dirichlet_grid_row_sums_convolution_prefix · actual bundle node 340
DF001C dirichlet_grid_column_sums_convolution_prefix · actual bundle node 341
DF001D dirichlet_convolution_fubini_interchange · actual bundle node 342
DF001E dirichlet_convolution_associative · actual bundle node 343
DF001F dirichlet_convolution_tables_associative · actual bundle node 344
DF0020 dirichlet_convolution_associative_tables_exists · actual bundle node 345
add_comm · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n m. n + m = m + n
```

arithmetic_signed_sum_exists · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F l. (exists dst_positive_code_sum_exists_input dst_positive_scale_sum_exists_input dst_negative_code_sum_exists_input dst_negative_scale_sum_exists_input. (((F) = (((((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) * S ((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) + ((dst_positive_scale_sum_exists_input) + (dst_positive_scale_sum_exists_input))) + (((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input)))) * S ((((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) * S ((dst_positive_code_sum_exists_input) + (dst_positive_scale_sum_exists_input)) + ((dst_positive_scale_sum_exists_input) + (dst_positive_scale_sum_exists_input))) + (((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input)))) + ((((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input))) + (((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) * S ((dst_negative_code_sum_exists_input) + (dst_negative_scale_sum_exists_input)) + ((dst_negative_scale_sum_exists_input) + (dst_negative_scale_sum_exists_input)))))) /\ (forall dst_index_sum_exists_input. (exists pvs_le_gap_sum_exists_inputdomain. pvs_le_gap_sum_exists_inputdomain + (dst_index_sum_exists_input) = (N)) -> exists dst_positive_sum_exists_input dst_negative_sum_exists_input dst_value_sum_exists_input. ((((exists ff_h_pvs_sum_exists_inputentrypositive. ff_h_pvs_sum_exists_inputentrypositive + S (dst_positive_sum_exists_input) = S ((S (dst_index_sum_exists_input)) * dst_positive_scale_sum_exists_input)) /\ exists ff_q_pvs_sum_exists_inputentrypositive. dst_positive_code_sum_exists_input = ff_q_pvs_sum_exists_inputentrypositive * S ((S (dst_index_sum_exists_input)) * dst_positive_scale_sum_exists_input) + (dst_positive_sum_exists_input))) /\ (((((exists ff_h_pvs_sum_exists_inputentrynegative. ff_h_pvs_sum_exists_inputentrynegative + S (dst_negative_sum_exists_input) = S ((S (dst_index_sum_exists_input)) * dst_negative_scale_sum_exists_input)) /\ exists ff_q_pvs_sum_exists_inputentrynegative. dst_negative_code_sum_exists_input = ff_q_pvs_sum_exists_inputentrynegative * S ((S (dst_index_sum_exists_input)) * dst_negative_scale_sum_exists_input) + (dst_negative_sum_exists_input))) /\ (exists ge_balance_positive_sum_exists_inputentryvalue ge_balance_negative_sum_exists_inputentryvalue. (((((dst_value_sum_exists_input) = 2 * (ge_balance_positive_sum_exists_inputentryvalue) /\ (ge_balance_negative_sum_exists_inputentryvalue) = 0) \/ exists ge_signed_half_sum_exists_inputentryvaluedecode. (((dst_value_sum_exists_input) = 2 * ge_signed_half_sum_exists_inputentryvaluedecode + 1 /\ (ge_balance_positive_sum_exists_inputentryvalue) = 0) /\ (ge_balance_negative_sum_exists_inputentryvalue) = S ge_signed_half_sum_exists_inputentryvaluedecode))) /\ ((dst_positive_sum_exists_input) + ge_balance_negative_sum_exists_inputentryvalue = (dst_negative_sum_exists_input) + ge_balance_positive_sum_exists_inputentryvalue))))))))) -> exists z. (exists dst_positive_code_sum_exists_output dst_positive_scale_sum_exists_output dst_negative_code_sum_exists_output dst_negative_scale_sum_exists_output dst_positive_sum_sum_exists_output dst_negative_sum_sum_exists_output. (((F) = (((((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) * S ((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) + ((dst_positive_scale_sum_exists_output) + (dst_positive_scale_sum_exists_output))) + (((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output)))) * S ((((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) * S ((dst_positive_code_sum_exists_output) + (dst_positive_scale_sum_exists_output)) + ((dst_positive_scale_sum_exists_output) + (dst_positive_scale_sum_exists_output))) + (((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output)))) + ((((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output))) + (((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) * S ((dst_negative_code_sum_exists_output) + (dst_negative_scale_sum_exists_output)) + ((dst_negative_scale_sum_exists_output) + (dst_negative_scale_sum_exists_output)))))) /\ (((exists fs_u_dst_sum_exists_outputpositive fs_v_dst_sum_exists_outputpositive. ((((exists fs_h_dst_sum_exists_outputpositive_body_start. fs_h_dst_sum_exists_outputpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_start. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_start * S ((S (0)) * fs_v_dst_sum_exists_outputpositive) + (0))) /\ ((((exists fs_h_dst_sum_exists_outputpositive_body_terminal. fs_h_dst_sum_exists_outputpositive_body_terminal + S (dst_positive_sum_sum_exists_output) = S ((S (l)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_terminal. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_outputpositive) + (dst_positive_sum_sum_exists_output))) /\ forall fs_i_dst_sum_exists_outputpositive_body_steps. (exists fs_lt_dst_sum_exists_outputpositive_body_steps_bound. fs_lt_dst_sum_exists_outputpositive_body_steps_bound + S fs_i_dst_sum_exists_outputpositive_body_steps = l) -> exists fs_a_dst_sum_exists_outputpositive_body_steps fs_r_dst_sum_exists_outputpositive_body_steps fs_s_dst_sum_exists_outputpositive_body_steps. ((((exists fs_h_dst_sum_exists_outputpositive_body_steps_summand. fs_h_dst_sum_exists_outputpositive_body_steps_summand + S (fs_a_dst_sum_exists_outputpositive_body_steps) = S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * dst_positive_scale_sum_exists_output)) /\ exists fs_q_dst_sum_exists_outputpositive_body_steps_summand. dst_positive_code_sum_exists_output = fs_q_dst_sum_exists_outputpositive_body_steps_summand * S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * dst_positive_scale_sum_exists_output) + (fs_a_dst_sum_exists_outputpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputpositive_body_steps_partial. fs_h_dst_sum_exists_outputpositive_body_steps_partial + S (fs_r_dst_sum_exists_outputpositive_body_steps) = S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_steps_partial. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_steps_partial * S ((S (fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive) + (fs_r_dst_sum_exists_outputpositive_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputpositive_body_steps_successor. fs_h_dst_sum_exists_outputpositive_body_steps_successor + S (fs_s_dst_sum_exists_outputpositive_body_steps) = S ((S (S fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive)) /\ exists fs_q_dst_sum_exists_outputpositive_body_steps_successor. fs_u_dst_sum_exists_outputpositive = fs_q_dst_sum_exists_outputpositive_body_steps_successor * S ((S (S fs_i_dst_sum_exists_outputpositive_body_steps)) * fs_v_dst_sum_exists_outputpositive) + (fs_s_dst_sum_exists_outputpositive_body_steps))) /\ fs_s_dst_sum_exists_outputpositive_body_steps = fs_r_dst_sum_exists_outputpositive_body_steps + fs_a_dst_sum_exists_outputpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_exists_outputnegative fs_v_dst_sum_exists_outputnegative. ((((exists fs_h_dst_sum_exists_outputnegative_body_start. fs_h_dst_sum_exists_outputnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_start. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_start * S ((S (0)) * fs_v_dst_sum_exists_outputnegative) + (0))) /\ ((((exists fs_h_dst_sum_exists_outputnegative_body_terminal. fs_h_dst_sum_exists_outputnegative_body_terminal + S (dst_negative_sum_sum_exists_output) = S ((S (l)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_terminal. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_exists_outputnegative) + (dst_negative_sum_sum_exists_output))) /\ forall fs_i_dst_sum_exists_outputnegative_body_steps. (exists fs_lt_dst_sum_exists_outputnegative_body_steps_bound. fs_lt_dst_sum_exists_outputnegative_body_steps_bound + S fs_i_dst_sum_exists_outputnegative_body_steps = l) -> exists fs_a_dst_sum_exists_outputnegative_body_steps fs_r_dst_sum_exists_outputnegative_body_steps fs_s_dst_sum_exists_outputnegative_body_steps. ((((exists fs_h_dst_sum_exists_outputnegative_body_steps_summand. fs_h_dst_sum_exists_outputnegative_body_steps_summand + S (fs_a_dst_sum_exists_outputnegative_body_steps) = S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * dst_negative_scale_sum_exists_output)) /\ exists fs_q_dst_sum_exists_outputnegative_body_steps_summand. dst_negative_code_sum_exists_output = fs_q_dst_sum_exists_outputnegative_body_steps_summand * S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * dst_negative_scale_sum_exists_output) + (fs_a_dst_sum_exists_outputnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputnegative_body_steps_partial. fs_h_dst_sum_exists_outputnegative_body_steps_partial + S (fs_r_dst_sum_exists_outputnegative_body_steps) = S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_steps_partial. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_steps_partial * S ((S (fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative) + (fs_r_dst_sum_exists_outputnegative_body_steps))) /\ ((((exists fs_h_dst_sum_exists_outputnegative_body_steps_successor. fs_h_dst_sum_exists_outputnegative_body_steps_successor + S (fs_s_dst_sum_exists_outputnegative_body_steps) = S ((S (S fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative)) /\ exists fs_q_dst_sum_exists_outputnegative_body_steps_successor. fs_u_dst_sum_exists_outputnegative = fs_q_dst_sum_exists_outputnegative_body_steps_successor * S ((S (S fs_i_dst_sum_exists_outputnegative_body_steps)) * fs_v_dst_sum_exists_outputnegative) + (fs_s_dst_sum_exists_outputnegative_body_steps))) /\ fs_s_dst_sum_exists_outputnegative_body_steps = fs_r_dst_sum_exists_outputnegative_body_steps + fs_a_dst_sum_exists_outputnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_exists_outputresult ge_balance_negative_sum_exists_outputresult. (((((z) = 2 * (ge_balance_positive_sum_exists_outputresult) /\ (ge_balance_negative_sum_exists_outputresult) = 0) \/ exists ge_signed_half_sum_exists_outputresultdecode. (((z) = 2 * ge_signed_half_sum_exists_outputresultdecode + 1 /\ (ge_balance_positive_sum_exists_outputresult) = 0) /\ (ge_balance_negative_sum_exists_outputresult) = S ge_signed_half_sum_exists_outputresultdecode))) /\ ((dst_positive_sum_sum_exists_output) + ge_balance_negative_sum_exists_outputresult = (dst_negative_sum_sum_exists_output) + ge_balance_positive_sum_exists_outputresult)))))))))

arithmetic_signed_table_append · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F z. (exists dst_positive_code_append_input dst_positive_scale_append_input dst_negative_code_append_input dst_negative_scale_append_input. (((F) = (((((dst_positive_code_append_input) + (dst_positive_scale_append_input)) * S ((dst_positive_code_append_input) + (dst_positive_scale_append_input)) + ((dst_positive_scale_append_input) + (dst_positive_scale_append_input))) + (((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input)))) * S ((((dst_positive_code_append_input) + (dst_positive_scale_append_input)) * S ((dst_positive_code_append_input) + (dst_positive_scale_append_input)) + ((dst_positive_scale_append_input) + (dst_positive_scale_append_input))) + (((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input)))) + ((((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input))) + (((dst_negative_code_append_input) + (dst_negative_scale_append_input)) * S ((dst_negative_code_append_input) + (dst_negative_scale_append_input)) + ((dst_negative_scale_append_input) + (dst_negative_scale_append_input)))))) /\ (forall dst_index_append_input. (exists pvs_le_gap_append_inputdomain. pvs_le_gap_append_inputdomain + (dst_index_append_input) = (N)) -> exists dst_positive_append_input dst_negative_append_input dst_value_append_input. ((((exists ff_h_pvs_append_inputentrypositive. ff_h_pvs_append_inputentrypositive + S (dst_positive_append_input) = S ((S (dst_index_append_input)) * dst_positive_scale_append_input)) /\ exists ff_q_pvs_append_inputentrypositive. dst_positive_code_append_input = ff_q_pvs_append_inputentrypositive * S ((S (dst_index_append_input)) * dst_positive_scale_append_input) + (dst_positive_append_input))) /\ (((((exists ff_h_pvs_append_inputentrynegative. ff_h_pvs_append_inputentrynegative + S (dst_negative_append_input) = S ((S (dst_index_append_input)) * dst_negative_scale_append_input)) /\ exists ff_q_pvs_append_inputentrynegative. dst_negative_code_append_input = ff_q_pvs_append_inputentrynegative * S ((S (dst_index_append_input)) * dst_negative_scale_append_input) + (dst_negative_append_input))) /\ (exists ge_balance_positive_append_inputentryvalue ge_balance_negative_append_inputentryvalue. (((((dst_value_append_input) = 2 * (ge_balance_positive_append_inputentryvalue) /\ (ge_balance_negative_append_inputentryvalue) = 0) \/ exists ge_signed_half_append_inputentryvaluedecode. (((dst_value_append_input) = 2 * ge_signed_half_append_inputentryvaluedecode + 1 /\ (ge_balance_positive_append_inputentryvalue) = 0) /\ (ge_balance_negative_append_inputentryvalue) = S ge_signed_half_append_inputentryvaluedecode))) /\ ((dst_positive_append_input) + ge_balance_negative_append_inputentryvalue = (dst_negative_append_input) + ge_balance_positive_append_inputentryvalue))))))))) -> exists G. (((exists dst_positive_code_append_outputtable dst_positive_scale_append_outputtable dst_negative_code_append_outputtable dst_negative_scale_append_outputtable. (((G) = (((((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) * S ((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) + ((dst_positive_scale_append_outputtable) + (dst_positive_scale_append_outputtable))) + (((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable)))) * S ((((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) * S ((dst_positive_code_append_outputtable) + (dst_positive_scale_append_outputtable)) + ((dst_positive_scale_append_outputtable) + (dst_positive_scale_append_outputtable))) + (((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable)))) + ((((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable))) + (((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) * S ((dst_negative_code_append_outputtable) + (dst_negative_scale_append_outputtable)) + ((dst_negative_scale_append_outputtable) + (dst_negative_scale_append_outputtable)))))) /\ (forall dst_index_append_outputtable. (exists pvs_le_gap_append_outputtabledomain. pvs_le_gap_append_outputtabledomain + (dst_index_append_outputtable) = (S N)) -> exists dst_positive_append_outputtable dst_negative_append_outputtable dst_value_append_outputtable. ((((exists ff_h_pvs_append_outputtableentrypositive. ff_h_pvs_append_outputtableentrypositive + S (dst_positive_append_outputtable) = S ((S (dst_index_append_outputtable)) * dst_positive_scale_append_outputtable)) /\ exists ff_q_pvs_append_outputtableentrypositive. dst_positive_code_append_outputtable = ff_q_pvs_append_outputtableentrypositive * S ((S (dst_index_append_outputtable)) * dst_positive_scale_append_outputtable) + (dst_positive_append_outputtable))) /\ (((((exists ff_h_pvs_append_outputtableentrynegative. ff_h_pvs_append_outputtableentrynegative + S (dst_negative_append_outputtable) = S ((S (dst_index_append_outputtable)) * dst_negative_scale_append_outputtable)) /\ exists ff_q_pvs_append_outputtableentrynegative. dst_negative_code_append_outputtable = ff_q_pvs_append_outputtableentrynegative * S ((S (dst_index_append_outputtable)) * dst_negative_scale_append_outputtable) + (dst_negative_append_outputtable))) /\ (exists ge_balance_positive_append_outputtableentryvalue ge_balance_negative_append_outputtableentryvalue. (((((dst_value_append_outputtable) = 2 * (ge_balance_positive_append_outputtableentryvalue) /\ (ge_balance_negative_append_outputtableentryvalue) = 0) \/ exists ge_signed_half_append_outputtableentryvaluedecode. (((dst_value_append_outputtable) = 2 * ge_signed_half_append_outputtableentryvaluedecode + 1 /\ (ge_balance_positive_append_outputtableentryvalue) = 0) /\ (ge_balance_negative_append_outputtableentryvalue) = S ge_signed_half_append_outputtableentryvaluedecode))) /\ ((dst_positive_append_outputtable) + ge_balance_negative_append_outputtableentryvalue = (dst_negative_append_outputtable) + ge_balance_positive_append_outputtableentryvalue))))))))) /\ (((forall dst_index_append_outputprefix dst_first_append_outputprefix dst_second_append_outputprefix. (exists pvs_gap_append_outputprefixbound. pvs_gap_append_outputprefixbound + S (dst_index_append_outputprefix) = (S N)) -> (exists dst_positive_code_append_outputprefixfirst dst_positive_scale_append_outputprefixfirst dst_negative_code_append_outputprefixfirst dst_negative_scale_append_outputprefixfirst dst_positive_append_outputprefixfirst dst_negative_append_outputprefixfirst. (((F) = (((((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) * S ((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) + ((dst_positive_scale_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst))) + (((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)))) * S ((((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) * S ((dst_positive_code_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst)) + ((dst_positive_scale_append_outputprefixfirst) + (dst_positive_scale_append_outputprefixfirst))) + (((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)))) + ((((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst))) + (((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) * S ((dst_negative_code_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)) + ((dst_negative_scale_append_outputprefixfirst) + (dst_negative_scale_append_outputprefixfirst)))))) /\ (((((exists ff_h_pvs_append_outputprefixfirstpositive. ff_h_pvs_append_outputprefixfirstpositive + S (dst_positive_append_outputprefixfirst) = S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixfirst)) /\ exists ff_q_pvs_append_outputprefixfirstpositive. dst_positive_code_append_outputprefixfirst = ff_q_pvs_append_outputprefixfirstpositive * S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixfirst) + (dst_positive_append_outputprefixfirst))) /\ (((((exists ff_h_pvs_append_outputprefixfirstnegative. ff_h_pvs_append_outputprefixfirstnegative + S (dst_negative_append_outputprefixfirst) = S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixfirst)) /\ exists ff_q_pvs_append_outputprefixfirstnegative. dst_negative_code_append_outputprefixfirst = ff_q_pvs_append_outputprefixfirstnegative * S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixfirst) + (dst_negative_append_outputprefixfirst))) /\ (exists ge_balance_positive_append_outputprefixfirstvalue ge_balance_negative_append_outputprefixfirstvalue. (((((dst_first_append_outputprefix) = 2 * (ge_balance_positive_append_outputprefixfirstvalue) /\ (ge_balance_negative_append_outputprefixfirstvalue) = 0) \/ exists ge_signed_half_append_outputprefixfirstvaluedecode. (((dst_first_append_outputprefix) = 2 * ge_signed_half_append_outputprefixfirstvaluedecode + 1 /\ (ge_balance_positive_append_outputprefixfirstvalue) = 0) /\ (ge_balance_negative_append_outputprefixfirstvalue) = S ge_signed_half_append_outputprefixfirstvaluedecode))) /\ ((dst_positive_append_outputprefixfirst) + ge_balance_negative_append_outputprefixfirstvalue = (dst_negative_append_outputprefixfirst) + ge_balance_positive_append_outputprefixfirstvalue))))))))) -> (exists dst_positive_code_append_outputprefixsecond dst_positive_scale_append_outputprefixsecond dst_negative_code_append_outputprefixsecond dst_negative_scale_append_outputprefixsecond dst_positive_append_outputprefixsecond dst_negative_append_outputprefixsecond. (((G) = (((((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) * S ((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) + ((dst_positive_scale_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond))) + (((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)))) * S ((((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) * S ((dst_positive_code_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond)) + ((dst_positive_scale_append_outputprefixsecond) + (dst_positive_scale_append_outputprefixsecond))) + (((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)))) + ((((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond))) + (((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) * S ((dst_negative_code_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)) + ((dst_negative_scale_append_outputprefixsecond) + (dst_negative_scale_append_outputprefixsecond)))))) /\ (((((exists ff_h_pvs_append_outputprefixsecondpositive. ff_h_pvs_append_outputprefixsecondpositive + S (dst_positive_append_outputprefixsecond) = S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixsecond)) /\ exists ff_q_pvs_append_outputprefixsecondpositive. dst_positive_code_append_outputprefixsecond = ff_q_pvs_append_outputprefixsecondpositive * S ((S (dst_index_append_outputprefix)) * dst_positive_scale_append_outputprefixsecond) + (dst_positive_append_outputprefixsecond))) /\ (((((exists ff_h_pvs_append_outputprefixsecondnegative. ff_h_pvs_append_outputprefixsecondnegative + S (dst_negative_append_outputprefixsecond) = S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixsecond)) /\ exists ff_q_pvs_append_outputprefixsecondnegative. dst_negative_code_append_outputprefixsecond = ff_q_pvs_append_outputprefixsecondnegative * S ((S (dst_index_append_outputprefix)) * dst_negative_scale_append_outputprefixsecond) + (dst_negative_append_outputprefixsecond))) /\ (exists ge_balance_positive_append_outputprefixsecondvalue ge_balance_negative_append_outputprefixsecondvalue. (((((dst_second_append_outputprefix) = 2 * (ge_balance_positive_append_outputprefixsecondvalue) /\ (ge_balance_negative_append_outputprefixsecondvalue) = 0) \/ exists ge_signed_half_append_outputprefixsecondvaluedecode. (((dst_second_append_outputprefix) = 2 * ge_signed_half_append_outputprefixsecondvaluedecode + 1 /\ (ge_balance_positive_append_outputprefixsecondvalue) = 0) /\ (ge_balance_negative_append_outputprefixsecondvalue) = S ge_signed_half_append_outputprefixsecondvaluedecode))) /\ ((dst_positive_append_outputprefixsecond) + ge_balance_negative_append_outputprefixsecondvalue = (dst_negative_append_outputprefixsecond) + ge_balance_positive_append_outputprefixsecondvalue))))))))) -> dst_first_append_outputprefix = dst_second_append_outputprefix) /\ (exists dst_positive_code_append_outputlast dst_positive_scale_append_outputlast dst_negative_code_append_outputlast dst_negative_scale_append_outputlast dst_positive_append_outputlast dst_negative_append_outputlast. (((G) = (((((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) * S ((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) + ((dst_positive_scale_append_outputlast) + (dst_positive_scale_append_outputlast))) + (((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast)))) * S ((((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) * S ((dst_positive_code_append_outputlast) + (dst_positive_scale_append_outputlast)) + ((dst_positive_scale_append_outputlast) + (dst_positive_scale_append_outputlast))) + (((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast)))) + ((((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast))) + (((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) * S ((dst_negative_code_append_outputlast) + (dst_negative_scale_append_outputlast)) + ((dst_negative_scale_append_outputlast) + (dst_negative_scale_append_outputlast)))))) /\ (((((exists ff_h_pvs_append_outputlastpositive. ff_h_pvs_append_outputlastpositive + S (dst_positive_append_outputlast) = S ((S (S N)) * dst_positive_scale_append_outputlast)) /\ exists ff_q_pvs_append_outputlastpositive. dst_positive_code_append_outputlast = ff_q_pvs_append_outputlastpositive * S ((S (S N)) * dst_positive_scale_append_outputlast) + (dst_positive_append_outputlast))) /\ (((((exists ff_h_pvs_append_outputlastnegative. ff_h_pvs_append_outputlastnegative + S (dst_negative_append_outputlast) = S ((S (S N)) * dst_negative_scale_append_outputlast)) /\ exists ff_q_pvs_append_outputlastnegative. dst_negative_code_append_outputlast = ff_q_pvs_append_outputlastnegative * S ((S (S N)) * dst_negative_scale_append_outputlast) + (dst_negative_append_outputlast))) /\ (exists ge_balance_positive_append_outputlastvalue ge_balance_negative_append_outputlastvalue. (((((z) = 2 * (ge_balance_positive_append_outputlastvalue) /\ (ge_balance_negative_append_outputlastvalue) = 0) \/ exists ge_signed_half_append_outputlastvaluedecode. (((z) = 2 * ge_signed_half_append_outputlastvaluedecode + 1 /\ (ge_balance_positive_append_outputlastvalue) = 0) /\ (ge_balance_negative_append_outputlastvalue) = S ge_signed_half_append_outputlastvaluedecode))) /\ ((dst_positive_append_outputlast) + ge_balance_negative_append_outputlastvalue = (dst_negative_append_outputlast) + ge_balance_positive_append_outputlastvalue)))))))))))))

arithmetic_signed_table_singleton · checked inherited prerequisite

Exact statement in the checked dependency cone

forall z. exists F. (exists dst_positive_code_singleton_valid dst_positive_scale_singleton_valid dst_negative_code_singleton_valid dst_negative_scale_singleton_valid. (((F) = (((((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) * S ((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) + ((dst_positive_scale_singleton_valid) + (dst_positive_scale_singleton_valid))) + (((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid)))) * S ((((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) * S ((dst_positive_code_singleton_valid) + (dst_positive_scale_singleton_valid)) + ((dst_positive_scale_singleton_valid) + (dst_positive_scale_singleton_valid))) + (((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid)))) + ((((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid))) + (((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) * S ((dst_negative_code_singleton_valid) + (dst_negative_scale_singleton_valid)) + ((dst_negative_scale_singleton_valid) + (dst_negative_scale_singleton_valid)))))) /\ (forall dst_index_singleton_valid. (exists pvs_le_gap_singleton_validdomain. pvs_le_gap_singleton_validdomain + (dst_index_singleton_valid) = (0)) -> exists dst_positive_singleton_valid dst_negative_singleton_valid dst_value_singleton_valid. ((((exists ff_h_pvs_singleton_validentrypositive. ff_h_pvs_singleton_validentrypositive + S (dst_positive_singleton_valid) = S ((S (dst_index_singleton_valid)) * dst_positive_scale_singleton_valid)) /\ exists ff_q_pvs_singleton_validentrypositive. dst_positive_code_singleton_valid = ff_q_pvs_singleton_validentrypositive * S ((S (dst_index_singleton_valid)) * dst_positive_scale_singleton_valid) + (dst_positive_singleton_valid))) /\ (((((exists ff_h_pvs_singleton_validentrynegative. ff_h_pvs_singleton_validentrynegative + S (dst_negative_singleton_valid) = S ((S (dst_index_singleton_valid)) * dst_negative_scale_singleton_valid)) /\ exists ff_q_pvs_singleton_validentrynegative. dst_negative_code_singleton_valid = ff_q_pvs_singleton_validentrynegative * S ((S (dst_index_singleton_valid)) * dst_negative_scale_singleton_valid) + (dst_negative_singleton_valid))) /\ (exists ge_balance_positive_singleton_validentryvalue ge_balance_negative_singleton_validentryvalue. (((((dst_value_singleton_valid) = 2 * (ge_balance_positive_singleton_validentryvalue) /\ (ge_balance_negative_singleton_validentryvalue) = 0) \/ exists ge_signed_half_singleton_validentryvaluedecode. (((dst_value_singleton_valid) = 2 * ge_signed_half_singleton_validentryvaluedecode + 1 /\ (ge_balance_positive_singleton_validentryvalue) = 0) /\ (ge_balance_negative_singleton_validentryvalue) = S ge_signed_half_singleton_validentryvaluedecode))) /\ ((dst_positive_singleton_valid) + ge_balance_negative_singleton_validentryvalue = (dst_negative_singleton_valid) + ge_balance_positive_singleton_validentryvalue))))))))) /\ (exists dst_positive_code_singleton_value dst_positive_scale_singleton_value dst_negative_code_singleton_value dst_negative_scale_singleton_value dst_positive_singleton_value dst_negative_singleton_value. (((F) = (((((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) * S ((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) + ((dst_positive_scale_singleton_value) + (dst_positive_scale_singleton_value))) + (((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value)))) * S ((((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) * S ((dst_positive_code_singleton_value) + (dst_positive_scale_singleton_value)) + ((dst_positive_scale_singleton_value) + (dst_positive_scale_singleton_value))) + (((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value)))) + ((((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value))) + (((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) * S ((dst_negative_code_singleton_value) + (dst_negative_scale_singleton_value)) + ((dst_negative_scale_singleton_value) + (dst_negative_scale_singleton_value)))))) /\ (((((exists ff_h_pvs_singleton_valuepositive. ff_h_pvs_singleton_valuepositive + S (dst_positive_singleton_value) = S ((S (0)) * dst_positive_scale_singleton_value)) /\ exists ff_q_pvs_singleton_valuepositive. dst_positive_code_singleton_value = ff_q_pvs_singleton_valuepositive * S ((S (0)) * dst_positive_scale_singleton_value) + (dst_positive_singleton_value))) /\ (((((exists ff_h_pvs_singleton_valuenegative. ff_h_pvs_singleton_valuenegative + S (dst_negative_singleton_value) = S ((S (0)) * dst_negative_scale_singleton_value)) /\ exists ff_q_pvs_singleton_valuenegative. dst_negative_code_singleton_value = ff_q_pvs_singleton_valuenegative * S ((S (0)) * dst_negative_scale_singleton_value) + (dst_negative_singleton_value))) /\ (exists ge_balance_positive_singleton_valuevalue ge_balance_negative_singleton_valuevalue. (((((z) = 2 * (ge_balance_positive_singleton_valuevalue) /\ (ge_balance_negative_singleton_valuevalue) = 0) \/ exists ge_signed_half_singleton_valuevaluedecode. (((z) = 2 * ge_signed_half_singleton_valuevaluedecode + 1 /\ (ge_balance_positive_singleton_valuevalue) = 0) /\ (ge_balance_negative_singleton_valuevalue) = S ge_signed_half_singleton_valuevaluedecode))) /\ ((dst_positive_singleton_value) + ge_balance_negative_singleton_valuevalue = (dst_negative_singleton_value) + ge_balance_positive_singleton_valuevalue)))))))))

dirichlet_convolution_entry_from_quotient · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n d q a b z. ~(d=0) -> n=d*q -> (exists dst_positive_code_keep_left dst_positive_scale_keep_left dst_negative_code_keep_left dst_negative_scale_keep_left dst_positive_keep_left dst_negative_keep_left. (((F) = (((((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) * S ((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) + ((dst_positive_scale_keep_left) + (dst_positive_scale_keep_left))) + (((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left)))) * S ((((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) * S ((dst_positive_code_keep_left) + (dst_positive_scale_keep_left)) + ((dst_positive_scale_keep_left) + (dst_positive_scale_keep_left))) + (((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left)))) + ((((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left))) + (((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) * S ((dst_negative_code_keep_left) + (dst_negative_scale_keep_left)) + ((dst_negative_scale_keep_left) + (dst_negative_scale_keep_left)))))) /\ (((((exists ff_h_pvs_keep_leftpositive. ff_h_pvs_keep_leftpositive + S (dst_positive_keep_left) = S ((S (d)) * dst_positive_scale_keep_left)) /\ exists ff_q_pvs_keep_leftpositive. dst_positive_code_keep_left = ff_q_pvs_keep_leftpositive * S ((S (d)) * dst_positive_scale_keep_left) + (dst_positive_keep_left))) /\ (((((exists ff_h_pvs_keep_leftnegative. ff_h_pvs_keep_leftnegative + S (dst_negative_keep_left) = S ((S (d)) * dst_negative_scale_keep_left)) /\ exists ff_q_pvs_keep_leftnegative. dst_negative_code_keep_left = ff_q_pvs_keep_leftnegative * S ((S (d)) * dst_negative_scale_keep_left) + (dst_negative_keep_left))) /\ (exists ge_balance_positive_keep_leftvalue ge_balance_negative_keep_leftvalue. (((((a) = 2 * (ge_balance_positive_keep_leftvalue) /\ (ge_balance_negative_keep_leftvalue) = 0) \/ exists ge_signed_half_keep_leftvaluedecode. (((a) = 2 * ge_signed_half_keep_leftvaluedecode + 1 /\ (ge_balance_positive_keep_leftvalue) = 0) /\ (ge_balance_negative_keep_leftvalue) = S ge_signed_half_keep_leftvaluedecode))) /\ ((dst_positive_keep_left) + ge_balance_negative_keep_leftvalue = (dst_negative_keep_left) + ge_balance_positive_keep_leftvalue))))))))) -> (exists dst_positive_code_keep_right dst_positive_scale_keep_right dst_negative_code_keep_right dst_negative_scale_keep_right dst_positive_keep_right dst_negative_keep_right. (((G) = (((((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) * S ((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) + ((dst_positive_scale_keep_right) + (dst_positive_scale_keep_right))) + (((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right)))) * S ((((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) * S ((dst_positive_code_keep_right) + (dst_positive_scale_keep_right)) + ((dst_positive_scale_keep_right) + (dst_positive_scale_keep_right))) + (((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right)))) + ((((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right))) + (((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) * S ((dst_negative_code_keep_right) + (dst_negative_scale_keep_right)) + ((dst_negative_scale_keep_right) + (dst_negative_scale_keep_right)))))) /\ (((((exists ff_h_pvs_keep_rightpositive. ff_h_pvs_keep_rightpositive + S (dst_positive_keep_right) = S ((S (q)) * dst_positive_scale_keep_right)) /\ exists ff_q_pvs_keep_rightpositive. dst_positive_code_keep_right = ff_q_pvs_keep_rightpositive * S ((S (q)) * dst_positive_scale_keep_right) + (dst_positive_keep_right))) /\ (((((exists ff_h_pvs_keep_rightnegative. ff_h_pvs_keep_rightnegative + S (dst_negative_keep_right) = S ((S (q)) * dst_negative_scale_keep_right)) /\ exists ff_q_pvs_keep_rightnegative. dst_negative_code_keep_right = ff_q_pvs_keep_rightnegative * S ((S (q)) * dst_negative_scale_keep_right) + (dst_negative_keep_right))) /\ (exists ge_balance_positive_keep_rightvalue ge_balance_negative_keep_rightvalue. (((((b) = 2 * (ge_balance_positive_keep_rightvalue) /\ (ge_balance_negative_keep_rightvalue) = 0) \/ exists ge_signed_half_keep_rightvaluedecode. (((b) = 2 * ge_signed_half_keep_rightvaluedecode + 1 /\ (ge_balance_positive_keep_rightvalue) = 0) /\ (ge_balance_negative_keep_rightvalue) = S ge_signed_half_keep_rightvaluedecode))) /\ ((dst_positive_keep_right) + ge_balance_negative_keep_rightvalue = (dst_negative_keep_right) + ge_balance_positive_keep_rightvalue))))))))) -> (exists sto_ap_keep_product sto_an_keep_product sto_bp_keep_product sto_bn_keep_product sto_cp_keep_product sto_cn_keep_product. (((((a) = 2 * (sto_ap_keep_product) /\ (sto_an_keep_product) = 0) \/ exists ge_signed_half_keep_productleft. (((a) = 2 * ge_signed_half_keep_productleft + 1 /\ (sto_ap_keep_product) = 0) /\ (sto_an_keep_product) = S ge_signed_half_keep_productleft))) /\ ((((((b) = 2 * (sto_bp_keep_product) /\ (sto_bn_keep_product) = 0) \/ exists ge_signed_half_keep_productright. (((b) = 2 * ge_signed_half_keep_productright + 1 /\ (sto_bp_keep_product) = 0) /\ (sto_bn_keep_product) = S ge_signed_half_keep_productright))) /\ ((((((z) = 2 * (sto_cp_keep_product) /\ (sto_cn_keep_product) = 0) \/ exists ge_signed_half_keep_productoutput. (((z) = 2 * ge_signed_half_keep_productoutput + 1 /\ (sto_cp_keep_product) = 0) /\ (sto_cn_keep_product) = S ge_signed_half_keep_productoutput))) /\ ((sto_ap_keep_product * sto_bp_keep_product + sto_an_keep_product * sto_bn_keep_product) + sto_cn_keep_product = (sto_ap_keep_product * sto_bn_keep_product + sto_an_keep_product * sto_bp_keep_product) + sto_cp_keep_product))))))) -> ((((~((d)=0)) /\ (exists dc_quotient_keep_result dc_left_keep_result dc_right_keep_result. (((n)=(d)*dc_quotient_keep_result) /\ (((exists dst_positive_code_keep_resultleft dst_positive_scale_keep_resultleft dst_negative_code_keep_resultleft dst_negative_scale_keep_resultleft dst_positive_keep_resultleft dst_negative_keep_resultleft. (((F) = (((((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) * S ((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) + ((dst_positive_scale_keep_resultleft) + (dst_positive_scale_keep_resultleft))) + (((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft)))) * S ((((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) * S ((dst_positive_code_keep_resultleft) + (dst_positive_scale_keep_resultleft)) + ((dst_positive_scale_keep_resultleft) + (dst_positive_scale_keep_resultleft))) + (((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft)))) + ((((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft))) + (((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) * S ((dst_negative_code_keep_resultleft) + (dst_negative_scale_keep_resultleft)) + ((dst_negative_scale_keep_resultleft) + (dst_negative_scale_keep_resultleft)))))) /\ (((((exists ff_h_pvs_keep_resultleftpositive. ff_h_pvs_keep_resultleftpositive + S (dst_positive_keep_resultleft) = S ((S (d)) * dst_positive_scale_keep_resultleft)) /\ exists ff_q_pvs_keep_resultleftpositive. dst_positive_code_keep_resultleft = ff_q_pvs_keep_resultleftpositive * S ((S (d)) * dst_positive_scale_keep_resultleft) + (dst_positive_keep_resultleft))) /\ (((((exists ff_h_pvs_keep_resultleftnegative. ff_h_pvs_keep_resultleftnegative + S (dst_negative_keep_resultleft) = S ((S (d)) * dst_negative_scale_keep_resultleft)) /\ exists ff_q_pvs_keep_resultleftnegative. dst_negative_code_keep_resultleft = ff_q_pvs_keep_resultleftnegative * S ((S (d)) * dst_negative_scale_keep_resultleft) + (dst_negative_keep_resultleft))) /\ (exists ge_balance_positive_keep_resultleftvalue ge_balance_negative_keep_resultleftvalue. (((((dc_left_keep_result) = 2 * (ge_balance_positive_keep_resultleftvalue) /\ (ge_balance_negative_keep_resultleftvalue) = 0) \/ exists ge_signed_half_keep_resultleftvaluedecode. (((dc_left_keep_result) = 2 * ge_signed_half_keep_resultleftvaluedecode + 1 /\ (ge_balance_positive_keep_resultleftvalue) = 0) /\ (ge_balance_negative_keep_resultleftvalue) = S ge_signed_half_keep_resultleftvaluedecode))) /\ ((dst_positive_keep_resultleft) + ge_balance_negative_keep_resultleftvalue = (dst_negative_keep_resultleft) + ge_balance_positive_keep_resultleftvalue))))))))) /\ (((exists dst_positive_code_keep_resultright dst_positive_scale_keep_resultright dst_negative_code_keep_resultright dst_negative_scale_keep_resultright dst_positive_keep_resultright dst_negative_keep_resultright. (((G) = (((((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) * S ((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) + ((dst_positive_scale_keep_resultright) + (dst_positive_scale_keep_resultright))) + (((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright)))) * S ((((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) * S ((dst_positive_code_keep_resultright) + (dst_positive_scale_keep_resultright)) + ((dst_positive_scale_keep_resultright) + (dst_positive_scale_keep_resultright))) + (((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright)))) + ((((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright))) + (((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) * S ((dst_negative_code_keep_resultright) + (dst_negative_scale_keep_resultright)) + ((dst_negative_scale_keep_resultright) + (dst_negative_scale_keep_resultright)))))) /\ (((((exists ff_h_pvs_keep_resultrightpositive. ff_h_pvs_keep_resultrightpositive + S (dst_positive_keep_resultright) = S ((S (dc_quotient_keep_result)) * dst_positive_scale_keep_resultright)) /\ exists ff_q_pvs_keep_resultrightpositive. dst_positive_code_keep_resultright = ff_q_pvs_keep_resultrightpositive * S ((S (dc_quotient_keep_result)) * dst_positive_scale_keep_resultright) + (dst_positive_keep_resultright))) /\ (((((exists ff_h_pvs_keep_resultrightnegative. ff_h_pvs_keep_resultrightnegative + S (dst_negative_keep_resultright) = S ((S (dc_quotient_keep_result)) * dst_negative_scale_keep_resultright)) /\ exists ff_q_pvs_keep_resultrightnegative. dst_negative_code_keep_resultright = ff_q_pvs_keep_resultrightnegative * S ((S (dc_quotient_keep_result)) * dst_negative_scale_keep_resultright) + (dst_negative_keep_resultright))) /\ (exists ge_balance_positive_keep_resultrightvalue ge_balance_negative_keep_resultrightvalue. (((((dc_right_keep_result) = 2 * (ge_balance_positive_keep_resultrightvalue) /\ (ge_balance_negative_keep_resultrightvalue) = 0) \/ exists ge_signed_half_keep_resultrightvaluedecode. (((dc_right_keep_result) = 2 * ge_signed_half_keep_resultrightvaluedecode + 1 /\ (ge_balance_positive_keep_resultrightvalue) = 0) /\ (ge_balance_negative_keep_resultrightvalue) = S ge_signed_half_keep_resultrightvaluedecode))) /\ ((dst_positive_keep_resultright) + ge_balance_negative_keep_resultrightvalue = (dst_negative_keep_resultright) + ge_balance_positive_keep_resultrightvalue))))))))) /\ (exists sto_ap_keep_resultproduct sto_an_keep_resultproduct sto_bp_keep_resultproduct sto_bn_keep_resultproduct sto_cp_keep_resultproduct sto_cn_keep_resultproduct. (((((dc_left_keep_result) = 2 * (sto_ap_keep_resultproduct) /\ (sto_an_keep_resultproduct) = 0) \/ exists ge_signed_half_keep_resultproductleft. (((dc_left_keep_result) = 2 * ge_signed_half_keep_resultproductleft + 1 /\ (sto_ap_keep_resultproduct) = 0) /\ (sto_an_keep_resultproduct) = S ge_signed_half_keep_resultproductleft))) /\ ((((((dc_right_keep_result) = 2 * (sto_bp_keep_resultproduct) /\ (sto_bn_keep_resultproduct) = 0) \/ exists ge_signed_half_keep_resultproductright. (((dc_right_keep_result) = 2 * ge_signed_half_keep_resultproductright + 1 /\ (sto_bp_keep_resultproduct) = 0) /\ (sto_bn_keep_resultproduct) = S ge_signed_half_keep_resultproductright))) /\ ((((((z) = 2 * (sto_cp_keep_resultproduct) /\ (sto_cn_keep_resultproduct) = 0) \/ exists ge_signed_half_keep_resultproductoutput. (((z) = 2 * ge_signed_half_keep_resultproductoutput + 1 /\ (sto_cp_keep_resultproduct) = 0) /\ (sto_cn_keep_resultproduct) = S ge_signed_half_keep_resultproductoutput))) /\ ((sto_ap_keep_resultproduct * sto_bp_keep_resultproduct + sto_an_keep_resultproduct * sto_bn_keep_resultproduct) + sto_cn_keep_resultproduct = (sto_ap_keep_resultproduct * sto_bn_keep_resultproduct + sto_an_keep_resultproduct * sto_bp_keep_resultproduct) + sto_cp_keep_resultproduct))))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_keep_resultnondivisor. (n) = (d) * pvs_factor_keep_resultnondivisor)) /\ ((z)=0))))

dirichlet_convolution_from_padded_prefix · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n L M z. ~(n=0) -> (exists pvs_le_gap_padded_bound. pvs_le_gap_padded_bound + (n) = (L)) -> (((exists dst_positive_code_padded_prefixtable dst_positive_scale_padded_prefixtable dst_negative_code_padded_prefixtable dst_negative_scale_padded_prefixtable. (((M) = (((((dst_positive_code_padded_prefixtable) + (dst_positive_scale_padded_prefixtable)) * S ((dst_positive_code_padded_prefixtable) + (dst_positive_scale_padded_prefixtable)) + ((dst_positive_scale_padded_prefixtable) + (dst_positive_scale_padded_prefixtable))) + (((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) * S ((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) + ((dst_negative_scale_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)))) * S ((((dst_positive_code_padded_prefixtable) + (dst_positive_scale_padded_prefixtable)) * S ((dst_positive_code_padded_prefixtable) + (dst_positive_scale_padded_prefixtable)) + ((dst_positive_scale_padded_prefixtable) + (dst_positive_scale_padded_prefixtable))) + (((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) * S ((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) + ((dst_negative_scale_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)))) + ((((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) * S ((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) + ((dst_negative_scale_padded_prefixtable) + (dst_negative_scale_padded_prefixtable))) + (((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) * S ((dst_negative_code_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)) + ((dst_negative_scale_padded_prefixtable) + (dst_negative_scale_padded_prefixtable)))))) /\ (forall dst_index_padded_prefixtable. (exists pvs_le_gap_padded_prefixtabledomain. pvs_le_gap_padded_prefixtabledomain + (dst_index_padded_prefixtable) = (L)) -> exists dst_positive_padded_prefixtable dst_negative_padded_prefixtable dst_value_padded_prefixtable. ((((exists ff_h_pvs_padded_prefixtableentrypositive. ff_h_pvs_padded_prefixtableentrypositive + S (dst_positive_padded_prefixtable) = S ((S (dst_index_padded_prefixtable)) * dst_positive_scale_padded_prefixtable)) /\ exists ff_q_pvs_padded_prefixtableentrypositive. dst_positive_code_padded_prefixtable = ff_q_pvs_padded_prefixtableentrypositive * S ((S (dst_index_padded_prefixtable)) * dst_positive_scale_padded_prefixtable) + (dst_positive_padded_prefixtable))) /\ (((((exists ff_h_pvs_padded_prefixtableentrynegative. ff_h_pvs_padded_prefixtableentrynegative + S (dst_negative_padded_prefixtable) = S ((S (dst_index_padded_prefixtable)) * dst_negative_scale_padded_prefixtable)) /\ exists ff_q_pvs_padded_prefixtableentrynegative. dst_negative_code_padded_prefixtable = ff_q_pvs_padded_prefixtableentrynegative * S ((S (dst_index_padded_prefixtable)) * dst_negative_scale_padded_prefixtable) + (dst_negative_padded_prefixtable))) /\ (exists ge_balance_positive_padded_prefixtableentryvalue ge_balance_negative_padded_prefixtableentryvalue. (((((dst_value_padded_prefixtable) = 2 * (ge_balance_positive_padded_prefixtableentryvalue) /\ (ge_balance_negative_padded_prefixtableentryvalue) = 0) \/ exists ge_signed_half_padded_prefixtableentryvaluedecode. (((dst_value_padded_prefixtable) = 2 * ge_signed_half_padded_prefixtableentryvaluedecode + 1 /\ (ge_balance_positive_padded_prefixtableentryvalue) = 0) /\ (ge_balance_negative_padded_prefixtableentryvalue) = S ge_signed_half_padded_prefixtableentryvaluedecode))) /\ ((dst_positive_padded_prefixtable) + ge_balance_negative_padded_prefixtableentryvalue = (dst_negative_padded_prefixtable) + ge_balance_positive_padded_prefixtableentryvalue))))))))) /\ (forall dc_index_padded_prefix dc_value_padded_prefix. (exists pvs_le_gap_padded_prefixdomain. pvs_le_gap_padded_prefixdomain + (dc_index_padded_prefix) = (L)) -> (exists dst_positive_code_padded_prefixlookup dst_positive_scale_padded_prefixlookup dst_negative_code_padded_prefixlookup dst_negative_scale_padded_prefixlookup dst_positive_padded_prefixlookup dst_negative_padded_prefixlookup. (((M) = (((((dst_positive_code_padded_prefixlookup) + (dst_positive_scale_padded_prefixlookup)) * S ((dst_positive_code_padded_prefixlookup) + (dst_positive_scale_padded_prefixlookup)) + ((dst_positive_scale_padded_prefixlookup) + (dst_positive_scale_padded_prefixlookup))) + (((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) * S ((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) + ((dst_negative_scale_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)))) * S ((((dst_positive_code_padded_prefixlookup) + (dst_positive_scale_padded_prefixlookup)) * S ((dst_positive_code_padded_prefixlookup) + (dst_positive_scale_padded_prefixlookup)) + ((dst_positive_scale_padded_prefixlookup) + (dst_positive_scale_padded_prefixlookup))) + (((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) * S ((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) + ((dst_negative_scale_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)))) + ((((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) * S ((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) + ((dst_negative_scale_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup))) + (((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) * S ((dst_negative_code_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)) + ((dst_negative_scale_padded_prefixlookup) + (dst_negative_scale_padded_prefixlookup)))))) /\ (((((exists ff_h_pvs_padded_prefixlookuppositive. ff_h_pvs_padded_prefixlookuppositive + S (dst_positive_padded_prefixlookup) = S ((S (dc_index_padded_prefix)) * dst_positive_scale_padded_prefixlookup)) /\ exists ff_q_pvs_padded_prefixlookuppositive. dst_positive_code_padded_prefixlookup = ff_q_pvs_padded_prefixlookuppositive * S ((S (dc_index_padded_prefix)) * dst_positive_scale_padded_prefixlookup) + (dst_positive_padded_prefixlookup))) /\ (((((exists ff_h_pvs_padded_prefixlookupnegative. ff_h_pvs_padded_prefixlookupnegative + S (dst_negative_padded_prefixlookup) = S ((S (dc_index_padded_prefix)) * dst_negative_scale_padded_prefixlookup)) /\ exists ff_q_pvs_padded_prefixlookupnegative. dst_negative_code_padded_prefixlookup = ff_q_pvs_padded_prefixlookupnegative * S ((S (dc_index_padded_prefix)) * dst_negative_scale_padded_prefixlookup) + (dst_negative_padded_prefixlookup))) /\ (exists ge_balance_positive_padded_prefixlookupvalue ge_balance_negative_padded_prefixlookupvalue. (((((dc_value_padded_prefix) = 2 * (ge_balance_positive_padded_prefixlookupvalue) /\ (ge_balance_negative_padded_prefixlookupvalue) = 0) \/ exists ge_signed_half_padded_prefixlookupvaluedecode. (((dc_value_padded_prefix) = 2 * ge_signed_half_padded_prefixlookupvaluedecode + 1 /\ (ge_balance_positive_padded_prefixlookupvalue) = 0) /\ (ge_balance_negative_padded_prefixlookupvalue) = S ge_signed_half_padded_prefixlookupvaluedecode))) /\ ((dst_positive_padded_prefixlookup) + ge_balance_negative_padded_prefixlookupvalue = (dst_negative_padded_prefixlookup) + ge_balance_positive_padded_prefixlookupvalue))))))))) -> ((((~((dc_index_padded_prefix)=0)) /\ (exists dc_quotient_padded_prefixentry dc_left_padded_prefixentry dc_right_padded_prefixentry. (((n)=(dc_index_padded_prefix)*dc_quotient_padded_prefixentry) /\ (((exists dst_positive_code_padded_prefixentryleft dst_positive_scale_padded_prefixentryleft dst_negative_code_padded_prefixentryleft dst_negative_scale_padded_prefixentryleft dst_positive_padded_prefixentryleft dst_negative_padded_prefixentryleft. (((F) = (((((dst_positive_code_padded_prefixentryleft) + (dst_positive_scale_padded_prefixentryleft)) * S ((dst_positive_code_padded_prefixentryleft) + (dst_positive_scale_padded_prefixentryleft)) + ((dst_positive_scale_padded_prefixentryleft) + (dst_positive_scale_padded_prefixentryleft))) + (((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) * S ((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) + ((dst_negative_scale_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)))) * S ((((dst_positive_code_padded_prefixentryleft) + (dst_positive_scale_padded_prefixentryleft)) * S ((dst_positive_code_padded_prefixentryleft) + (dst_positive_scale_padded_prefixentryleft)) + ((dst_positive_scale_padded_prefixentryleft) + (dst_positive_scale_padded_prefixentryleft))) + (((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) * S ((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) + ((dst_negative_scale_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)))) + ((((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) * S ((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) + ((dst_negative_scale_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft))) + (((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) * S ((dst_negative_code_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)) + ((dst_negative_scale_padded_prefixentryleft) + (dst_negative_scale_padded_prefixentryleft)))))) /\ (((((exists ff_h_pvs_padded_prefixentryleftpositive. ff_h_pvs_padded_prefixentryleftpositive + S (dst_positive_padded_prefixentryleft) = S ((S (dc_index_padded_prefix)) * dst_positive_scale_padded_prefixentryleft)) /\ exists ff_q_pvs_padded_prefixentryleftpositive. dst_positive_code_padded_prefixentryleft = ff_q_pvs_padded_prefixentryleftpositive * S ((S (dc_index_padded_prefix)) * dst_positive_scale_padded_prefixentryleft) + (dst_positive_padded_prefixentryleft))) /\ (((((exists ff_h_pvs_padded_prefixentryleftnegative. ff_h_pvs_padded_prefixentryleftnegative + S (dst_negative_padded_prefixentryleft) = S ((S (dc_index_padded_prefix)) * dst_negative_scale_padded_prefixentryleft)) /\ exists ff_q_pvs_padded_prefixentryleftnegative. dst_negative_code_padded_prefixentryleft = ff_q_pvs_padded_prefixentryleftnegative * S ((S (dc_index_padded_prefix)) * dst_negative_scale_padded_prefixentryleft) + (dst_negative_padded_prefixentryleft))) /\ (exists ge_balance_positive_padded_prefixentryleftvalue ge_balance_negative_padded_prefixentryleftvalue. (((((dc_left_padded_prefixentry) = 2 * (ge_balance_positive_padded_prefixentryleftvalue) /\ (ge_balance_negative_padded_prefixentryleftvalue) = 0) \/ exists ge_signed_half_padded_prefixentryleftvaluedecode. (((dc_left_padded_prefixentry) = 2 * ge_signed_half_padded_prefixentryleftvaluedecode + 1 /\ (ge_balance_positive_padded_prefixentryleftvalue) = 0) /\ (ge_balance_negative_padded_prefixentryleftvalue) = S ge_signed_half_padded_prefixentryleftvaluedecode))) /\ ((dst_positive_padded_prefixentryleft) + ge_balance_negative_padded_prefixentryleftvalue = (dst_negative_padded_prefixentryleft) + ge_balance_positive_padded_prefixentryleftvalue))))))))) /\ (((exists dst_positive_code_padded_prefixentryright dst_positive_scale_padded_prefixentryright dst_negative_code_padded_prefixentryright dst_negative_scale_padded_prefixentryright dst_positive_padded_prefixentryright dst_negative_padded_prefixentryright. (((G) = (((((dst_positive_code_padded_prefixentryright) + (dst_positive_scale_padded_prefixentryright)) * S ((dst_positive_code_padded_prefixentryright) + (dst_positive_scale_padded_prefixentryright)) + ((dst_positive_scale_padded_prefixentryright) + (dst_positive_scale_padded_prefixentryright))) + (((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) * S ((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) + ((dst_negative_scale_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)))) * S ((((dst_positive_code_padded_prefixentryright) + (dst_positive_scale_padded_prefixentryright)) * S ((dst_positive_code_padded_prefixentryright) + (dst_positive_scale_padded_prefixentryright)) + ((dst_positive_scale_padded_prefixentryright) + (dst_positive_scale_padded_prefixentryright))) + (((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) * S ((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) + ((dst_negative_scale_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)))) + ((((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) * S ((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) + ((dst_negative_scale_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright))) + (((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) * S ((dst_negative_code_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)) + ((dst_negative_scale_padded_prefixentryright) + (dst_negative_scale_padded_prefixentryright)))))) /\ (((((exists ff_h_pvs_padded_prefixentryrightpositive. ff_h_pvs_padded_prefixentryrightpositive + S (dst_positive_padded_prefixentryright) = S ((S (dc_quotient_padded_prefixentry)) * dst_positive_scale_padded_prefixentryright)) /\ exists ff_q_pvs_padded_prefixentryrightpositive. dst_positive_code_padded_prefixentryright = ff_q_pvs_padded_prefixentryrightpositive * S ((S (dc_quotient_padded_prefixentry)) * dst_positive_scale_padded_prefixentryright) + (dst_positive_padded_prefixentryright))) /\ (((((exists ff_h_pvs_padded_prefixentryrightnegative. ff_h_pvs_padded_prefixentryrightnegative + S (dst_negative_padded_prefixentryright) = S ((S (dc_quotient_padded_prefixentry)) * dst_negative_scale_padded_prefixentryright)) /\ exists ff_q_pvs_padded_prefixentryrightnegative. dst_negative_code_padded_prefixentryright = ff_q_pvs_padded_prefixentryrightnegative * S ((S (dc_quotient_padded_prefixentry)) * dst_negative_scale_padded_prefixentryright) + (dst_negative_padded_prefixentryright))) /\ (exists ge_balance_positive_padded_prefixentryrightvalue ge_balance_negative_padded_prefixentryrightvalue. (((((dc_right_padded_prefixentry) = 2 * (ge_balance_positive_padded_prefixentryrightvalue) /\ (ge_balance_negative_padded_prefixentryrightvalue) = 0) \/ exists ge_signed_half_padded_prefixentryrightvaluedecode. (((dc_right_padded_prefixentry) = 2 * ge_signed_half_padded_prefixentryrightvaluedecode + 1 /\ (ge_balance_positive_padded_prefixentryrightvalue) = 0) /\ (ge_balance_negative_padded_prefixentryrightvalue) = S ge_signed_half_padded_prefixentryrightvaluedecode))) /\ ((dst_positive_padded_prefixentryright) + ge_balance_negative_padded_prefixentryrightvalue = (dst_negative_padded_prefixentryright) + ge_balance_positive_padded_prefixentryrightvalue))))))))) /\ (exists sto_ap_padded_prefixentryproduct sto_an_padded_prefixentryproduct sto_bp_padded_prefixentryproduct sto_bn_padded_prefixentryproduct sto_cp_padded_prefixentryproduct sto_cn_padded_prefixentryproduct. (((((dc_left_padded_prefixentry) = 2 * (sto_ap_padded_prefixentryproduct) /\ (sto_an_padded_prefixentryproduct) = 0) \/ exists ge_signed_half_padded_prefixentryproductleft. (((dc_left_padded_prefixentry) = 2 * ge_signed_half_padded_prefixentryproductleft + 1 /\ (sto_ap_padded_prefixentryproduct) = 0) /\ (sto_an_padded_prefixentryproduct) = S ge_signed_half_padded_prefixentryproductleft))) /\ ((((((dc_right_padded_prefixentry) = 2 * (sto_bp_padded_prefixentryproduct) /\ (sto_bn_padded_prefixentryproduct) = 0) \/ exists ge_signed_half_padded_prefixentryproductright. (((dc_right_padded_prefixentry) = 2 * ge_signed_half_padded_prefixentryproductright + 1 /\ (sto_bp_padded_prefixentryproduct) = 0) /\ (sto_bn_padded_prefixentryproduct) = S ge_signed_half_padded_prefixentryproductright))) /\ ((((((dc_value_padded_prefix) = 2 * (sto_cp_padded_prefixentryproduct) /\ (sto_cn_padded_prefixentryproduct) = 0) \/ exists ge_signed_half_padded_prefixentryproductoutput. (((dc_value_padded_prefix) = 2 * ge_signed_half_padded_prefixentryproductoutput + 1 /\ (sto_cp_padded_prefixentryproduct) = 0) /\ (sto_cn_padded_prefixentryproduct) = S ge_signed_half_padded_prefixentryproductoutput))) /\ ((sto_ap_padded_prefixentryproduct * sto_bp_padded_prefixentryproduct + sto_an_padded_prefixentryproduct * sto_bn_padded_prefixentryproduct) + sto_cn_padded_prefixentryproduct = (sto_ap_padded_prefixentryproduct * sto_bn_padded_prefixentryproduct + sto_an_padded_prefixentryproduct * sto_bp_padded_prefixentryproduct) + sto_cp_padded_prefixentryproduct))))))))))))))) \/ ((((dc_index_padded_prefix)=0 \/ ~(exists pvs_factor_padded_prefixentrynondivisor. (n) = (dc_index_padded_prefix) * pvs_factor_padded_prefixentrynondivisor)) /\ ((dc_value_padded_prefix)=0))))))) -> (exists dst_positive_code_padded_sum dst_positive_scale_padded_sum dst_negative_code_padded_sum dst_negative_scale_padded_sum dst_positive_sum_padded_sum dst_negative_sum_padded_sum. (((M) = (((((dst_positive_code_padded_sum) + (dst_positive_scale_padded_sum)) * S ((dst_positive_code_padded_sum) + (dst_positive_scale_padded_sum)) + ((dst_positive_scale_padded_sum) + (dst_positive_scale_padded_sum))) + (((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) * S ((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) + ((dst_negative_scale_padded_sum) + (dst_negative_scale_padded_sum)))) * S ((((dst_positive_code_padded_sum) + (dst_positive_scale_padded_sum)) * S ((dst_positive_code_padded_sum) + (dst_positive_scale_padded_sum)) + ((dst_positive_scale_padded_sum) + (dst_positive_scale_padded_sum))) + (((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) * S ((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) + ((dst_negative_scale_padded_sum) + (dst_negative_scale_padded_sum)))) + ((((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) * S ((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) + ((dst_negative_scale_padded_sum) + (dst_negative_scale_padded_sum))) + (((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) * S ((dst_negative_code_padded_sum) + (dst_negative_scale_padded_sum)) + ((dst_negative_scale_padded_sum) + (dst_negative_scale_padded_sum)))))) /\ (((exists fs_u_dst_padded_sumpositive fs_v_dst_padded_sumpositive. ((((exists fs_h_dst_padded_sumpositive_body_start. fs_h_dst_padded_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_padded_sumpositive)) /\ exists fs_q_dst_padded_sumpositive_body_start. fs_u_dst_padded_sumpositive = fs_q_dst_padded_sumpositive_body_start * S ((S (0)) * fs_v_dst_padded_sumpositive) + (0))) /\ ((((exists fs_h_dst_padded_sumpositive_body_terminal. fs_h_dst_padded_sumpositive_body_terminal + S (dst_positive_sum_padded_sum) = S ((S (S L)) * fs_v_dst_padded_sumpositive)) /\ exists fs_q_dst_padded_sumpositive_body_terminal. fs_u_dst_padded_sumpositive = fs_q_dst_padded_sumpositive_body_terminal * S ((S (S L)) * fs_v_dst_padded_sumpositive) + (dst_positive_sum_padded_sum))) /\ forall fs_i_dst_padded_sumpositive_body_steps. (exists fs_lt_dst_padded_sumpositive_body_steps_bound. fs_lt_dst_padded_sumpositive_body_steps_bound + S fs_i_dst_padded_sumpositive_body_steps = S L) -> exists fs_a_dst_padded_sumpositive_body_steps fs_r_dst_padded_sumpositive_body_steps fs_s_dst_padded_sumpositive_body_steps. ((((exists fs_h_dst_padded_sumpositive_body_steps_summand. fs_h_dst_padded_sumpositive_body_steps_summand + S (fs_a_dst_padded_sumpositive_body_steps) = S ((S (fs_i_dst_padded_sumpositive_body_steps)) * dst_positive_scale_padded_sum)) /\ exists fs_q_dst_padded_sumpositive_body_steps_summand. dst_positive_code_padded_sum = fs_q_dst_padded_sumpositive_body_steps_summand * S ((S (fs_i_dst_padded_sumpositive_body_steps)) * dst_positive_scale_padded_sum) + (fs_a_dst_padded_sumpositive_body_steps))) /\ ((((exists fs_h_dst_padded_sumpositive_body_steps_partial. fs_h_dst_padded_sumpositive_body_steps_partial + S (fs_r_dst_padded_sumpositive_body_steps) = S ((S (fs_i_dst_padded_sumpositive_body_steps)) * fs_v_dst_padded_sumpositive)) /\ exists fs_q_dst_padded_sumpositive_body_steps_partial. fs_u_dst_padded_sumpositive = fs_q_dst_padded_sumpositive_body_steps_partial * S ((S (fs_i_dst_padded_sumpositive_body_steps)) * fs_v_dst_padded_sumpositive) + (fs_r_dst_padded_sumpositive_body_steps))) /\ ((((exists fs_h_dst_padded_sumpositive_body_steps_successor. fs_h_dst_padded_sumpositive_body_steps_successor + S (fs_s_dst_padded_sumpositive_body_steps) = S ((S (S fs_i_dst_padded_sumpositive_body_steps)) * fs_v_dst_padded_sumpositive)) /\ exists fs_q_dst_padded_sumpositive_body_steps_successor. fs_u_dst_padded_sumpositive = fs_q_dst_padded_sumpositive_body_steps_successor * S ((S (S fs_i_dst_padded_sumpositive_body_steps)) * fs_v_dst_padded_sumpositive) + (fs_s_dst_padded_sumpositive_body_steps))) /\ fs_s_dst_padded_sumpositive_body_steps = fs_r_dst_padded_sumpositive_body_steps + fs_a_dst_padded_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_padded_sumnegative fs_v_dst_padded_sumnegative. ((((exists fs_h_dst_padded_sumnegative_body_start. fs_h_dst_padded_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_padded_sumnegative)) /\ exists fs_q_dst_padded_sumnegative_body_start. fs_u_dst_padded_sumnegative = fs_q_dst_padded_sumnegative_body_start * S ((S (0)) * fs_v_dst_padded_sumnegative) + (0))) /\ ((((exists fs_h_dst_padded_sumnegative_body_terminal. fs_h_dst_padded_sumnegative_body_terminal + S (dst_negative_sum_padded_sum) = S ((S (S L)) * fs_v_dst_padded_sumnegative)) /\ exists fs_q_dst_padded_sumnegative_body_terminal. fs_u_dst_padded_sumnegative = fs_q_dst_padded_sumnegative_body_terminal * S ((S (S L)) * fs_v_dst_padded_sumnegative) + (dst_negative_sum_padded_sum))) /\ forall fs_i_dst_padded_sumnegative_body_steps. (exists fs_lt_dst_padded_sumnegative_body_steps_bound. fs_lt_dst_padded_sumnegative_body_steps_bound + S fs_i_dst_padded_sumnegative_body_steps = S L) -> exists fs_a_dst_padded_sumnegative_body_steps fs_r_dst_padded_sumnegative_body_steps fs_s_dst_padded_sumnegative_body_steps. ((((exists fs_h_dst_padded_sumnegative_body_steps_summand. fs_h_dst_padded_sumnegative_body_steps_summand + S (fs_a_dst_padded_sumnegative_body_steps) = S ((S (fs_i_dst_padded_sumnegative_body_steps)) * dst_negative_scale_padded_sum)) /\ exists fs_q_dst_padded_sumnegative_body_steps_summand. dst_negative_code_padded_sum = fs_q_dst_padded_sumnegative_body_steps_summand * S ((S (fs_i_dst_padded_sumnegative_body_steps)) * dst_negative_scale_padded_sum) + (fs_a_dst_padded_sumnegative_body_steps))) /\ ((((exists fs_h_dst_padded_sumnegative_body_steps_partial. fs_h_dst_padded_sumnegative_body_steps_partial + S (fs_r_dst_padded_sumnegative_body_steps) = S ((S (fs_i_dst_padded_sumnegative_body_steps)) * fs_v_dst_padded_sumnegative)) /\ exists fs_q_dst_padded_sumnegative_body_steps_partial. fs_u_dst_padded_sumnegative = fs_q_dst_padded_sumnegative_body_steps_partial * S ((S (fs_i_dst_padded_sumnegative_body_steps)) * fs_v_dst_padded_sumnegative) + (fs_r_dst_padded_sumnegative_body_steps))) /\ ((((exists fs_h_dst_padded_sumnegative_body_steps_successor. fs_h_dst_padded_sumnegative_body_steps_successor + S (fs_s_dst_padded_sumnegative_body_steps) = S ((S (S fs_i_dst_padded_sumnegative_body_steps)) * fs_v_dst_padded_sumnegative)) /\ exists fs_q_dst_padded_sumnegative_body_steps_successor. fs_u_dst_padded_sumnegative = fs_q_dst_padded_sumnegative_body_steps_successor * S ((S (S fs_i_dst_padded_sumnegative_body_steps)) * fs_v_dst_padded_sumnegative) + (fs_s_dst_padded_sumnegative_body_steps))) /\ fs_s_dst_padded_sumnegative_body_steps = fs_r_dst_padded_sumnegative_body_steps + fs_a_dst_padded_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_padded_sumresult ge_balance_negative_padded_sumresult. (((((z) = 2 * (ge_balance_positive_padded_sumresult) /\ (ge_balance_negative_padded_sumresult) = 0) \/ exists ge_signed_half_padded_sumresultdecode. (((z) = 2 * ge_signed_half_padded_sumresultdecode + 1 /\ (ge_balance_positive_padded_sumresult) = 0) /\ (ge_balance_negative_padded_sumresult) = S ge_signed_half_padded_sumresultdecode))) /\ ((dst_positive_sum_padded_sum) + ge_balance_negative_padded_sumresult = (dst_negative_sum_padded_sum) + ge_balance_positive_padded_sumresult))))))))) -> (((~((n)=0)) /\ (exists dc_mask_padded_result. ((((exists dst_positive_code_padded_resultmasktable dst_positive_scale_padded_resultmasktable dst_negative_code_padded_resultmasktable dst_negative_scale_padded_resultmasktable. (((dc_mask_padded_result) = (((((dst_positive_code_padded_resultmasktable) + (dst_positive_scale_padded_resultmasktable)) * S ((dst_positive_code_padded_resultmasktable) + (dst_positive_scale_padded_resultmasktable)) + ((dst_positive_scale_padded_resultmasktable) + (dst_positive_scale_padded_resultmasktable))) + (((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) * S ((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) + ((dst_negative_scale_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)))) * S ((((dst_positive_code_padded_resultmasktable) + (dst_positive_scale_padded_resultmasktable)) * S ((dst_positive_code_padded_resultmasktable) + (dst_positive_scale_padded_resultmasktable)) + ((dst_positive_scale_padded_resultmasktable) + (dst_positive_scale_padded_resultmasktable))) + (((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) * S ((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) + ((dst_negative_scale_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)))) + ((((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) * S ((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) + ((dst_negative_scale_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable))) + (((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) * S ((dst_negative_code_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)) + ((dst_negative_scale_padded_resultmasktable) + (dst_negative_scale_padded_resultmasktable)))))) /\ (forall dst_index_padded_resultmasktable. (exists pvs_le_gap_padded_resultmasktabledomain. pvs_le_gap_padded_resultmasktabledomain + (dst_index_padded_resultmasktable) = (n)) -> exists dst_positive_padded_resultmasktable dst_negative_padded_resultmasktable dst_value_padded_resultmasktable. ((((exists ff_h_pvs_padded_resultmasktableentrypositive. ff_h_pvs_padded_resultmasktableentrypositive + S (dst_positive_padded_resultmasktable) = S ((S (dst_index_padded_resultmasktable)) * dst_positive_scale_padded_resultmasktable)) /\ exists ff_q_pvs_padded_resultmasktableentrypositive. dst_positive_code_padded_resultmasktable = ff_q_pvs_padded_resultmasktableentrypositive * S ((S (dst_index_padded_resultmasktable)) * dst_positive_scale_padded_resultmasktable) + (dst_positive_padded_resultmasktable))) /\ (((((exists ff_h_pvs_padded_resultmasktableentrynegative. ff_h_pvs_padded_resultmasktableentrynegative + S (dst_negative_padded_resultmasktable) = S ((S (dst_index_padded_resultmasktable)) * dst_negative_scale_padded_resultmasktable)) /\ exists ff_q_pvs_padded_resultmasktableentrynegative. dst_negative_code_padded_resultmasktable = ff_q_pvs_padded_resultmasktableentrynegative * S ((S (dst_index_padded_resultmasktable)) * dst_negative_scale_padded_resultmasktable) + (dst_negative_padded_resultmasktable))) /\ (exists ge_balance_positive_padded_resultmasktableentryvalue ge_balance_negative_padded_resultmasktableentryvalue. (((((dst_value_padded_resultmasktable) = 2 * (ge_balance_positive_padded_resultmasktableentryvalue) /\ (ge_balance_negative_padded_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_padded_resultmasktableentryvaluedecode. (((dst_value_padded_resultmasktable) = 2 * ge_signed_half_padded_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_padded_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_padded_resultmasktableentryvalue) = S ge_signed_half_padded_resultmasktableentryvaluedecode))) /\ ((dst_positive_padded_resultmasktable) + ge_balance_negative_padded_resultmasktableentryvalue = (dst_negative_padded_resultmasktable) + ge_balance_positive_padded_resultmasktableentryvalue))))))))) /\ (forall dc_index_padded_resultmask dc_value_padded_resultmask. (exists pvs_le_gap_padded_resultmaskdomain. pvs_le_gap_padded_resultmaskdomain + (dc_index_padded_resultmask) = (n)) -> (exists dst_positive_code_padded_resultmasklookup dst_positive_scale_padded_resultmasklookup dst_negative_code_padded_resultmasklookup dst_negative_scale_padded_resultmasklookup dst_positive_padded_resultmasklookup dst_negative_padded_resultmasklookup. (((dc_mask_padded_result) = (((((dst_positive_code_padded_resultmasklookup) + (dst_positive_scale_padded_resultmasklookup)) * S ((dst_positive_code_padded_resultmasklookup) + (dst_positive_scale_padded_resultmasklookup)) + ((dst_positive_scale_padded_resultmasklookup) + (dst_positive_scale_padded_resultmasklookup))) + (((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) * S ((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) + ((dst_negative_scale_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)))) * S ((((dst_positive_code_padded_resultmasklookup) + (dst_positive_scale_padded_resultmasklookup)) * S ((dst_positive_code_padded_resultmasklookup) + (dst_positive_scale_padded_resultmasklookup)) + ((dst_positive_scale_padded_resultmasklookup) + (dst_positive_scale_padded_resultmasklookup))) + (((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) * S ((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) + ((dst_negative_scale_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)))) + ((((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) * S ((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) + ((dst_negative_scale_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup))) + (((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) * S ((dst_negative_code_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)) + ((dst_negative_scale_padded_resultmasklookup) + (dst_negative_scale_padded_resultmasklookup)))))) /\ (((((exists ff_h_pvs_padded_resultmasklookuppositive. ff_h_pvs_padded_resultmasklookuppositive + S (dst_positive_padded_resultmasklookup) = S ((S (dc_index_padded_resultmask)) * dst_positive_scale_padded_resultmasklookup)) /\ exists ff_q_pvs_padded_resultmasklookuppositive. dst_positive_code_padded_resultmasklookup = ff_q_pvs_padded_resultmasklookuppositive * S ((S (dc_index_padded_resultmask)) * dst_positive_scale_padded_resultmasklookup) + (dst_positive_padded_resultmasklookup))) /\ (((((exists ff_h_pvs_padded_resultmasklookupnegative. ff_h_pvs_padded_resultmasklookupnegative + S (dst_negative_padded_resultmasklookup) = S ((S (dc_index_padded_resultmask)) * dst_negative_scale_padded_resultmasklookup)) /\ exists ff_q_pvs_padded_resultmasklookupnegative. dst_negative_code_padded_resultmasklookup = ff_q_pvs_padded_resultmasklookupnegative * S ((S (dc_index_padded_resultmask)) * dst_negative_scale_padded_resultmasklookup) + (dst_negative_padded_resultmasklookup))) /\ (exists ge_balance_positive_padded_resultmasklookupvalue ge_balance_negative_padded_resultmasklookupvalue. (((((dc_value_padded_resultmask) = 2 * (ge_balance_positive_padded_resultmasklookupvalue) /\ (ge_balance_negative_padded_resultmasklookupvalue) = 0) \/ exists ge_signed_half_padded_resultmasklookupvaluedecode. (((dc_value_padded_resultmask) = 2 * ge_signed_half_padded_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_padded_resultmasklookupvalue) = 0) /\ (ge_balance_negative_padded_resultmasklookupvalue) = S ge_signed_half_padded_resultmasklookupvaluedecode))) /\ ((dst_positive_padded_resultmasklookup) + ge_balance_negative_padded_resultmasklookupvalue = (dst_negative_padded_resultmasklookup) + ge_balance_positive_padded_resultmasklookupvalue))))))))) -> ((((~((dc_index_padded_resultmask)=0)) /\ (exists dc_quotient_padded_resultmaskentry dc_left_padded_resultmaskentry dc_right_padded_resultmaskentry. (((n)=(dc_index_padded_resultmask)*dc_quotient_padded_resultmaskentry) /\ (((exists dst_positive_code_padded_resultmaskentryleft dst_positive_scale_padded_resultmaskentryleft dst_negative_code_padded_resultmaskentryleft dst_negative_scale_padded_resultmaskentryleft dst_positive_padded_resultmaskentryleft dst_negative_padded_resultmaskentryleft. (((F) = (((((dst_positive_code_padded_resultmaskentryleft) + (dst_positive_scale_padded_resultmaskentryleft)) * S ((dst_positive_code_padded_resultmaskentryleft) + (dst_positive_scale_padded_resultmaskentryleft)) + ((dst_positive_scale_padded_resultmaskentryleft) + (dst_positive_scale_padded_resultmaskentryleft))) + (((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) * S ((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) + ((dst_negative_scale_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)))) * S ((((dst_positive_code_padded_resultmaskentryleft) + (dst_positive_scale_padded_resultmaskentryleft)) * S ((dst_positive_code_padded_resultmaskentryleft) + (dst_positive_scale_padded_resultmaskentryleft)) + ((dst_positive_scale_padded_resultmaskentryleft) + (dst_positive_scale_padded_resultmaskentryleft))) + (((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) * S ((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) + ((dst_negative_scale_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)))) + ((((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) * S ((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) + ((dst_negative_scale_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft))) + (((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) * S ((dst_negative_code_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)) + ((dst_negative_scale_padded_resultmaskentryleft) + (dst_negative_scale_padded_resultmaskentryleft)))))) /\ (((((exists ff_h_pvs_padded_resultmaskentryleftpositive. ff_h_pvs_padded_resultmaskentryleftpositive + S (dst_positive_padded_resultmaskentryleft) = S ((S (dc_index_padded_resultmask)) * dst_positive_scale_padded_resultmaskentryleft)) /\ exists ff_q_pvs_padded_resultmaskentryleftpositive. dst_positive_code_padded_resultmaskentryleft = ff_q_pvs_padded_resultmaskentryleftpositive * S ((S (dc_index_padded_resultmask)) * dst_positive_scale_padded_resultmaskentryleft) + (dst_positive_padded_resultmaskentryleft))) /\ (((((exists ff_h_pvs_padded_resultmaskentryleftnegative. ff_h_pvs_padded_resultmaskentryleftnegative + S (dst_negative_padded_resultmaskentryleft) = S ((S (dc_index_padded_resultmask)) * dst_negative_scale_padded_resultmaskentryleft)) /\ exists ff_q_pvs_padded_resultmaskentryleftnegative. dst_negative_code_padded_resultmaskentryleft = ff_q_pvs_padded_resultmaskentryleftnegative * S ((S (dc_index_padded_resultmask)) * dst_negative_scale_padded_resultmaskentryleft) + (dst_negative_padded_resultmaskentryleft))) /\ (exists ge_balance_positive_padded_resultmaskentryleftvalue ge_balance_negative_padded_resultmaskentryleftvalue. (((((dc_left_padded_resultmaskentry) = 2 * (ge_balance_positive_padded_resultmaskentryleftvalue) /\ (ge_balance_negative_padded_resultmaskentryleftvalue) = 0) \/ exists ge_signed_half_padded_resultmaskentryleftvaluedecode. (((dc_left_padded_resultmaskentry) = 2 * ge_signed_half_padded_resultmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_padded_resultmaskentryleftvalue) = 0) /\ (ge_balance_negative_padded_resultmaskentryleftvalue) = S ge_signed_half_padded_resultmaskentryleftvaluedecode))) /\ ((dst_positive_padded_resultmaskentryleft) + ge_balance_negative_padded_resultmaskentryleftvalue = (dst_negative_padded_resultmaskentryleft) + ge_balance_positive_padded_resultmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_padded_resultmaskentryright dst_positive_scale_padded_resultmaskentryright dst_negative_code_padded_resultmaskentryright dst_negative_scale_padded_resultmaskentryright dst_positive_padded_resultmaskentryright dst_negative_padded_resultmaskentryright. (((G) = (((((dst_positive_code_padded_resultmaskentryright) + (dst_positive_scale_padded_resultmaskentryright)) * S ((dst_positive_code_padded_resultmaskentryright) + (dst_positive_scale_padded_resultmaskentryright)) + ((dst_positive_scale_padded_resultmaskentryright) + (dst_positive_scale_padded_resultmaskentryright))) + (((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) * S ((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) + ((dst_negative_scale_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)))) * S ((((dst_positive_code_padded_resultmaskentryright) + (dst_positive_scale_padded_resultmaskentryright)) * S ((dst_positive_code_padded_resultmaskentryright) + (dst_positive_scale_padded_resultmaskentryright)) + ((dst_positive_scale_padded_resultmaskentryright) + (dst_positive_scale_padded_resultmaskentryright))) + (((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) * S ((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) + ((dst_negative_scale_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)))) + ((((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) * S ((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) + ((dst_negative_scale_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright))) + (((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) * S ((dst_negative_code_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)) + ((dst_negative_scale_padded_resultmaskentryright) + (dst_negative_scale_padded_resultmaskentryright)))))) /\ (((((exists ff_h_pvs_padded_resultmaskentryrightpositive. ff_h_pvs_padded_resultmaskentryrightpositive + S (dst_positive_padded_resultmaskentryright) = S ((S (dc_quotient_padded_resultmaskentry)) * dst_positive_scale_padded_resultmaskentryright)) /\ exists ff_q_pvs_padded_resultmaskentryrightpositive. dst_positive_code_padded_resultmaskentryright = ff_q_pvs_padded_resultmaskentryrightpositive * S ((S (dc_quotient_padded_resultmaskentry)) * dst_positive_scale_padded_resultmaskentryright) + (dst_positive_padded_resultmaskentryright))) /\ (((((exists ff_h_pvs_padded_resultmaskentryrightnegative. ff_h_pvs_padded_resultmaskentryrightnegative + S (dst_negative_padded_resultmaskentryright) = S ((S (dc_quotient_padded_resultmaskentry)) * dst_negative_scale_padded_resultmaskentryright)) /\ exists ff_q_pvs_padded_resultmaskentryrightnegative. dst_negative_code_padded_resultmaskentryright = ff_q_pvs_padded_resultmaskentryrightnegative * S ((S (dc_quotient_padded_resultmaskentry)) * dst_negative_scale_padded_resultmaskentryright) + (dst_negative_padded_resultmaskentryright))) /\ (exists ge_balance_positive_padded_resultmaskentryrightvalue ge_balance_negative_padded_resultmaskentryrightvalue. (((((dc_right_padded_resultmaskentry) = 2 * (ge_balance_positive_padded_resultmaskentryrightvalue) /\ (ge_balance_negative_padded_resultmaskentryrightvalue) = 0) \/ exists ge_signed_half_padded_resultmaskentryrightvaluedecode. (((dc_right_padded_resultmaskentry) = 2 * ge_signed_half_padded_resultmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_padded_resultmaskentryrightvalue) = 0) /\ (ge_balance_negative_padded_resultmaskentryrightvalue) = S ge_signed_half_padded_resultmaskentryrightvaluedecode))) /\ ((dst_positive_padded_resultmaskentryright) + ge_balance_negative_padded_resultmaskentryrightvalue = (dst_negative_padded_resultmaskentryright) + ge_balance_positive_padded_resultmaskentryrightvalue))))))))) /\ (exists sto_ap_padded_resultmaskentryproduct sto_an_padded_resultmaskentryproduct sto_bp_padded_resultmaskentryproduct sto_bn_padded_resultmaskentryproduct sto_cp_padded_resultmaskentryproduct sto_cn_padded_resultmaskentryproduct. (((((dc_left_padded_resultmaskentry) = 2 * (sto_ap_padded_resultmaskentryproduct) /\ (sto_an_padded_resultmaskentryproduct) = 0) \/ exists ge_signed_half_padded_resultmaskentryproductleft. (((dc_left_padded_resultmaskentry) = 2 * ge_signed_half_padded_resultmaskentryproductleft + 1 /\ (sto_ap_padded_resultmaskentryproduct) = 0) /\ (sto_an_padded_resultmaskentryproduct) = S ge_signed_half_padded_resultmaskentryproductleft))) /\ ((((((dc_right_padded_resultmaskentry) = 2 * (sto_bp_padded_resultmaskentryproduct) /\ (sto_bn_padded_resultmaskentryproduct) = 0) \/ exists ge_signed_half_padded_resultmaskentryproductright. (((dc_right_padded_resultmaskentry) = 2 * ge_signed_half_padded_resultmaskentryproductright + 1 /\ (sto_bp_padded_resultmaskentryproduct) = 0) /\ (sto_bn_padded_resultmaskentryproduct) = S ge_signed_half_padded_resultmaskentryproductright))) /\ ((((((dc_value_padded_resultmask) = 2 * (sto_cp_padded_resultmaskentryproduct) /\ (sto_cn_padded_resultmaskentryproduct) = 0) \/ exists ge_signed_half_padded_resultmaskentryproductoutput. (((dc_value_padded_resultmask) = 2 * ge_signed_half_padded_resultmaskentryproductoutput + 1 /\ (sto_cp_padded_resultmaskentryproduct) = 0) /\ (sto_cn_padded_resultmaskentryproduct) = S ge_signed_half_padded_resultmaskentryproductoutput))) /\ ((sto_ap_padded_resultmaskentryproduct * sto_bp_padded_resultmaskentryproduct + sto_an_padded_resultmaskentryproduct * sto_bn_padded_resultmaskentryproduct) + sto_cn_padded_resultmaskentryproduct = (sto_ap_padded_resultmaskentryproduct * sto_bn_padded_resultmaskentryproduct + sto_an_padded_resultmaskentryproduct * sto_bp_padded_resultmaskentryproduct) + sto_cp_padded_resultmaskentryproduct))))))))))))))) \/ ((((dc_index_padded_resultmask)=0 \/ ~(exists pvs_factor_padded_resultmaskentrynondivisor. (n) = (dc_index_padded_resultmask) * pvs_factor_padded_resultmaskentrynondivisor)) /\ ((dc_value_padded_resultmask)=0))))))) /\ (exists dst_positive_code_padded_resultfold dst_positive_scale_padded_resultfold dst_negative_code_padded_resultfold dst_negative_scale_padded_resultfold dst_positive_sum_padded_resultfold dst_negative_sum_padded_resultfold. (((dc_mask_padded_result) = (((((dst_positive_code_padded_resultfold) + (dst_positive_scale_padded_resultfold)) * S ((dst_positive_code_padded_resultfold) + (dst_positive_scale_padded_resultfold)) + ((dst_positive_scale_padded_resultfold) + (dst_positive_scale_padded_resultfold))) + (((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) * S ((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) + ((dst_negative_scale_padded_resultfold) + (dst_negative_scale_padded_resultfold)))) * S ((((dst_positive_code_padded_resultfold) + (dst_positive_scale_padded_resultfold)) * S ((dst_positive_code_padded_resultfold) + (dst_positive_scale_padded_resultfold)) + ((dst_positive_scale_padded_resultfold) + (dst_positive_scale_padded_resultfold))) + (((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) * S ((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) + ((dst_negative_scale_padded_resultfold) + (dst_negative_scale_padded_resultfold)))) + ((((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) * S ((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) + ((dst_negative_scale_padded_resultfold) + (dst_negative_scale_padded_resultfold))) + (((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) * S ((dst_negative_code_padded_resultfold) + (dst_negative_scale_padded_resultfold)) + ((dst_negative_scale_padded_resultfold) + (dst_negative_scale_padded_resultfold)))))) /\ (((exists fs_u_dst_padded_resultfoldpositive fs_v_dst_padded_resultfoldpositive. ((((exists fs_h_dst_padded_resultfoldpositive_body_start. fs_h_dst_padded_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_padded_resultfoldpositive)) /\ exists fs_q_dst_padded_resultfoldpositive_body_start. fs_u_dst_padded_resultfoldpositive = fs_q_dst_padded_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_padded_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_padded_resultfoldpositive_body_terminal. fs_h_dst_padded_resultfoldpositive_body_terminal + S (dst_positive_sum_padded_resultfold) = S ((S (S (n))) * fs_v_dst_padded_resultfoldpositive)) /\ exists fs_q_dst_padded_resultfoldpositive_body_terminal. fs_u_dst_padded_resultfoldpositive = fs_q_dst_padded_resultfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_padded_resultfoldpositive) + (dst_positive_sum_padded_resultfold))) /\ forall fs_i_dst_padded_resultfoldpositive_body_steps. (exists fs_lt_dst_padded_resultfoldpositive_body_steps_bound. fs_lt_dst_padded_resultfoldpositive_body_steps_bound + S fs_i_dst_padded_resultfoldpositive_body_steps = S (n)) -> exists fs_a_dst_padded_resultfoldpositive_body_steps fs_r_dst_padded_resultfoldpositive_body_steps fs_s_dst_padded_resultfoldpositive_body_steps. ((((exists fs_h_dst_padded_resultfoldpositive_body_steps_summand. fs_h_dst_padded_resultfoldpositive_body_steps_summand + S (fs_a_dst_padded_resultfoldpositive_body_steps) = S ((S (fs_i_dst_padded_resultfoldpositive_body_steps)) * dst_positive_scale_padded_resultfold)) /\ exists fs_q_dst_padded_resultfoldpositive_body_steps_summand. dst_positive_code_padded_resultfold = fs_q_dst_padded_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_padded_resultfoldpositive_body_steps)) * dst_positive_scale_padded_resultfold) + (fs_a_dst_padded_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_padded_resultfoldpositive_body_steps_partial. fs_h_dst_padded_resultfoldpositive_body_steps_partial + S (fs_r_dst_padded_resultfoldpositive_body_steps) = S ((S (fs_i_dst_padded_resultfoldpositive_body_steps)) * fs_v_dst_padded_resultfoldpositive)) /\ exists fs_q_dst_padded_resultfoldpositive_body_steps_partial. fs_u_dst_padded_resultfoldpositive = fs_q_dst_padded_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_padded_resultfoldpositive_body_steps)) * fs_v_dst_padded_resultfoldpositive) + (fs_r_dst_padded_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_padded_resultfoldpositive_body_steps_successor. fs_h_dst_padded_resultfoldpositive_body_steps_successor + S (fs_s_dst_padded_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_padded_resultfoldpositive_body_steps)) * fs_v_dst_padded_resultfoldpositive)) /\ exists fs_q_dst_padded_resultfoldpositive_body_steps_successor. fs_u_dst_padded_resultfoldpositive = fs_q_dst_padded_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_padded_resultfoldpositive_body_steps)) * fs_v_dst_padded_resultfoldpositive) + (fs_s_dst_padded_resultfoldpositive_body_steps))) /\ fs_s_dst_padded_resultfoldpositive_body_steps = fs_r_dst_padded_resultfoldpositive_body_steps + fs_a_dst_padded_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_padded_resultfoldnegative fs_v_dst_padded_resultfoldnegative. ((((exists fs_h_dst_padded_resultfoldnegative_body_start. fs_h_dst_padded_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_padded_resultfoldnegative)) /\ exists fs_q_dst_padded_resultfoldnegative_body_start. fs_u_dst_padded_resultfoldnegative = fs_q_dst_padded_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_padded_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_padded_resultfoldnegative_body_terminal. fs_h_dst_padded_resultfoldnegative_body_terminal + S (dst_negative_sum_padded_resultfold) = S ((S (S (n))) * fs_v_dst_padded_resultfoldnegative)) /\ exists fs_q_dst_padded_resultfoldnegative_body_terminal. fs_u_dst_padded_resultfoldnegative = fs_q_dst_padded_resultfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_padded_resultfoldnegative) + (dst_negative_sum_padded_resultfold))) /\ forall fs_i_dst_padded_resultfoldnegative_body_steps. (exists fs_lt_dst_padded_resultfoldnegative_body_steps_bound. fs_lt_dst_padded_resultfoldnegative_body_steps_bound + S fs_i_dst_padded_resultfoldnegative_body_steps = S (n)) -> exists fs_a_dst_padded_resultfoldnegative_body_steps fs_r_dst_padded_resultfoldnegative_body_steps fs_s_dst_padded_resultfoldnegative_body_steps. ((((exists fs_h_dst_padded_resultfoldnegative_body_steps_summand. fs_h_dst_padded_resultfoldnegative_body_steps_summand + S (fs_a_dst_padded_resultfoldnegative_body_steps) = S ((S (fs_i_dst_padded_resultfoldnegative_body_steps)) * dst_negative_scale_padded_resultfold)) /\ exists fs_q_dst_padded_resultfoldnegative_body_steps_summand. dst_negative_code_padded_resultfold = fs_q_dst_padded_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_padded_resultfoldnegative_body_steps)) * dst_negative_scale_padded_resultfold) + (fs_a_dst_padded_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_padded_resultfoldnegative_body_steps_partial. fs_h_dst_padded_resultfoldnegative_body_steps_partial + S (fs_r_dst_padded_resultfoldnegative_body_steps) = S ((S (fs_i_dst_padded_resultfoldnegative_body_steps)) * fs_v_dst_padded_resultfoldnegative)) /\ exists fs_q_dst_padded_resultfoldnegative_body_steps_partial. fs_u_dst_padded_resultfoldnegative = fs_q_dst_padded_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_padded_resultfoldnegative_body_steps)) * fs_v_dst_padded_resultfoldnegative) + (fs_r_dst_padded_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_padded_resultfoldnegative_body_steps_successor. fs_h_dst_padded_resultfoldnegative_body_steps_successor + S (fs_s_dst_padded_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_padded_resultfoldnegative_body_steps)) * fs_v_dst_padded_resultfoldnegative)) /\ exists fs_q_dst_padded_resultfoldnegative_body_steps_successor. fs_u_dst_padded_resultfoldnegative = fs_q_dst_padded_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_padded_resultfoldnegative_body_steps)) * fs_v_dst_padded_resultfoldnegative) + (fs_s_dst_padded_resultfoldnegative_body_steps))) /\ fs_s_dst_padded_resultfoldnegative_body_steps = fs_r_dst_padded_resultfoldnegative_body_steps + fs_a_dst_padded_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_padded_resultfoldresult ge_balance_negative_padded_resultfoldresult. (((((z) = 2 * (ge_balance_positive_padded_resultfoldresult) /\ (ge_balance_negative_padded_resultfoldresult) = 0) \/ exists ge_signed_half_padded_resultfoldresultdecode. (((z) = 2 * ge_signed_half_padded_resultfoldresultdecode + 1 /\ (ge_balance_positive_padded_resultfoldresult) = 0) /\ (ge_balance_negative_padded_resultfoldresult) = S ge_signed_half_padded_resultfoldresultdecode))) /\ ((dst_positive_sum_padded_resultfold) + ge_balance_negative_padded_resultfoldresult = (dst_negative_sum_padded_resultfold) + ge_balance_positive_padded_resultfoldresult)))))))))))))

dirichlet_convolution_prefix_exists · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n l. (exists dst_positive_code_exists_left dst_positive_scale_exists_left dst_negative_code_exists_left dst_negative_scale_exists_left. (((F) = (((((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) * S ((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) + ((dst_positive_scale_exists_left) + (dst_positive_scale_exists_left))) + (((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left)))) * S ((((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) * S ((dst_positive_code_exists_left) + (dst_positive_scale_exists_left)) + ((dst_positive_scale_exists_left) + (dst_positive_scale_exists_left))) + (((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left)))) + ((((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left))) + (((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) * S ((dst_negative_code_exists_left) + (dst_negative_scale_exists_left)) + ((dst_negative_scale_exists_left) + (dst_negative_scale_exists_left)))))) /\ (forall dst_index_exists_left. (exists pvs_le_gap_exists_leftdomain. pvs_le_gap_exists_leftdomain + (dst_index_exists_left) = (0)) -> exists dst_positive_exists_left dst_negative_exists_left dst_value_exists_left. ((((exists ff_h_pvs_exists_leftentrypositive. ff_h_pvs_exists_leftentrypositive + S (dst_positive_exists_left) = S ((S (dst_index_exists_left)) * dst_positive_scale_exists_left)) /\ exists ff_q_pvs_exists_leftentrypositive. dst_positive_code_exists_left = ff_q_pvs_exists_leftentrypositive * S ((S (dst_index_exists_left)) * dst_positive_scale_exists_left) + (dst_positive_exists_left))) /\ (((((exists ff_h_pvs_exists_leftentrynegative. ff_h_pvs_exists_leftentrynegative + S (dst_negative_exists_left) = S ((S (dst_index_exists_left)) * dst_negative_scale_exists_left)) /\ exists ff_q_pvs_exists_leftentrynegative. dst_negative_code_exists_left = ff_q_pvs_exists_leftentrynegative * S ((S (dst_index_exists_left)) * dst_negative_scale_exists_left) + (dst_negative_exists_left))) /\ (exists ge_balance_positive_exists_leftentryvalue ge_balance_negative_exists_leftentryvalue. (((((dst_value_exists_left) = 2 * (ge_balance_positive_exists_leftentryvalue) /\ (ge_balance_negative_exists_leftentryvalue) = 0) \/ exists ge_signed_half_exists_leftentryvaluedecode. (((dst_value_exists_left) = 2 * ge_signed_half_exists_leftentryvaluedecode + 1 /\ (ge_balance_positive_exists_leftentryvalue) = 0) /\ (ge_balance_negative_exists_leftentryvalue) = S ge_signed_half_exists_leftentryvaluedecode))) /\ ((dst_positive_exists_left) + ge_balance_negative_exists_leftentryvalue = (dst_negative_exists_left) + ge_balance_positive_exists_leftentryvalue))))))))) -> (exists dst_positive_code_exists_right dst_positive_scale_exists_right dst_negative_code_exists_right dst_negative_scale_exists_right. (((G) = (((((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) * S ((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) + ((dst_positive_scale_exists_right) + (dst_positive_scale_exists_right))) + (((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right)))) * S ((((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) * S ((dst_positive_code_exists_right) + (dst_positive_scale_exists_right)) + ((dst_positive_scale_exists_right) + (dst_positive_scale_exists_right))) + (((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right)))) + ((((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right))) + (((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) * S ((dst_negative_code_exists_right) + (dst_negative_scale_exists_right)) + ((dst_negative_scale_exists_right) + (dst_negative_scale_exists_right)))))) /\ (forall dst_index_exists_right. (exists pvs_le_gap_exists_rightdomain. pvs_le_gap_exists_rightdomain + (dst_index_exists_right) = (0)) -> exists dst_positive_exists_right dst_negative_exists_right dst_value_exists_right. ((((exists ff_h_pvs_exists_rightentrypositive. ff_h_pvs_exists_rightentrypositive + S (dst_positive_exists_right) = S ((S (dst_index_exists_right)) * dst_positive_scale_exists_right)) /\ exists ff_q_pvs_exists_rightentrypositive. dst_positive_code_exists_right = ff_q_pvs_exists_rightentrypositive * S ((S (dst_index_exists_right)) * dst_positive_scale_exists_right) + (dst_positive_exists_right))) /\ (((((exists ff_h_pvs_exists_rightentrynegative. ff_h_pvs_exists_rightentrynegative + S (dst_negative_exists_right) = S ((S (dst_index_exists_right)) * dst_negative_scale_exists_right)) /\ exists ff_q_pvs_exists_rightentrynegative. dst_negative_code_exists_right = ff_q_pvs_exists_rightentrynegative * S ((S (dst_index_exists_right)) * dst_negative_scale_exists_right) + (dst_negative_exists_right))) /\ (exists ge_balance_positive_exists_rightentryvalue ge_balance_negative_exists_rightentryvalue. (((((dst_value_exists_right) = 2 * (ge_balance_positive_exists_rightentryvalue) /\ (ge_balance_negative_exists_rightentryvalue) = 0) \/ exists ge_signed_half_exists_rightentryvaluedecode. (((dst_value_exists_right) = 2 * ge_signed_half_exists_rightentryvaluedecode + 1 /\ (ge_balance_positive_exists_rightentryvalue) = 0) /\ (ge_balance_negative_exists_rightentryvalue) = S ge_signed_half_exists_rightentryvaluedecode))) /\ ((dst_positive_exists_right) + ge_balance_negative_exists_rightentryvalue = (dst_negative_exists_right) + ge_balance_positive_exists_rightentryvalue))))))))) -> exists M. (((exists dst_positive_code_exists_resulttable dst_positive_scale_exists_resulttable dst_negative_code_exists_resulttable dst_negative_scale_exists_resulttable. (((M) = (((((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) * S ((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) + ((dst_positive_scale_exists_resulttable) + (dst_positive_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))) * S ((((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) * S ((dst_positive_code_exists_resulttable) + (dst_positive_scale_exists_resulttable)) + ((dst_positive_scale_exists_resulttable) + (dst_positive_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))) + ((((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable))) + (((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) * S ((dst_negative_code_exists_resulttable) + (dst_negative_scale_exists_resulttable)) + ((dst_negative_scale_exists_resulttable) + (dst_negative_scale_exists_resulttable)))))) /\ (forall dst_index_exists_resulttable. (exists pvs_le_gap_exists_resulttabledomain. pvs_le_gap_exists_resulttabledomain + (dst_index_exists_resulttable) = (l)) -> exists dst_positive_exists_resulttable dst_negative_exists_resulttable dst_value_exists_resulttable. ((((exists ff_h_pvs_exists_resulttableentrypositive. ff_h_pvs_exists_resulttableentrypositive + S (dst_positive_exists_resulttable) = S ((S (dst_index_exists_resulttable)) * dst_positive_scale_exists_resulttable)) /\ exists ff_q_pvs_exists_resulttableentrypositive. dst_positive_code_exists_resulttable = ff_q_pvs_exists_resulttableentrypositive * S ((S (dst_index_exists_resulttable)) * dst_positive_scale_exists_resulttable) + (dst_positive_exists_resulttable))) /\ (((((exists ff_h_pvs_exists_resulttableentrynegative. ff_h_pvs_exists_resulttableentrynegative + S (dst_negative_exists_resulttable) = S ((S (dst_index_exists_resulttable)) * dst_negative_scale_exists_resulttable)) /\ exists ff_q_pvs_exists_resulttableentrynegative. dst_negative_code_exists_resulttable = ff_q_pvs_exists_resulttableentrynegative * S ((S (dst_index_exists_resulttable)) * dst_negative_scale_exists_resulttable) + (dst_negative_exists_resulttable))) /\ (exists ge_balance_positive_exists_resulttableentryvalue ge_balance_negative_exists_resulttableentryvalue. (((((dst_value_exists_resulttable) = 2 * (ge_balance_positive_exists_resulttableentryvalue) /\ (ge_balance_negative_exists_resulttableentryvalue) = 0) \/ exists ge_signed_half_exists_resulttableentryvaluedecode. (((dst_value_exists_resulttable) = 2 * ge_signed_half_exists_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_exists_resulttableentryvalue) = 0) /\ (ge_balance_negative_exists_resulttableentryvalue) = S ge_signed_half_exists_resulttableentryvaluedecode))) /\ ((dst_positive_exists_resulttable) + ge_balance_negative_exists_resulttableentryvalue = (dst_negative_exists_resulttable) + ge_balance_positive_exists_resulttableentryvalue))))))))) /\ (forall dc_index_exists_result dc_value_exists_result. (exists pvs_le_gap_exists_resultdomain. pvs_le_gap_exists_resultdomain + (dc_index_exists_result) = (l)) -> (exists dst_positive_code_exists_resultlookup dst_positive_scale_exists_resultlookup dst_negative_code_exists_resultlookup dst_negative_scale_exists_resultlookup dst_positive_exists_resultlookup dst_negative_exists_resultlookup. (((M) = (((((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) * S ((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) + ((dst_positive_scale_exists_resultlookup) + (dst_positive_scale_exists_resultlookup))) + (((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)))) * S ((((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) * S ((dst_positive_code_exists_resultlookup) + (dst_positive_scale_exists_resultlookup)) + ((dst_positive_scale_exists_resultlookup) + (dst_positive_scale_exists_resultlookup))) + (((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)))) + ((((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup))) + (((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) * S ((dst_negative_code_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)) + ((dst_negative_scale_exists_resultlookup) + (dst_negative_scale_exists_resultlookup)))))) /\ (((((exists ff_h_pvs_exists_resultlookuppositive. ff_h_pvs_exists_resultlookuppositive + S (dst_positive_exists_resultlookup) = S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultlookup)) /\ exists ff_q_pvs_exists_resultlookuppositive. dst_positive_code_exists_resultlookup = ff_q_pvs_exists_resultlookuppositive * S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultlookup) + (dst_positive_exists_resultlookup))) /\ (((((exists ff_h_pvs_exists_resultlookupnegative. ff_h_pvs_exists_resultlookupnegative + S (dst_negative_exists_resultlookup) = S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultlookup)) /\ exists ff_q_pvs_exists_resultlookupnegative. dst_negative_code_exists_resultlookup = ff_q_pvs_exists_resultlookupnegative * S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultlookup) + (dst_negative_exists_resultlookup))) /\ (exists ge_balance_positive_exists_resultlookupvalue ge_balance_negative_exists_resultlookupvalue. (((((dc_value_exists_result) = 2 * (ge_balance_positive_exists_resultlookupvalue) /\ (ge_balance_negative_exists_resultlookupvalue) = 0) \/ exists ge_signed_half_exists_resultlookupvaluedecode. (((dc_value_exists_result) = 2 * ge_signed_half_exists_resultlookupvaluedecode + 1 /\ (ge_balance_positive_exists_resultlookupvalue) = 0) /\ (ge_balance_negative_exists_resultlookupvalue) = S ge_signed_half_exists_resultlookupvaluedecode))) /\ ((dst_positive_exists_resultlookup) + ge_balance_negative_exists_resultlookupvalue = (dst_negative_exists_resultlookup) + ge_balance_positive_exists_resultlookupvalue))))))))) -> ((((~((dc_index_exists_result)=0)) /\ (exists dc_quotient_exists_resultentry dc_left_exists_resultentry dc_right_exists_resultentry. (((n)=(dc_index_exists_result)*dc_quotient_exists_resultentry) /\ (((exists dst_positive_code_exists_resultentryleft dst_positive_scale_exists_resultentryleft dst_negative_code_exists_resultentryleft dst_negative_scale_exists_resultentryleft dst_positive_exists_resultentryleft dst_negative_exists_resultentryleft. (((F) = (((((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) * S ((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) + ((dst_positive_scale_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft))) + (((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)))) * S ((((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) * S ((dst_positive_code_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft)) + ((dst_positive_scale_exists_resultentryleft) + (dst_positive_scale_exists_resultentryleft))) + (((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)))) + ((((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft))) + (((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) * S ((dst_negative_code_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)) + ((dst_negative_scale_exists_resultentryleft) + (dst_negative_scale_exists_resultentryleft)))))) /\ (((((exists ff_h_pvs_exists_resultentryleftpositive. ff_h_pvs_exists_resultentryleftpositive + S (dst_positive_exists_resultentryleft) = S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultentryleft)) /\ exists ff_q_pvs_exists_resultentryleftpositive. dst_positive_code_exists_resultentryleft = ff_q_pvs_exists_resultentryleftpositive * S ((S (dc_index_exists_result)) * dst_positive_scale_exists_resultentryleft) + (dst_positive_exists_resultentryleft))) /\ (((((exists ff_h_pvs_exists_resultentryleftnegative. ff_h_pvs_exists_resultentryleftnegative + S (dst_negative_exists_resultentryleft) = S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultentryleft)) /\ exists ff_q_pvs_exists_resultentryleftnegative. dst_negative_code_exists_resultentryleft = ff_q_pvs_exists_resultentryleftnegative * S ((S (dc_index_exists_result)) * dst_negative_scale_exists_resultentryleft) + (dst_negative_exists_resultentryleft))) /\ (exists ge_balance_positive_exists_resultentryleftvalue ge_balance_negative_exists_resultentryleftvalue. (((((dc_left_exists_resultentry) = 2 * (ge_balance_positive_exists_resultentryleftvalue) /\ (ge_balance_negative_exists_resultentryleftvalue) = 0) \/ exists ge_signed_half_exists_resultentryleftvaluedecode. (((dc_left_exists_resultentry) = 2 * ge_signed_half_exists_resultentryleftvaluedecode + 1 /\ (ge_balance_positive_exists_resultentryleftvalue) = 0) /\ (ge_balance_negative_exists_resultentryleftvalue) = S ge_signed_half_exists_resultentryleftvaluedecode))) /\ ((dst_positive_exists_resultentryleft) + ge_balance_negative_exists_resultentryleftvalue = (dst_negative_exists_resultentryleft) + ge_balance_positive_exists_resultentryleftvalue))))))))) /\ (((exists dst_positive_code_exists_resultentryright dst_positive_scale_exists_resultentryright dst_negative_code_exists_resultentryright dst_negative_scale_exists_resultentryright dst_positive_exists_resultentryright dst_negative_exists_resultentryright. (((G) = (((((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) * S ((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) + ((dst_positive_scale_exists_resultentryright) + (dst_positive_scale_exists_resultentryright))) + (((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)))) * S ((((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) * S ((dst_positive_code_exists_resultentryright) + (dst_positive_scale_exists_resultentryright)) + ((dst_positive_scale_exists_resultentryright) + (dst_positive_scale_exists_resultentryright))) + (((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)))) + ((((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright))) + (((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) * S ((dst_negative_code_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)) + ((dst_negative_scale_exists_resultentryright) + (dst_negative_scale_exists_resultentryright)))))) /\ (((((exists ff_h_pvs_exists_resultentryrightpositive. ff_h_pvs_exists_resultentryrightpositive + S (dst_positive_exists_resultentryright) = S ((S (dc_quotient_exists_resultentry)) * dst_positive_scale_exists_resultentryright)) /\ exists ff_q_pvs_exists_resultentryrightpositive. dst_positive_code_exists_resultentryright = ff_q_pvs_exists_resultentryrightpositive * S ((S (dc_quotient_exists_resultentry)) * dst_positive_scale_exists_resultentryright) + (dst_positive_exists_resultentryright))) /\ (((((exists ff_h_pvs_exists_resultentryrightnegative. ff_h_pvs_exists_resultentryrightnegative + S (dst_negative_exists_resultentryright) = S ((S (dc_quotient_exists_resultentry)) * dst_negative_scale_exists_resultentryright)) /\ exists ff_q_pvs_exists_resultentryrightnegative. dst_negative_code_exists_resultentryright = ff_q_pvs_exists_resultentryrightnegative * S ((S (dc_quotient_exists_resultentry)) * dst_negative_scale_exists_resultentryright) + (dst_negative_exists_resultentryright))) /\ (exists ge_balance_positive_exists_resultentryrightvalue ge_balance_negative_exists_resultentryrightvalue. (((((dc_right_exists_resultentry) = 2 * (ge_balance_positive_exists_resultentryrightvalue) /\ (ge_balance_negative_exists_resultentryrightvalue) = 0) \/ exists ge_signed_half_exists_resultentryrightvaluedecode. (((dc_right_exists_resultentry) = 2 * ge_signed_half_exists_resultentryrightvaluedecode + 1 /\ (ge_balance_positive_exists_resultentryrightvalue) = 0) /\ (ge_balance_negative_exists_resultentryrightvalue) = S ge_signed_half_exists_resultentryrightvaluedecode))) /\ ((dst_positive_exists_resultentryright) + ge_balance_negative_exists_resultentryrightvalue = (dst_negative_exists_resultentryright) + ge_balance_positive_exists_resultentryrightvalue))))))))) /\ (exists sto_ap_exists_resultentryproduct sto_an_exists_resultentryproduct sto_bp_exists_resultentryproduct sto_bn_exists_resultentryproduct sto_cp_exists_resultentryproduct sto_cn_exists_resultentryproduct. (((((dc_left_exists_resultentry) = 2 * (sto_ap_exists_resultentryproduct) /\ (sto_an_exists_resultentryproduct) = 0) \/ exists ge_signed_half_exists_resultentryproductleft. (((dc_left_exists_resultentry) = 2 * ge_signed_half_exists_resultentryproductleft + 1 /\ (sto_ap_exists_resultentryproduct) = 0) /\ (sto_an_exists_resultentryproduct) = S ge_signed_half_exists_resultentryproductleft))) /\ ((((((dc_right_exists_resultentry) = 2 * (sto_bp_exists_resultentryproduct) /\ (sto_bn_exists_resultentryproduct) = 0) \/ exists ge_signed_half_exists_resultentryproductright. (((dc_right_exists_resultentry) = 2 * ge_signed_half_exists_resultentryproductright + 1 /\ (sto_bp_exists_resultentryproduct) = 0) /\ (sto_bn_exists_resultentryproduct) = S ge_signed_half_exists_resultentryproductright))) /\ ((((((dc_value_exists_result) = 2 * (sto_cp_exists_resultentryproduct) /\ (sto_cn_exists_resultentryproduct) = 0) \/ exists ge_signed_half_exists_resultentryproductoutput. (((dc_value_exists_result) = 2 * ge_signed_half_exists_resultentryproductoutput + 1 /\ (sto_cp_exists_resultentryproduct) = 0) /\ (sto_cn_exists_resultentryproduct) = S ge_signed_half_exists_resultentryproductoutput))) /\ ((sto_ap_exists_resultentryproduct * sto_bp_exists_resultentryproduct + sto_an_exists_resultentryproduct * sto_bn_exists_resultentryproduct) + sto_cn_exists_resultentryproduct = (sto_ap_exists_resultentryproduct * sto_bn_exists_resultentryproduct + sto_an_exists_resultentryproduct * sto_bp_exists_resultentryproduct) + sto_cp_exists_resultentryproduct))))))))))))))) \/ ((((dc_index_exists_result)=0 \/ ~(exists pvs_factor_exists_resultentrynondivisor. (n) = (dc_index_exists_result) * pvs_factor_exists_resultentrynondivisor)) /\ ((dc_value_exists_result)=0)))))))

dirichlet_convolution_prefix_lookup · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n l M d z. (((exists dst_positive_code_lookup_prefixtable dst_positive_scale_lookup_prefixtable dst_negative_code_lookup_prefixtable dst_negative_scale_lookup_prefixtable. (((M) = (((((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) * S ((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) + ((dst_positive_scale_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable))) + (((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)))) * S ((((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) * S ((dst_positive_code_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable)) + ((dst_positive_scale_lookup_prefixtable) + (dst_positive_scale_lookup_prefixtable))) + (((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)))) + ((((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable))) + (((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) * S ((dst_negative_code_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)) + ((dst_negative_scale_lookup_prefixtable) + (dst_negative_scale_lookup_prefixtable)))))) /\ (forall dst_index_lookup_prefixtable. (exists pvs_le_gap_lookup_prefixtabledomain. pvs_le_gap_lookup_prefixtabledomain + (dst_index_lookup_prefixtable) = (l)) -> exists dst_positive_lookup_prefixtable dst_negative_lookup_prefixtable dst_value_lookup_prefixtable. ((((exists ff_h_pvs_lookup_prefixtableentrypositive. ff_h_pvs_lookup_prefixtableentrypositive + S (dst_positive_lookup_prefixtable) = S ((S (dst_index_lookup_prefixtable)) * dst_positive_scale_lookup_prefixtable)) /\ exists ff_q_pvs_lookup_prefixtableentrypositive. dst_positive_code_lookup_prefixtable = ff_q_pvs_lookup_prefixtableentrypositive * S ((S (dst_index_lookup_prefixtable)) * dst_positive_scale_lookup_prefixtable) + (dst_positive_lookup_prefixtable))) /\ (((((exists ff_h_pvs_lookup_prefixtableentrynegative. ff_h_pvs_lookup_prefixtableentrynegative + S (dst_negative_lookup_prefixtable) = S ((S (dst_index_lookup_prefixtable)) * dst_negative_scale_lookup_prefixtable)) /\ exists ff_q_pvs_lookup_prefixtableentrynegative. dst_negative_code_lookup_prefixtable = ff_q_pvs_lookup_prefixtableentrynegative * S ((S (dst_index_lookup_prefixtable)) * dst_negative_scale_lookup_prefixtable) + (dst_negative_lookup_prefixtable))) /\ (exists ge_balance_positive_lookup_prefixtableentryvalue ge_balance_negative_lookup_prefixtableentryvalue. (((((dst_value_lookup_prefixtable) = 2 * (ge_balance_positive_lookup_prefixtableentryvalue) /\ (ge_balance_negative_lookup_prefixtableentryvalue) = 0) \/ exists ge_signed_half_lookup_prefixtableentryvaluedecode. (((dst_value_lookup_prefixtable) = 2 * ge_signed_half_lookup_prefixtableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixtableentryvalue) = 0) /\ (ge_balance_negative_lookup_prefixtableentryvalue) = S ge_signed_half_lookup_prefixtableentryvaluedecode))) /\ ((dst_positive_lookup_prefixtable) + ge_balance_negative_lookup_prefixtableentryvalue = (dst_negative_lookup_prefixtable) + ge_balance_positive_lookup_prefixtableentryvalue))))))))) /\ (forall dc_index_lookup_prefix dc_value_lookup_prefix. (exists pvs_le_gap_lookup_prefixdomain. pvs_le_gap_lookup_prefixdomain + (dc_index_lookup_prefix) = (l)) -> (exists dst_positive_code_lookup_prefixlookup dst_positive_scale_lookup_prefixlookup dst_negative_code_lookup_prefixlookup dst_negative_scale_lookup_prefixlookup dst_positive_lookup_prefixlookup dst_negative_lookup_prefixlookup. (((M) = (((((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) * S ((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) + ((dst_positive_scale_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup))) + (((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)))) * S ((((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) * S ((dst_positive_code_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup)) + ((dst_positive_scale_lookup_prefixlookup) + (dst_positive_scale_lookup_prefixlookup))) + (((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)))) + ((((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup))) + (((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) * S ((dst_negative_code_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)) + ((dst_negative_scale_lookup_prefixlookup) + (dst_negative_scale_lookup_prefixlookup)))))) /\ (((((exists ff_h_pvs_lookup_prefixlookuppositive. ff_h_pvs_lookup_prefixlookuppositive + S (dst_positive_lookup_prefixlookup) = S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixlookup)) /\ exists ff_q_pvs_lookup_prefixlookuppositive. dst_positive_code_lookup_prefixlookup = ff_q_pvs_lookup_prefixlookuppositive * S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixlookup) + (dst_positive_lookup_prefixlookup))) /\ (((((exists ff_h_pvs_lookup_prefixlookupnegative. ff_h_pvs_lookup_prefixlookupnegative + S (dst_negative_lookup_prefixlookup) = S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixlookup)) /\ exists ff_q_pvs_lookup_prefixlookupnegative. dst_negative_code_lookup_prefixlookup = ff_q_pvs_lookup_prefixlookupnegative * S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixlookup) + (dst_negative_lookup_prefixlookup))) /\ (exists ge_balance_positive_lookup_prefixlookupvalue ge_balance_negative_lookup_prefixlookupvalue. (((((dc_value_lookup_prefix) = 2 * (ge_balance_positive_lookup_prefixlookupvalue) /\ (ge_balance_negative_lookup_prefixlookupvalue) = 0) \/ exists ge_signed_half_lookup_prefixlookupvaluedecode. (((dc_value_lookup_prefix) = 2 * ge_signed_half_lookup_prefixlookupvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixlookupvalue) = 0) /\ (ge_balance_negative_lookup_prefixlookupvalue) = S ge_signed_half_lookup_prefixlookupvaluedecode))) /\ ((dst_positive_lookup_prefixlookup) + ge_balance_negative_lookup_prefixlookupvalue = (dst_negative_lookup_prefixlookup) + ge_balance_positive_lookup_prefixlookupvalue))))))))) -> ((((~((dc_index_lookup_prefix)=0)) /\ (exists dc_quotient_lookup_prefixentry dc_left_lookup_prefixentry dc_right_lookup_prefixentry. (((n)=(dc_index_lookup_prefix)*dc_quotient_lookup_prefixentry) /\ (((exists dst_positive_code_lookup_prefixentryleft dst_positive_scale_lookup_prefixentryleft dst_negative_code_lookup_prefixentryleft dst_negative_scale_lookup_prefixentryleft dst_positive_lookup_prefixentryleft dst_negative_lookup_prefixentryleft. (((F) = (((((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) * S ((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) + ((dst_positive_scale_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft))) + (((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)))) * S ((((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) * S ((dst_positive_code_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft)) + ((dst_positive_scale_lookup_prefixentryleft) + (dst_positive_scale_lookup_prefixentryleft))) + (((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)))) + ((((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft))) + (((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) * S ((dst_negative_code_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)) + ((dst_negative_scale_lookup_prefixentryleft) + (dst_negative_scale_lookup_prefixentryleft)))))) /\ (((((exists ff_h_pvs_lookup_prefixentryleftpositive. ff_h_pvs_lookup_prefixentryleftpositive + S (dst_positive_lookup_prefixentryleft) = S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixentryleft)) /\ exists ff_q_pvs_lookup_prefixentryleftpositive. dst_positive_code_lookup_prefixentryleft = ff_q_pvs_lookup_prefixentryleftpositive * S ((S (dc_index_lookup_prefix)) * dst_positive_scale_lookup_prefixentryleft) + (dst_positive_lookup_prefixentryleft))) /\ (((((exists ff_h_pvs_lookup_prefixentryleftnegative. ff_h_pvs_lookup_prefixentryleftnegative + S (dst_negative_lookup_prefixentryleft) = S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixentryleft)) /\ exists ff_q_pvs_lookup_prefixentryleftnegative. dst_negative_code_lookup_prefixentryleft = ff_q_pvs_lookup_prefixentryleftnegative * S ((S (dc_index_lookup_prefix)) * dst_negative_scale_lookup_prefixentryleft) + (dst_negative_lookup_prefixentryleft))) /\ (exists ge_balance_positive_lookup_prefixentryleftvalue ge_balance_negative_lookup_prefixentryleftvalue. (((((dc_left_lookup_prefixentry) = 2 * (ge_balance_positive_lookup_prefixentryleftvalue) /\ (ge_balance_negative_lookup_prefixentryleftvalue) = 0) \/ exists ge_signed_half_lookup_prefixentryleftvaluedecode. (((dc_left_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryleftvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixentryleftvalue) = 0) /\ (ge_balance_negative_lookup_prefixentryleftvalue) = S ge_signed_half_lookup_prefixentryleftvaluedecode))) /\ ((dst_positive_lookup_prefixentryleft) + ge_balance_negative_lookup_prefixentryleftvalue = (dst_negative_lookup_prefixentryleft) + ge_balance_positive_lookup_prefixentryleftvalue))))))))) /\ (((exists dst_positive_code_lookup_prefixentryright dst_positive_scale_lookup_prefixentryright dst_negative_code_lookup_prefixentryright dst_negative_scale_lookup_prefixentryright dst_positive_lookup_prefixentryright dst_negative_lookup_prefixentryright. (((G) = (((((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) * S ((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) + ((dst_positive_scale_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright))) + (((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)))) * S ((((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) * S ((dst_positive_code_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright)) + ((dst_positive_scale_lookup_prefixentryright) + (dst_positive_scale_lookup_prefixentryright))) + (((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)))) + ((((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright))) + (((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) * S ((dst_negative_code_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)) + ((dst_negative_scale_lookup_prefixentryright) + (dst_negative_scale_lookup_prefixentryright)))))) /\ (((((exists ff_h_pvs_lookup_prefixentryrightpositive. ff_h_pvs_lookup_prefixentryrightpositive + S (dst_positive_lookup_prefixentryright) = S ((S (dc_quotient_lookup_prefixentry)) * dst_positive_scale_lookup_prefixentryright)) /\ exists ff_q_pvs_lookup_prefixentryrightpositive. dst_positive_code_lookup_prefixentryright = ff_q_pvs_lookup_prefixentryrightpositive * S ((S (dc_quotient_lookup_prefixentry)) * dst_positive_scale_lookup_prefixentryright) + (dst_positive_lookup_prefixentryright))) /\ (((((exists ff_h_pvs_lookup_prefixentryrightnegative. ff_h_pvs_lookup_prefixentryrightnegative + S (dst_negative_lookup_prefixentryright) = S ((S (dc_quotient_lookup_prefixentry)) * dst_negative_scale_lookup_prefixentryright)) /\ exists ff_q_pvs_lookup_prefixentryrightnegative. dst_negative_code_lookup_prefixentryright = ff_q_pvs_lookup_prefixentryrightnegative * S ((S (dc_quotient_lookup_prefixentry)) * dst_negative_scale_lookup_prefixentryright) + (dst_negative_lookup_prefixentryright))) /\ (exists ge_balance_positive_lookup_prefixentryrightvalue ge_balance_negative_lookup_prefixentryrightvalue. (((((dc_right_lookup_prefixentry) = 2 * (ge_balance_positive_lookup_prefixentryrightvalue) /\ (ge_balance_negative_lookup_prefixentryrightvalue) = 0) \/ exists ge_signed_half_lookup_prefixentryrightvaluedecode. (((dc_right_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryrightvaluedecode + 1 /\ (ge_balance_positive_lookup_prefixentryrightvalue) = 0) /\ (ge_balance_negative_lookup_prefixentryrightvalue) = S ge_signed_half_lookup_prefixentryrightvaluedecode))) /\ ((dst_positive_lookup_prefixentryright) + ge_balance_negative_lookup_prefixentryrightvalue = (dst_negative_lookup_prefixentryright) + ge_balance_positive_lookup_prefixentryrightvalue))))))))) /\ (exists sto_ap_lookup_prefixentryproduct sto_an_lookup_prefixentryproduct sto_bp_lookup_prefixentryproduct sto_bn_lookup_prefixentryproduct sto_cp_lookup_prefixentryproduct sto_cn_lookup_prefixentryproduct. (((((dc_left_lookup_prefixentry) = 2 * (sto_ap_lookup_prefixentryproduct) /\ (sto_an_lookup_prefixentryproduct) = 0) \/ exists ge_signed_half_lookup_prefixentryproductleft. (((dc_left_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryproductleft + 1 /\ (sto_ap_lookup_prefixentryproduct) = 0) /\ (sto_an_lookup_prefixentryproduct) = S ge_signed_half_lookup_prefixentryproductleft))) /\ ((((((dc_right_lookup_prefixentry) = 2 * (sto_bp_lookup_prefixentryproduct) /\ (sto_bn_lookup_prefixentryproduct) = 0) \/ exists ge_signed_half_lookup_prefixentryproductright. (((dc_right_lookup_prefixentry) = 2 * ge_signed_half_lookup_prefixentryproductright + 1 /\ (sto_bp_lookup_prefixentryproduct) = 0) /\ (sto_bn_lookup_prefixentryproduct) = S ge_signed_half_lookup_prefixentryproductright))) /\ ((((((dc_value_lookup_prefix) = 2 * (sto_cp_lookup_prefixentryproduct) /\ (sto_cn_lookup_prefixentryproduct) = 0) \/ exists ge_signed_half_lookup_prefixentryproductoutput. (((dc_value_lookup_prefix) = 2 * ge_signed_half_lookup_prefixentryproductoutput + 1 /\ (sto_cp_lookup_prefixentryproduct) = 0) /\ (sto_cn_lookup_prefixentryproduct) = S ge_signed_half_lookup_prefixentryproductoutput))) /\ ((sto_ap_lookup_prefixentryproduct * sto_bp_lookup_prefixentryproduct + sto_an_lookup_prefixentryproduct * sto_bn_lookup_prefixentryproduct) + sto_cn_lookup_prefixentryproduct = (sto_ap_lookup_prefixentryproduct * sto_bn_lookup_prefixentryproduct + sto_an_lookup_prefixentryproduct * sto_bp_lookup_prefixentryproduct) + sto_cp_lookup_prefixentryproduct))))))))))))))) \/ ((((dc_index_lookup_prefix)=0 \/ ~(exists pvs_factor_lookup_prefixentrynondivisor. (n) = (dc_index_lookup_prefix) * pvs_factor_lookup_prefixentrynondivisor)) /\ ((dc_value_lookup_prefix)=0))))))) -> (exists pvs_le_gap_lookup_bound. pvs_le_gap_lookup_bound + (d) = (l)) -> (exists dst_positive_code_lookup_entry dst_positive_scale_lookup_entry dst_negative_code_lookup_entry dst_negative_scale_lookup_entry dst_positive_lookup_entry dst_negative_lookup_entry. (((M) = (((((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) * S ((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) + ((dst_positive_scale_lookup_entry) + (dst_positive_scale_lookup_entry))) + (((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry)))) * S ((((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) * S ((dst_positive_code_lookup_entry) + (dst_positive_scale_lookup_entry)) + ((dst_positive_scale_lookup_entry) + (dst_positive_scale_lookup_entry))) + (((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry)))) + ((((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry))) + (((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) * S ((dst_negative_code_lookup_entry) + (dst_negative_scale_lookup_entry)) + ((dst_negative_scale_lookup_entry) + (dst_negative_scale_lookup_entry)))))) /\ (((((exists ff_h_pvs_lookup_entrypositive. ff_h_pvs_lookup_entrypositive + S (dst_positive_lookup_entry) = S ((S (d)) * dst_positive_scale_lookup_entry)) /\ exists ff_q_pvs_lookup_entrypositive. dst_positive_code_lookup_entry = ff_q_pvs_lookup_entrypositive * S ((S (d)) * dst_positive_scale_lookup_entry) + (dst_positive_lookup_entry))) /\ (((((exists ff_h_pvs_lookup_entrynegative. ff_h_pvs_lookup_entrynegative + S (dst_negative_lookup_entry) = S ((S (d)) * dst_negative_scale_lookup_entry)) /\ exists ff_q_pvs_lookup_entrynegative. dst_negative_code_lookup_entry = ff_q_pvs_lookup_entrynegative * S ((S (d)) * dst_negative_scale_lookup_entry) + (dst_negative_lookup_entry))) /\ (exists ge_balance_positive_lookup_entryvalue ge_balance_negative_lookup_entryvalue. (((((z) = 2 * (ge_balance_positive_lookup_entryvalue) /\ (ge_balance_negative_lookup_entryvalue) = 0) \/ exists ge_signed_half_lookup_entryvaluedecode. (((z) = 2 * ge_signed_half_lookup_entryvaluedecode + 1 /\ (ge_balance_positive_lookup_entryvalue) = 0) /\ (ge_balance_negative_lookup_entryvalue) = S ge_signed_half_lookup_entryvaluedecode))) /\ ((dst_positive_lookup_entry) + ge_balance_negative_lookup_entryvalue = (dst_negative_lookup_entry) + ge_balance_positive_lookup_entryvalue))))))))) -> ((((~((d)=0)) /\ (exists dc_quotient_lookup_result dc_left_lookup_result dc_right_lookup_result. (((n)=(d)*dc_quotient_lookup_result) /\ (((exists dst_positive_code_lookup_resultleft dst_positive_scale_lookup_resultleft dst_negative_code_lookup_resultleft dst_negative_scale_lookup_resultleft dst_positive_lookup_resultleft dst_negative_lookup_resultleft. (((F) = (((((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) * S ((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) + ((dst_positive_scale_lookup_resultleft) + (dst_positive_scale_lookup_resultleft))) + (((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)))) * S ((((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) * S ((dst_positive_code_lookup_resultleft) + (dst_positive_scale_lookup_resultleft)) + ((dst_positive_scale_lookup_resultleft) + (dst_positive_scale_lookup_resultleft))) + (((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)))) + ((((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft))) + (((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) * S ((dst_negative_code_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)) + ((dst_negative_scale_lookup_resultleft) + (dst_negative_scale_lookup_resultleft)))))) /\ (((((exists ff_h_pvs_lookup_resultleftpositive. ff_h_pvs_lookup_resultleftpositive + S (dst_positive_lookup_resultleft) = S ((S (d)) * dst_positive_scale_lookup_resultleft)) /\ exists ff_q_pvs_lookup_resultleftpositive. dst_positive_code_lookup_resultleft = ff_q_pvs_lookup_resultleftpositive * S ((S (d)) * dst_positive_scale_lookup_resultleft) + (dst_positive_lookup_resultleft))) /\ (((((exists ff_h_pvs_lookup_resultleftnegative. ff_h_pvs_lookup_resultleftnegative + S (dst_negative_lookup_resultleft) = S ((S (d)) * dst_negative_scale_lookup_resultleft)) /\ exists ff_q_pvs_lookup_resultleftnegative. dst_negative_code_lookup_resultleft = ff_q_pvs_lookup_resultleftnegative * S ((S (d)) * dst_negative_scale_lookup_resultleft) + (dst_negative_lookup_resultleft))) /\ (exists ge_balance_positive_lookup_resultleftvalue ge_balance_negative_lookup_resultleftvalue. (((((dc_left_lookup_result) = 2 * (ge_balance_positive_lookup_resultleftvalue) /\ (ge_balance_negative_lookup_resultleftvalue) = 0) \/ exists ge_signed_half_lookup_resultleftvaluedecode. (((dc_left_lookup_result) = 2 * ge_signed_half_lookup_resultleftvaluedecode + 1 /\ (ge_balance_positive_lookup_resultleftvalue) = 0) /\ (ge_balance_negative_lookup_resultleftvalue) = S ge_signed_half_lookup_resultleftvaluedecode))) /\ ((dst_positive_lookup_resultleft) + ge_balance_negative_lookup_resultleftvalue = (dst_negative_lookup_resultleft) + ge_balance_positive_lookup_resultleftvalue))))))))) /\ (((exists dst_positive_code_lookup_resultright dst_positive_scale_lookup_resultright dst_negative_code_lookup_resultright dst_negative_scale_lookup_resultright dst_positive_lookup_resultright dst_negative_lookup_resultright. (((G) = (((((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) * S ((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) + ((dst_positive_scale_lookup_resultright) + (dst_positive_scale_lookup_resultright))) + (((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright)))) * S ((((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) * S ((dst_positive_code_lookup_resultright) + (dst_positive_scale_lookup_resultright)) + ((dst_positive_scale_lookup_resultright) + (dst_positive_scale_lookup_resultright))) + (((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright)))) + ((((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright))) + (((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) * S ((dst_negative_code_lookup_resultright) + (dst_negative_scale_lookup_resultright)) + ((dst_negative_scale_lookup_resultright) + (dst_negative_scale_lookup_resultright)))))) /\ (((((exists ff_h_pvs_lookup_resultrightpositive. ff_h_pvs_lookup_resultrightpositive + S (dst_positive_lookup_resultright) = S ((S (dc_quotient_lookup_result)) * dst_positive_scale_lookup_resultright)) /\ exists ff_q_pvs_lookup_resultrightpositive. dst_positive_code_lookup_resultright = ff_q_pvs_lookup_resultrightpositive * S ((S (dc_quotient_lookup_result)) * dst_positive_scale_lookup_resultright) + (dst_positive_lookup_resultright))) /\ (((((exists ff_h_pvs_lookup_resultrightnegative. ff_h_pvs_lookup_resultrightnegative + S (dst_negative_lookup_resultright) = S ((S (dc_quotient_lookup_result)) * dst_negative_scale_lookup_resultright)) /\ exists ff_q_pvs_lookup_resultrightnegative. dst_negative_code_lookup_resultright = ff_q_pvs_lookup_resultrightnegative * S ((S (dc_quotient_lookup_result)) * dst_negative_scale_lookup_resultright) + (dst_negative_lookup_resultright))) /\ (exists ge_balance_positive_lookup_resultrightvalue ge_balance_negative_lookup_resultrightvalue. (((((dc_right_lookup_result) = 2 * (ge_balance_positive_lookup_resultrightvalue) /\ (ge_balance_negative_lookup_resultrightvalue) = 0) \/ exists ge_signed_half_lookup_resultrightvaluedecode. (((dc_right_lookup_result) = 2 * ge_signed_half_lookup_resultrightvaluedecode + 1 /\ (ge_balance_positive_lookup_resultrightvalue) = 0) /\ (ge_balance_negative_lookup_resultrightvalue) = S ge_signed_half_lookup_resultrightvaluedecode))) /\ ((dst_positive_lookup_resultright) + ge_balance_negative_lookup_resultrightvalue = (dst_negative_lookup_resultright) + ge_balance_positive_lookup_resultrightvalue))))))))) /\ (exists sto_ap_lookup_resultproduct sto_an_lookup_resultproduct sto_bp_lookup_resultproduct sto_bn_lookup_resultproduct sto_cp_lookup_resultproduct sto_cn_lookup_resultproduct. (((((dc_left_lookup_result) = 2 * (sto_ap_lookup_resultproduct) /\ (sto_an_lookup_resultproduct) = 0) \/ exists ge_signed_half_lookup_resultproductleft. (((dc_left_lookup_result) = 2 * ge_signed_half_lookup_resultproductleft + 1 /\ (sto_ap_lookup_resultproduct) = 0) /\ (sto_an_lookup_resultproduct) = S ge_signed_half_lookup_resultproductleft))) /\ ((((((dc_right_lookup_result) = 2 * (sto_bp_lookup_resultproduct) /\ (sto_bn_lookup_resultproduct) = 0) \/ exists ge_signed_half_lookup_resultproductright. (((dc_right_lookup_result) = 2 * ge_signed_half_lookup_resultproductright + 1 /\ (sto_bp_lookup_resultproduct) = 0) /\ (sto_bn_lookup_resultproduct) = S ge_signed_half_lookup_resultproductright))) /\ ((((((z) = 2 * (sto_cp_lookup_resultproduct) /\ (sto_cn_lookup_resultproduct) = 0) \/ exists ge_signed_half_lookup_resultproductoutput. (((z) = 2 * ge_signed_half_lookup_resultproductoutput + 1 /\ (sto_cp_lookup_resultproduct) = 0) /\ (sto_cn_lookup_resultproduct) = S ge_signed_half_lookup_resultproductoutput))) /\ ((sto_ap_lookup_resultproduct * sto_bp_lookup_resultproduct + sto_an_lookup_resultproduct * sto_bn_lookup_resultproduct) + sto_cn_lookup_resultproduct = (sto_ap_lookup_resultproduct * sto_bn_lookup_resultproduct + sto_an_lookup_resultproduct * sto_bp_lookup_resultproduct) + sto_cp_lookup_resultproduct))))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_lookup_resultnondivisor. (n) = (d) * pvs_factor_lookup_resultnondivisor)) /\ ((z)=0))))

dirichlet_convolution_sum_functional · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G n a b. (((~((n)=0)) /\ (exists dc_mask_sum_unique_first. ((((exists dst_positive_code_sum_unique_firstmasktable dst_positive_scale_sum_unique_firstmasktable dst_negative_code_sum_unique_firstmasktable dst_negative_scale_sum_unique_firstmasktable. (((dc_mask_sum_unique_first) = (((((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) * S ((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) + ((dst_positive_scale_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable))) + (((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)))) * S ((((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) * S ((dst_positive_code_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable)) + ((dst_positive_scale_sum_unique_firstmasktable) + (dst_positive_scale_sum_unique_firstmasktable))) + (((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)))) + ((((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable))) + (((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) * S ((dst_negative_code_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)) + ((dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_scale_sum_unique_firstmasktable)))))) /\ (forall dst_index_sum_unique_firstmasktable. (exists pvs_le_gap_sum_unique_firstmasktabledomain. pvs_le_gap_sum_unique_firstmasktabledomain + (dst_index_sum_unique_firstmasktable) = (n)) -> exists dst_positive_sum_unique_firstmasktable dst_negative_sum_unique_firstmasktable dst_value_sum_unique_firstmasktable. ((((exists ff_h_pvs_sum_unique_firstmasktableentrypositive. ff_h_pvs_sum_unique_firstmasktableentrypositive + S (dst_positive_sum_unique_firstmasktable) = S ((S (dst_index_sum_unique_firstmasktable)) * dst_positive_scale_sum_unique_firstmasktable)) /\ exists ff_q_pvs_sum_unique_firstmasktableentrypositive. dst_positive_code_sum_unique_firstmasktable = ff_q_pvs_sum_unique_firstmasktableentrypositive * S ((S (dst_index_sum_unique_firstmasktable)) * dst_positive_scale_sum_unique_firstmasktable) + (dst_positive_sum_unique_firstmasktable))) /\ (((((exists ff_h_pvs_sum_unique_firstmasktableentrynegative. ff_h_pvs_sum_unique_firstmasktableentrynegative + S (dst_negative_sum_unique_firstmasktable) = S ((S (dst_index_sum_unique_firstmasktable)) * dst_negative_scale_sum_unique_firstmasktable)) /\ exists ff_q_pvs_sum_unique_firstmasktableentrynegative. dst_negative_code_sum_unique_firstmasktable = ff_q_pvs_sum_unique_firstmasktableentrynegative * S ((S (dst_index_sum_unique_firstmasktable)) * dst_negative_scale_sum_unique_firstmasktable) + (dst_negative_sum_unique_firstmasktable))) /\ (exists ge_balance_positive_sum_unique_firstmasktableentryvalue ge_balance_negative_sum_unique_firstmasktableentryvalue. (((((dst_value_sum_unique_firstmasktable) = 2 * (ge_balance_positive_sum_unique_firstmasktableentryvalue) /\ (ge_balance_negative_sum_unique_firstmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmasktableentryvaluedecode. (((dst_value_sum_unique_firstmasktable) = 2 * ge_signed_half_sum_unique_firstmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmasktableentryvalue) = S ge_signed_half_sum_unique_firstmasktableentryvaluedecode))) /\ ((dst_positive_sum_unique_firstmasktable) + ge_balance_negative_sum_unique_firstmasktableentryvalue = (dst_negative_sum_unique_firstmasktable) + ge_balance_positive_sum_unique_firstmasktableentryvalue))))))))) /\ (forall dc_index_sum_unique_firstmask dc_value_sum_unique_firstmask. (exists pvs_le_gap_sum_unique_firstmaskdomain. pvs_le_gap_sum_unique_firstmaskdomain + (dc_index_sum_unique_firstmask) = (n)) -> (exists dst_positive_code_sum_unique_firstmasklookup dst_positive_scale_sum_unique_firstmasklookup dst_negative_code_sum_unique_firstmasklookup dst_negative_scale_sum_unique_firstmasklookup dst_positive_sum_unique_firstmasklookup dst_negative_sum_unique_firstmasklookup. (((dc_mask_sum_unique_first) = (((((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) * S ((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) + ((dst_positive_scale_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup))) + (((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)))) * S ((((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) * S ((dst_positive_code_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup)) + ((dst_positive_scale_sum_unique_firstmasklookup) + (dst_positive_scale_sum_unique_firstmasklookup))) + (((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)))) + ((((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup))) + (((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) * S ((dst_negative_code_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)) + ((dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_scale_sum_unique_firstmasklookup)))))) /\ (((((exists ff_h_pvs_sum_unique_firstmasklookuppositive. ff_h_pvs_sum_unique_firstmasklookuppositive + S (dst_positive_sum_unique_firstmasklookup) = S ((S (dc_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmasklookup)) /\ exists ff_q_pvs_sum_unique_firstmasklookuppositive. dst_positive_code_sum_unique_firstmasklookup = ff_q_pvs_sum_unique_firstmasklookuppositive * S ((S (dc_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmasklookup) + (dst_positive_sum_unique_firstmasklookup))) /\ (((((exists ff_h_pvs_sum_unique_firstmasklookupnegative. ff_h_pvs_sum_unique_firstmasklookupnegative + S (dst_negative_sum_unique_firstmasklookup) = S ((S (dc_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmasklookup)) /\ exists ff_q_pvs_sum_unique_firstmasklookupnegative. dst_negative_code_sum_unique_firstmasklookup = ff_q_pvs_sum_unique_firstmasklookupnegative * S ((S (dc_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmasklookup) + (dst_negative_sum_unique_firstmasklookup))) /\ (exists ge_balance_positive_sum_unique_firstmasklookupvalue ge_balance_negative_sum_unique_firstmasklookupvalue. (((((dc_value_sum_unique_firstmask) = 2 * (ge_balance_positive_sum_unique_firstmasklookupvalue) /\ (ge_balance_negative_sum_unique_firstmasklookupvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmasklookupvaluedecode. (((dc_value_sum_unique_firstmask) = 2 * ge_signed_half_sum_unique_firstmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmasklookupvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmasklookupvalue) = S ge_signed_half_sum_unique_firstmasklookupvaluedecode))) /\ ((dst_positive_sum_unique_firstmasklookup) + ge_balance_negative_sum_unique_firstmasklookupvalue = (dst_negative_sum_unique_firstmasklookup) + ge_balance_positive_sum_unique_firstmasklookupvalue))))))))) -> ((((~((dc_index_sum_unique_firstmask)=0)) /\ (exists dc_quotient_sum_unique_firstmaskentry dc_left_sum_unique_firstmaskentry dc_right_sum_unique_firstmaskentry. (((n)=(dc_index_sum_unique_firstmask)*dc_quotient_sum_unique_firstmaskentry) /\ (((exists dst_positive_code_sum_unique_firstmaskentryleft dst_positive_scale_sum_unique_firstmaskentryleft dst_negative_code_sum_unique_firstmaskentryleft dst_negative_scale_sum_unique_firstmaskentryleft dst_positive_sum_unique_firstmaskentryleft dst_negative_sum_unique_firstmaskentryleft. (((F) = (((((dst_positive_code_sum_unique_firstmaskentryleft) + (dst_positive_scale_sum_unique_firstmaskentryleft)) * S ((dst_positive_code_sum_unique_firstmaskentryleft) + (dst_positive_scale_sum_unique_firstmaskentryleft)) + ((dst_positive_scale_sum_unique_firstmaskentryleft) + (dst_positive_scale_sum_unique_firstmaskentryleft))) + (((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) * S ((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) + ((dst_negative_scale_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)))) * S ((((dst_positive_code_sum_unique_firstmaskentryleft) + (dst_positive_scale_sum_unique_firstmaskentryleft)) * S ((dst_positive_code_sum_unique_firstmaskentryleft) + (dst_positive_scale_sum_unique_firstmaskentryleft)) + ((dst_positive_scale_sum_unique_firstmaskentryleft) + (dst_positive_scale_sum_unique_firstmaskentryleft))) + (((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) * S ((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) + ((dst_negative_scale_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)))) + ((((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) * S ((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) + ((dst_negative_scale_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft))) + (((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) * S ((dst_negative_code_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)) + ((dst_negative_scale_sum_unique_firstmaskentryleft) + (dst_negative_scale_sum_unique_firstmaskentryleft)))))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryleftpositive. ff_h_pvs_sum_unique_firstmaskentryleftpositive + S (dst_positive_sum_unique_firstmaskentryleft) = S ((S (dc_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmaskentryleft)) /\ exists ff_q_pvs_sum_unique_firstmaskentryleftpositive. dst_positive_code_sum_unique_firstmaskentryleft = ff_q_pvs_sum_unique_firstmaskentryleftpositive * S ((S (dc_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmaskentryleft) + (dst_positive_sum_unique_firstmaskentryleft))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryleftnegative. ff_h_pvs_sum_unique_firstmaskentryleftnegative + S (dst_negative_sum_unique_firstmaskentryleft) = S ((S (dc_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmaskentryleft)) /\ exists ff_q_pvs_sum_unique_firstmaskentryleftnegative. dst_negative_code_sum_unique_firstmaskentryleft = ff_q_pvs_sum_unique_firstmaskentryleftnegative * S ((S (dc_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmaskentryleft) + (dst_negative_sum_unique_firstmaskentryleft))) /\ (exists ge_balance_positive_sum_unique_firstmaskentryleftvalue ge_balance_negative_sum_unique_firstmaskentryleftvalue. (((((dc_left_sum_unique_firstmaskentry) = 2 * (ge_balance_positive_sum_unique_firstmaskentryleftvalue) /\ (ge_balance_negative_sum_unique_firstmaskentryleftvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmaskentryleftvaluedecode. (((dc_left_sum_unique_firstmaskentry) = 2 * ge_signed_half_sum_unique_firstmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmaskentryleftvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmaskentryleftvalue) = S ge_signed_half_sum_unique_firstmaskentryleftvaluedecode))) /\ ((dst_positive_sum_unique_firstmaskentryleft) + ge_balance_negative_sum_unique_firstmaskentryleftvalue = (dst_negative_sum_unique_firstmaskentryleft) + ge_balance_positive_sum_unique_firstmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_sum_unique_firstmaskentryright dst_positive_scale_sum_unique_firstmaskentryright dst_negative_code_sum_unique_firstmaskentryright dst_negative_scale_sum_unique_firstmaskentryright dst_positive_sum_unique_firstmaskentryright dst_negative_sum_unique_firstmaskentryright. (((G) = (((((dst_positive_code_sum_unique_firstmaskentryright) + (dst_positive_scale_sum_unique_firstmaskentryright)) * S ((dst_positive_code_sum_unique_firstmaskentryright) + (dst_positive_scale_sum_unique_firstmaskentryright)) + ((dst_positive_scale_sum_unique_firstmaskentryright) + (dst_positive_scale_sum_unique_firstmaskentryright))) + (((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) * S ((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) + ((dst_negative_scale_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)))) * S ((((dst_positive_code_sum_unique_firstmaskentryright) + (dst_positive_scale_sum_unique_firstmaskentryright)) * S ((dst_positive_code_sum_unique_firstmaskentryright) + (dst_positive_scale_sum_unique_firstmaskentryright)) + ((dst_positive_scale_sum_unique_firstmaskentryright) + (dst_positive_scale_sum_unique_firstmaskentryright))) + (((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) * S ((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) + ((dst_negative_scale_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)))) + ((((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) * S ((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) + ((dst_negative_scale_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright))) + (((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) * S ((dst_negative_code_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)) + ((dst_negative_scale_sum_unique_firstmaskentryright) + (dst_negative_scale_sum_unique_firstmaskentryright)))))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryrightpositive. ff_h_pvs_sum_unique_firstmaskentryrightpositive + S (dst_positive_sum_unique_firstmaskentryright) = S ((S (dc_quotient_sum_unique_firstmaskentry)) * dst_positive_scale_sum_unique_firstmaskentryright)) /\ exists ff_q_pvs_sum_unique_firstmaskentryrightpositive. dst_positive_code_sum_unique_firstmaskentryright = ff_q_pvs_sum_unique_firstmaskentryrightpositive * S ((S (dc_quotient_sum_unique_firstmaskentry)) * dst_positive_scale_sum_unique_firstmaskentryright) + (dst_positive_sum_unique_firstmaskentryright))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryrightnegative. ff_h_pvs_sum_unique_firstmaskentryrightnegative + S (dst_negative_sum_unique_firstmaskentryright) = S ((S (dc_quotient_sum_unique_firstmaskentry)) * dst_negative_scale_sum_unique_firstmaskentryright)) /\ exists ff_q_pvs_sum_unique_firstmaskentryrightnegative. dst_negative_code_sum_unique_firstmaskentryright = ff_q_pvs_sum_unique_firstmaskentryrightnegative * S ((S (dc_quotient_sum_unique_firstmaskentry)) * dst_negative_scale_sum_unique_firstmaskentryright) + (dst_negative_sum_unique_firstmaskentryright))) /\ (exists ge_balance_positive_sum_unique_firstmaskentryrightvalue ge_balance_negative_sum_unique_firstmaskentryrightvalue. (((((dc_right_sum_unique_firstmaskentry) = 2 * (ge_balance_positive_sum_unique_firstmaskentryrightvalue) /\ (ge_balance_negative_sum_unique_firstmaskentryrightvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmaskentryrightvaluedecode. (((dc_right_sum_unique_firstmaskentry) = 2 * ge_signed_half_sum_unique_firstmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmaskentryrightvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmaskentryrightvalue) = S ge_signed_half_sum_unique_firstmaskentryrightvaluedecode))) /\ ((dst_positive_sum_unique_firstmaskentryright) + ge_balance_negative_sum_unique_firstmaskentryrightvalue = (dst_negative_sum_unique_firstmaskentryright) + ge_balance_positive_sum_unique_firstmaskentryrightvalue))))))))) /\ (exists sto_ap_sum_unique_firstmaskentryproduct sto_an_sum_unique_firstmaskentryproduct sto_bp_sum_unique_firstmaskentryproduct sto_bn_sum_unique_firstmaskentryproduct sto_cp_sum_unique_firstmaskentryproduct sto_cn_sum_unique_firstmaskentryproduct. (((((dc_left_sum_unique_firstmaskentry) = 2 * (sto_ap_sum_unique_firstmaskentryproduct) /\ (sto_an_sum_unique_firstmaskentryproduct) = 0) \/ exists ge_signed_half_sum_unique_firstmaskentryproductleft. (((dc_left_sum_unique_firstmaskentry) = 2 * ge_signed_half_sum_unique_firstmaskentryproductleft + 1 /\ (sto_ap_sum_unique_firstmaskentryproduct) = 0) /\ (sto_an_sum_unique_firstmaskentryproduct) = S ge_signed_half_sum_unique_firstmaskentryproductleft))) /\ ((((((dc_right_sum_unique_firstmaskentry) = 2 * (sto_bp_sum_unique_firstmaskentryproduct) /\ (sto_bn_sum_unique_firstmaskentryproduct) = 0) \/ exists ge_signed_half_sum_unique_firstmaskentryproductright. (((dc_right_sum_unique_firstmaskentry) = 2 * ge_signed_half_sum_unique_firstmaskentryproductright + 1 /\ (sto_bp_sum_unique_firstmaskentryproduct) = 0) /\ (sto_bn_sum_unique_firstmaskentryproduct) = S ge_signed_half_sum_unique_firstmaskentryproductright))) /\ ((((((dc_value_sum_unique_firstmask) = 2 * (sto_cp_sum_unique_firstmaskentryproduct) /\ (sto_cn_sum_unique_firstmaskentryproduct) = 0) \/ exists ge_signed_half_sum_unique_firstmaskentryproductoutput. (((dc_value_sum_unique_firstmask) = 2 * ge_signed_half_sum_unique_firstmaskentryproductoutput + 1 /\ (sto_cp_sum_unique_firstmaskentryproduct) = 0) /\ (sto_cn_sum_unique_firstmaskentryproduct) = S ge_signed_half_sum_unique_firstmaskentryproductoutput))) /\ ((sto_ap_sum_unique_firstmaskentryproduct * sto_bp_sum_unique_firstmaskentryproduct + sto_an_sum_unique_firstmaskentryproduct * sto_bn_sum_unique_firstmaskentryproduct) + sto_cn_sum_unique_firstmaskentryproduct = (sto_ap_sum_unique_firstmaskentryproduct * sto_bn_sum_unique_firstmaskentryproduct + sto_an_sum_unique_firstmaskentryproduct * sto_bp_sum_unique_firstmaskentryproduct) + sto_cp_sum_unique_firstmaskentryproduct))))))))))))))) \/ ((((dc_index_sum_unique_firstmask)=0 \/ ~(exists pvs_factor_sum_unique_firstmaskentrynondivisor. (n) = (dc_index_sum_unique_firstmask) * pvs_factor_sum_unique_firstmaskentrynondivisor)) /\ ((dc_value_sum_unique_firstmask)=0))))))) /\ (exists dst_positive_code_sum_unique_firstfold dst_positive_scale_sum_unique_firstfold dst_negative_code_sum_unique_firstfold dst_negative_scale_sum_unique_firstfold dst_positive_sum_sum_unique_firstfold dst_negative_sum_sum_unique_firstfold. (((dc_mask_sum_unique_first) = (((((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) * S ((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) + ((dst_positive_scale_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold))) + (((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)))) * S ((((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) * S ((dst_positive_code_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold)) + ((dst_positive_scale_sum_unique_firstfold) + (dst_positive_scale_sum_unique_firstfold))) + (((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)))) + ((((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold))) + (((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) * S ((dst_negative_code_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)) + ((dst_negative_scale_sum_unique_firstfold) + (dst_negative_scale_sum_unique_firstfold)))))) /\ (((exists fs_u_dst_sum_unique_firstfoldpositive fs_v_dst_sum_unique_firstfoldpositive. ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_start. fs_h_dst_sum_unique_firstfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_start. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_terminal. fs_h_dst_sum_unique_firstfoldpositive_body_terminal + S (dst_positive_sum_sum_unique_firstfold) = S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_terminal. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldpositive) + (dst_positive_sum_sum_unique_firstfold))) /\ forall fs_i_dst_sum_unique_firstfoldpositive_body_steps. (exists fs_lt_dst_sum_unique_firstfoldpositive_body_steps_bound. fs_lt_dst_sum_unique_firstfoldpositive_body_steps_bound + S fs_i_dst_sum_unique_firstfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_unique_firstfoldpositive_body_steps fs_r_dst_sum_unique_firstfoldpositive_body_steps fs_s_dst_sum_unique_firstfoldpositive_body_steps. ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_steps_summand. fs_h_dst_sum_unique_firstfoldpositive_body_steps_summand + S (fs_a_dst_sum_unique_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * dst_positive_scale_sum_unique_firstfold)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_steps_summand. dst_positive_code_sum_unique_firstfold = fs_q_dst_sum_unique_firstfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * dst_positive_scale_sum_unique_firstfold) + (fs_a_dst_sum_unique_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_steps_partial. fs_h_dst_sum_unique_firstfoldpositive_body_steps_partial + S (fs_r_dst_sum_unique_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_steps_partial. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive) + (fs_r_dst_sum_unique_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldpositive_body_steps_successor. fs_h_dst_sum_unique_firstfoldpositive_body_steps_successor + S (fs_s_dst_sum_unique_firstfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive)) /\ exists fs_q_dst_sum_unique_firstfoldpositive_body_steps_successor. fs_u_dst_sum_unique_firstfoldpositive = fs_q_dst_sum_unique_firstfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstfoldpositive_body_steps)) * fs_v_dst_sum_unique_firstfoldpositive) + (fs_s_dst_sum_unique_firstfoldpositive_body_steps))) /\ fs_s_dst_sum_unique_firstfoldpositive_body_steps = fs_r_dst_sum_unique_firstfoldpositive_body_steps + fs_a_dst_sum_unique_firstfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_firstfoldnegative fs_v_dst_sum_unique_firstfoldnegative. ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_start. fs_h_dst_sum_unique_firstfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_start. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_firstfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_terminal. fs_h_dst_sum_unique_firstfoldnegative_body_terminal + S (dst_negative_sum_sum_unique_firstfold) = S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_terminal. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_firstfoldnegative) + (dst_negative_sum_sum_unique_firstfold))) /\ forall fs_i_dst_sum_unique_firstfoldnegative_body_steps. (exists fs_lt_dst_sum_unique_firstfoldnegative_body_steps_bound. fs_lt_dst_sum_unique_firstfoldnegative_body_steps_bound + S fs_i_dst_sum_unique_firstfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_unique_firstfoldnegative_body_steps fs_r_dst_sum_unique_firstfoldnegative_body_steps fs_s_dst_sum_unique_firstfoldnegative_body_steps. ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_steps_summand. fs_h_dst_sum_unique_firstfoldnegative_body_steps_summand + S (fs_a_dst_sum_unique_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * dst_negative_scale_sum_unique_firstfold)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_steps_summand. dst_negative_code_sum_unique_firstfold = fs_q_dst_sum_unique_firstfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * dst_negative_scale_sum_unique_firstfold) + (fs_a_dst_sum_unique_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_steps_partial. fs_h_dst_sum_unique_firstfoldnegative_body_steps_partial + S (fs_r_dst_sum_unique_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_steps_partial. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative) + (fs_r_dst_sum_unique_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_firstfoldnegative_body_steps_successor. fs_h_dst_sum_unique_firstfoldnegative_body_steps_successor + S (fs_s_dst_sum_unique_firstfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative)) /\ exists fs_q_dst_sum_unique_firstfoldnegative_body_steps_successor. fs_u_dst_sum_unique_firstfoldnegative = fs_q_dst_sum_unique_firstfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_firstfoldnegative_body_steps)) * fs_v_dst_sum_unique_firstfoldnegative) + (fs_s_dst_sum_unique_firstfoldnegative_body_steps))) /\ fs_s_dst_sum_unique_firstfoldnegative_body_steps = fs_r_dst_sum_unique_firstfoldnegative_body_steps + fs_a_dst_sum_unique_firstfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_firstfoldresult ge_balance_negative_sum_unique_firstfoldresult. (((((a) = 2 * (ge_balance_positive_sum_unique_firstfoldresult) /\ (ge_balance_negative_sum_unique_firstfoldresult) = 0) \/ exists ge_signed_half_sum_unique_firstfoldresultdecode. (((a) = 2 * ge_signed_half_sum_unique_firstfoldresultdecode + 1 /\ (ge_balance_positive_sum_unique_firstfoldresult) = 0) /\ (ge_balance_negative_sum_unique_firstfoldresult) = S ge_signed_half_sum_unique_firstfoldresultdecode))) /\ ((dst_positive_sum_sum_unique_firstfold) + ge_balance_negative_sum_unique_firstfoldresult = (dst_negative_sum_sum_unique_firstfold) + ge_balance_positive_sum_unique_firstfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dc_mask_sum_unique_second. ((((exists dst_positive_code_sum_unique_secondmasktable dst_positive_scale_sum_unique_secondmasktable dst_negative_code_sum_unique_secondmasktable dst_negative_scale_sum_unique_secondmasktable. (((dc_mask_sum_unique_second) = (((((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) * S ((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) + ((dst_positive_scale_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable))) + (((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)))) * S ((((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) * S ((dst_positive_code_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable)) + ((dst_positive_scale_sum_unique_secondmasktable) + (dst_positive_scale_sum_unique_secondmasktable))) + (((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)))) + ((((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable))) + (((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) * S ((dst_negative_code_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)) + ((dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_scale_sum_unique_secondmasktable)))))) /\ (forall dst_index_sum_unique_secondmasktable. (exists pvs_le_gap_sum_unique_secondmasktabledomain. pvs_le_gap_sum_unique_secondmasktabledomain + (dst_index_sum_unique_secondmasktable) = (n)) -> exists dst_positive_sum_unique_secondmasktable dst_negative_sum_unique_secondmasktable dst_value_sum_unique_secondmasktable. ((((exists ff_h_pvs_sum_unique_secondmasktableentrypositive. ff_h_pvs_sum_unique_secondmasktableentrypositive + S (dst_positive_sum_unique_secondmasktable) = S ((S (dst_index_sum_unique_secondmasktable)) * dst_positive_scale_sum_unique_secondmasktable)) /\ exists ff_q_pvs_sum_unique_secondmasktableentrypositive. dst_positive_code_sum_unique_secondmasktable = ff_q_pvs_sum_unique_secondmasktableentrypositive * S ((S (dst_index_sum_unique_secondmasktable)) * dst_positive_scale_sum_unique_secondmasktable) + (dst_positive_sum_unique_secondmasktable))) /\ (((((exists ff_h_pvs_sum_unique_secondmasktableentrynegative. ff_h_pvs_sum_unique_secondmasktableentrynegative + S (dst_negative_sum_unique_secondmasktable) = S ((S (dst_index_sum_unique_secondmasktable)) * dst_negative_scale_sum_unique_secondmasktable)) /\ exists ff_q_pvs_sum_unique_secondmasktableentrynegative. dst_negative_code_sum_unique_secondmasktable = ff_q_pvs_sum_unique_secondmasktableentrynegative * S ((S (dst_index_sum_unique_secondmasktable)) * dst_negative_scale_sum_unique_secondmasktable) + (dst_negative_sum_unique_secondmasktable))) /\ (exists ge_balance_positive_sum_unique_secondmasktableentryvalue ge_balance_negative_sum_unique_secondmasktableentryvalue. (((((dst_value_sum_unique_secondmasktable) = 2 * (ge_balance_positive_sum_unique_secondmasktableentryvalue) /\ (ge_balance_negative_sum_unique_secondmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmasktableentryvaluedecode. (((dst_value_sum_unique_secondmasktable) = 2 * ge_signed_half_sum_unique_secondmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmasktableentryvalue) = S ge_signed_half_sum_unique_secondmasktableentryvaluedecode))) /\ ((dst_positive_sum_unique_secondmasktable) + ge_balance_negative_sum_unique_secondmasktableentryvalue = (dst_negative_sum_unique_secondmasktable) + ge_balance_positive_sum_unique_secondmasktableentryvalue))))))))) /\ (forall dc_index_sum_unique_secondmask dc_value_sum_unique_secondmask. (exists pvs_le_gap_sum_unique_secondmaskdomain. pvs_le_gap_sum_unique_secondmaskdomain + (dc_index_sum_unique_secondmask) = (n)) -> (exists dst_positive_code_sum_unique_secondmasklookup dst_positive_scale_sum_unique_secondmasklookup dst_negative_code_sum_unique_secondmasklookup dst_negative_scale_sum_unique_secondmasklookup dst_positive_sum_unique_secondmasklookup dst_negative_sum_unique_secondmasklookup. (((dc_mask_sum_unique_second) = (((((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) * S ((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) + ((dst_positive_scale_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup))) + (((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)))) * S ((((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) * S ((dst_positive_code_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup)) + ((dst_positive_scale_sum_unique_secondmasklookup) + (dst_positive_scale_sum_unique_secondmasklookup))) + (((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)))) + ((((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup))) + (((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) * S ((dst_negative_code_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)) + ((dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_scale_sum_unique_secondmasklookup)))))) /\ (((((exists ff_h_pvs_sum_unique_secondmasklookuppositive. ff_h_pvs_sum_unique_secondmasklookuppositive + S (dst_positive_sum_unique_secondmasklookup) = S ((S (dc_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmasklookup)) /\ exists ff_q_pvs_sum_unique_secondmasklookuppositive. dst_positive_code_sum_unique_secondmasklookup = ff_q_pvs_sum_unique_secondmasklookuppositive * S ((S (dc_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmasklookup) + (dst_positive_sum_unique_secondmasklookup))) /\ (((((exists ff_h_pvs_sum_unique_secondmasklookupnegative. ff_h_pvs_sum_unique_secondmasklookupnegative + S (dst_negative_sum_unique_secondmasklookup) = S ((S (dc_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmasklookup)) /\ exists ff_q_pvs_sum_unique_secondmasklookupnegative. dst_negative_code_sum_unique_secondmasklookup = ff_q_pvs_sum_unique_secondmasklookupnegative * S ((S (dc_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmasklookup) + (dst_negative_sum_unique_secondmasklookup))) /\ (exists ge_balance_positive_sum_unique_secondmasklookupvalue ge_balance_negative_sum_unique_secondmasklookupvalue. (((((dc_value_sum_unique_secondmask) = 2 * (ge_balance_positive_sum_unique_secondmasklookupvalue) /\ (ge_balance_negative_sum_unique_secondmasklookupvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmasklookupvaluedecode. (((dc_value_sum_unique_secondmask) = 2 * ge_signed_half_sum_unique_secondmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmasklookupvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmasklookupvalue) = S ge_signed_half_sum_unique_secondmasklookupvaluedecode))) /\ ((dst_positive_sum_unique_secondmasklookup) + ge_balance_negative_sum_unique_secondmasklookupvalue = (dst_negative_sum_unique_secondmasklookup) + ge_balance_positive_sum_unique_secondmasklookupvalue))))))))) -> ((((~((dc_index_sum_unique_secondmask)=0)) /\ (exists dc_quotient_sum_unique_secondmaskentry dc_left_sum_unique_secondmaskentry dc_right_sum_unique_secondmaskentry. (((n)=(dc_index_sum_unique_secondmask)*dc_quotient_sum_unique_secondmaskentry) /\ (((exists dst_positive_code_sum_unique_secondmaskentryleft dst_positive_scale_sum_unique_secondmaskentryleft dst_negative_code_sum_unique_secondmaskentryleft dst_negative_scale_sum_unique_secondmaskentryleft dst_positive_sum_unique_secondmaskentryleft dst_negative_sum_unique_secondmaskentryleft. (((F) = (((((dst_positive_code_sum_unique_secondmaskentryleft) + (dst_positive_scale_sum_unique_secondmaskentryleft)) * S ((dst_positive_code_sum_unique_secondmaskentryleft) + (dst_positive_scale_sum_unique_secondmaskentryleft)) + ((dst_positive_scale_sum_unique_secondmaskentryleft) + (dst_positive_scale_sum_unique_secondmaskentryleft))) + (((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) * S ((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) + ((dst_negative_scale_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)))) * S ((((dst_positive_code_sum_unique_secondmaskentryleft) + (dst_positive_scale_sum_unique_secondmaskentryleft)) * S ((dst_positive_code_sum_unique_secondmaskentryleft) + (dst_positive_scale_sum_unique_secondmaskentryleft)) + ((dst_positive_scale_sum_unique_secondmaskentryleft) + (dst_positive_scale_sum_unique_secondmaskentryleft))) + (((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) * S ((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) + ((dst_negative_scale_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)))) + ((((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) * S ((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) + ((dst_negative_scale_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft))) + (((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) * S ((dst_negative_code_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)) + ((dst_negative_scale_sum_unique_secondmaskentryleft) + (dst_negative_scale_sum_unique_secondmaskentryleft)))))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryleftpositive. ff_h_pvs_sum_unique_secondmaskentryleftpositive + S (dst_positive_sum_unique_secondmaskentryleft) = S ((S (dc_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmaskentryleft)) /\ exists ff_q_pvs_sum_unique_secondmaskentryleftpositive. dst_positive_code_sum_unique_secondmaskentryleft = ff_q_pvs_sum_unique_secondmaskentryleftpositive * S ((S (dc_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmaskentryleft) + (dst_positive_sum_unique_secondmaskentryleft))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryleftnegative. ff_h_pvs_sum_unique_secondmaskentryleftnegative + S (dst_negative_sum_unique_secondmaskentryleft) = S ((S (dc_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmaskentryleft)) /\ exists ff_q_pvs_sum_unique_secondmaskentryleftnegative. dst_negative_code_sum_unique_secondmaskentryleft = ff_q_pvs_sum_unique_secondmaskentryleftnegative * S ((S (dc_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmaskentryleft) + (dst_negative_sum_unique_secondmaskentryleft))) /\ (exists ge_balance_positive_sum_unique_secondmaskentryleftvalue ge_balance_negative_sum_unique_secondmaskentryleftvalue. (((((dc_left_sum_unique_secondmaskentry) = 2 * (ge_balance_positive_sum_unique_secondmaskentryleftvalue) /\ (ge_balance_negative_sum_unique_secondmaskentryleftvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmaskentryleftvaluedecode. (((dc_left_sum_unique_secondmaskentry) = 2 * ge_signed_half_sum_unique_secondmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmaskentryleftvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmaskentryleftvalue) = S ge_signed_half_sum_unique_secondmaskentryleftvaluedecode))) /\ ((dst_positive_sum_unique_secondmaskentryleft) + ge_balance_negative_sum_unique_secondmaskentryleftvalue = (dst_negative_sum_unique_secondmaskentryleft) + ge_balance_positive_sum_unique_secondmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_sum_unique_secondmaskentryright dst_positive_scale_sum_unique_secondmaskentryright dst_negative_code_sum_unique_secondmaskentryright dst_negative_scale_sum_unique_secondmaskentryright dst_positive_sum_unique_secondmaskentryright dst_negative_sum_unique_secondmaskentryright. (((G) = (((((dst_positive_code_sum_unique_secondmaskentryright) + (dst_positive_scale_sum_unique_secondmaskentryright)) * S ((dst_positive_code_sum_unique_secondmaskentryright) + (dst_positive_scale_sum_unique_secondmaskentryright)) + ((dst_positive_scale_sum_unique_secondmaskentryright) + (dst_positive_scale_sum_unique_secondmaskentryright))) + (((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) * S ((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) + ((dst_negative_scale_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)))) * S ((((dst_positive_code_sum_unique_secondmaskentryright) + (dst_positive_scale_sum_unique_secondmaskentryright)) * S ((dst_positive_code_sum_unique_secondmaskentryright) + (dst_positive_scale_sum_unique_secondmaskentryright)) + ((dst_positive_scale_sum_unique_secondmaskentryright) + (dst_positive_scale_sum_unique_secondmaskentryright))) + (((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) * S ((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) + ((dst_negative_scale_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)))) + ((((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) * S ((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) + ((dst_negative_scale_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright))) + (((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) * S ((dst_negative_code_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)) + ((dst_negative_scale_sum_unique_secondmaskentryright) + (dst_negative_scale_sum_unique_secondmaskentryright)))))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryrightpositive. ff_h_pvs_sum_unique_secondmaskentryrightpositive + S (dst_positive_sum_unique_secondmaskentryright) = S ((S (dc_quotient_sum_unique_secondmaskentry)) * dst_positive_scale_sum_unique_secondmaskentryright)) /\ exists ff_q_pvs_sum_unique_secondmaskentryrightpositive. dst_positive_code_sum_unique_secondmaskentryright = ff_q_pvs_sum_unique_secondmaskentryrightpositive * S ((S (dc_quotient_sum_unique_secondmaskentry)) * dst_positive_scale_sum_unique_secondmaskentryright) + (dst_positive_sum_unique_secondmaskentryright))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryrightnegative. ff_h_pvs_sum_unique_secondmaskentryrightnegative + S (dst_negative_sum_unique_secondmaskentryright) = S ((S (dc_quotient_sum_unique_secondmaskentry)) * dst_negative_scale_sum_unique_secondmaskentryright)) /\ exists ff_q_pvs_sum_unique_secondmaskentryrightnegative. dst_negative_code_sum_unique_secondmaskentryright = ff_q_pvs_sum_unique_secondmaskentryrightnegative * S ((S (dc_quotient_sum_unique_secondmaskentry)) * dst_negative_scale_sum_unique_secondmaskentryright) + (dst_negative_sum_unique_secondmaskentryright))) /\ (exists ge_balance_positive_sum_unique_secondmaskentryrightvalue ge_balance_negative_sum_unique_secondmaskentryrightvalue. (((((dc_right_sum_unique_secondmaskentry) = 2 * (ge_balance_positive_sum_unique_secondmaskentryrightvalue) /\ (ge_balance_negative_sum_unique_secondmaskentryrightvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmaskentryrightvaluedecode. (((dc_right_sum_unique_secondmaskentry) = 2 * ge_signed_half_sum_unique_secondmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmaskentryrightvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmaskentryrightvalue) = S ge_signed_half_sum_unique_secondmaskentryrightvaluedecode))) /\ ((dst_positive_sum_unique_secondmaskentryright) + ge_balance_negative_sum_unique_secondmaskentryrightvalue = (dst_negative_sum_unique_secondmaskentryright) + ge_balance_positive_sum_unique_secondmaskentryrightvalue))))))))) /\ (exists sto_ap_sum_unique_secondmaskentryproduct sto_an_sum_unique_secondmaskentryproduct sto_bp_sum_unique_secondmaskentryproduct sto_bn_sum_unique_secondmaskentryproduct sto_cp_sum_unique_secondmaskentryproduct sto_cn_sum_unique_secondmaskentryproduct. (((((dc_left_sum_unique_secondmaskentry) = 2 * (sto_ap_sum_unique_secondmaskentryproduct) /\ (sto_an_sum_unique_secondmaskentryproduct) = 0) \/ exists ge_signed_half_sum_unique_secondmaskentryproductleft. (((dc_left_sum_unique_secondmaskentry) = 2 * ge_signed_half_sum_unique_secondmaskentryproductleft + 1 /\ (sto_ap_sum_unique_secondmaskentryproduct) = 0) /\ (sto_an_sum_unique_secondmaskentryproduct) = S ge_signed_half_sum_unique_secondmaskentryproductleft))) /\ ((((((dc_right_sum_unique_secondmaskentry) = 2 * (sto_bp_sum_unique_secondmaskentryproduct) /\ (sto_bn_sum_unique_secondmaskentryproduct) = 0) \/ exists ge_signed_half_sum_unique_secondmaskentryproductright. (((dc_right_sum_unique_secondmaskentry) = 2 * ge_signed_half_sum_unique_secondmaskentryproductright + 1 /\ (sto_bp_sum_unique_secondmaskentryproduct) = 0) /\ (sto_bn_sum_unique_secondmaskentryproduct) = S ge_signed_half_sum_unique_secondmaskentryproductright))) /\ ((((((dc_value_sum_unique_secondmask) = 2 * (sto_cp_sum_unique_secondmaskentryproduct) /\ (sto_cn_sum_unique_secondmaskentryproduct) = 0) \/ exists ge_signed_half_sum_unique_secondmaskentryproductoutput. (((dc_value_sum_unique_secondmask) = 2 * ge_signed_half_sum_unique_secondmaskentryproductoutput + 1 /\ (sto_cp_sum_unique_secondmaskentryproduct) = 0) /\ (sto_cn_sum_unique_secondmaskentryproduct) = S ge_signed_half_sum_unique_secondmaskentryproductoutput))) /\ ((sto_ap_sum_unique_secondmaskentryproduct * sto_bp_sum_unique_secondmaskentryproduct + sto_an_sum_unique_secondmaskentryproduct * sto_bn_sum_unique_secondmaskentryproduct) + sto_cn_sum_unique_secondmaskentryproduct = (sto_ap_sum_unique_secondmaskentryproduct * sto_bn_sum_unique_secondmaskentryproduct + sto_an_sum_unique_secondmaskentryproduct * sto_bp_sum_unique_secondmaskentryproduct) + sto_cp_sum_unique_secondmaskentryproduct))))))))))))))) \/ ((((dc_index_sum_unique_secondmask)=0 \/ ~(exists pvs_factor_sum_unique_secondmaskentrynondivisor. (n) = (dc_index_sum_unique_secondmask) * pvs_factor_sum_unique_secondmaskentrynondivisor)) /\ ((dc_value_sum_unique_secondmask)=0))))))) /\ (exists dst_positive_code_sum_unique_secondfold dst_positive_scale_sum_unique_secondfold dst_negative_code_sum_unique_secondfold dst_negative_scale_sum_unique_secondfold dst_positive_sum_sum_unique_secondfold dst_negative_sum_sum_unique_secondfold. (((dc_mask_sum_unique_second) = (((((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) * S ((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) + ((dst_positive_scale_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold))) + (((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)))) * S ((((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) * S ((dst_positive_code_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold)) + ((dst_positive_scale_sum_unique_secondfold) + (dst_positive_scale_sum_unique_secondfold))) + (((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)))) + ((((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold))) + (((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) * S ((dst_negative_code_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)) + ((dst_negative_scale_sum_unique_secondfold) + (dst_negative_scale_sum_unique_secondfold)))))) /\ (((exists fs_u_dst_sum_unique_secondfoldpositive fs_v_dst_sum_unique_secondfoldpositive. ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_start. fs_h_dst_sum_unique_secondfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_start. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_terminal. fs_h_dst_sum_unique_secondfoldpositive_body_terminal + S (dst_positive_sum_sum_unique_secondfold) = S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_terminal. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldpositive) + (dst_positive_sum_sum_unique_secondfold))) /\ forall fs_i_dst_sum_unique_secondfoldpositive_body_steps. (exists fs_lt_dst_sum_unique_secondfoldpositive_body_steps_bound. fs_lt_dst_sum_unique_secondfoldpositive_body_steps_bound + S fs_i_dst_sum_unique_secondfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_unique_secondfoldpositive_body_steps fs_r_dst_sum_unique_secondfoldpositive_body_steps fs_s_dst_sum_unique_secondfoldpositive_body_steps. ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_steps_summand. fs_h_dst_sum_unique_secondfoldpositive_body_steps_summand + S (fs_a_dst_sum_unique_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * dst_positive_scale_sum_unique_secondfold)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_steps_summand. dst_positive_code_sum_unique_secondfold = fs_q_dst_sum_unique_secondfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * dst_positive_scale_sum_unique_secondfold) + (fs_a_dst_sum_unique_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_steps_partial. fs_h_dst_sum_unique_secondfoldpositive_body_steps_partial + S (fs_r_dst_sum_unique_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_steps_partial. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive) + (fs_r_dst_sum_unique_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldpositive_body_steps_successor. fs_h_dst_sum_unique_secondfoldpositive_body_steps_successor + S (fs_s_dst_sum_unique_secondfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive)) /\ exists fs_q_dst_sum_unique_secondfoldpositive_body_steps_successor. fs_u_dst_sum_unique_secondfoldpositive = fs_q_dst_sum_unique_secondfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondfoldpositive_body_steps)) * fs_v_dst_sum_unique_secondfoldpositive) + (fs_s_dst_sum_unique_secondfoldpositive_body_steps))) /\ fs_s_dst_sum_unique_secondfoldpositive_body_steps = fs_r_dst_sum_unique_secondfoldpositive_body_steps + fs_a_dst_sum_unique_secondfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_unique_secondfoldnegative fs_v_dst_sum_unique_secondfoldnegative. ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_start. fs_h_dst_sum_unique_secondfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_start. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_unique_secondfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_terminal. fs_h_dst_sum_unique_secondfoldnegative_body_terminal + S (dst_negative_sum_sum_unique_secondfold) = S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_terminal. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_unique_secondfoldnegative) + (dst_negative_sum_sum_unique_secondfold))) /\ forall fs_i_dst_sum_unique_secondfoldnegative_body_steps. (exists fs_lt_dst_sum_unique_secondfoldnegative_body_steps_bound. fs_lt_dst_sum_unique_secondfoldnegative_body_steps_bound + S fs_i_dst_sum_unique_secondfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_unique_secondfoldnegative_body_steps fs_r_dst_sum_unique_secondfoldnegative_body_steps fs_s_dst_sum_unique_secondfoldnegative_body_steps. ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_steps_summand. fs_h_dst_sum_unique_secondfoldnegative_body_steps_summand + S (fs_a_dst_sum_unique_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * dst_negative_scale_sum_unique_secondfold)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_steps_summand. dst_negative_code_sum_unique_secondfold = fs_q_dst_sum_unique_secondfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * dst_negative_scale_sum_unique_secondfold) + (fs_a_dst_sum_unique_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_steps_partial. fs_h_dst_sum_unique_secondfoldnegative_body_steps_partial + S (fs_r_dst_sum_unique_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_steps_partial. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative) + (fs_r_dst_sum_unique_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_unique_secondfoldnegative_body_steps_successor. fs_h_dst_sum_unique_secondfoldnegative_body_steps_successor + S (fs_s_dst_sum_unique_secondfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative)) /\ exists fs_q_dst_sum_unique_secondfoldnegative_body_steps_successor. fs_u_dst_sum_unique_secondfoldnegative = fs_q_dst_sum_unique_secondfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_unique_secondfoldnegative_body_steps)) * fs_v_dst_sum_unique_secondfoldnegative) + (fs_s_dst_sum_unique_secondfoldnegative_body_steps))) /\ fs_s_dst_sum_unique_secondfoldnegative_body_steps = fs_r_dst_sum_unique_secondfoldnegative_body_steps + fs_a_dst_sum_unique_secondfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_unique_secondfoldresult ge_balance_negative_sum_unique_secondfoldresult. (((((b) = 2 * (ge_balance_positive_sum_unique_secondfoldresult) /\ (ge_balance_negative_sum_unique_secondfoldresult) = 0) \/ exists ge_signed_half_sum_unique_secondfoldresultdecode. (((b) = 2 * ge_signed_half_sum_unique_secondfoldresultdecode + 1 /\ (ge_balance_positive_sum_unique_secondfoldresult) = 0) /\ (ge_balance_negative_sum_unique_secondfoldresult) = S ge_signed_half_sum_unique_secondfoldresultdecode))) /\ ((dst_positive_sum_sum_unique_secondfold) + ge_balance_negative_sum_unique_secondfoldresult = (dst_negative_sum_sum_unique_secondfold) + ge_balance_positive_sum_unique_secondfoldresult))))))))))))) -> a=b

dirichlet_convolution_sum_swap · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F G n z. (exists dst_positive_code_swap_left dst_positive_scale_swap_left dst_negative_code_swap_left dst_negative_scale_swap_left. (((F) = (((((dst_positive_code_swap_left) + (dst_positive_scale_swap_left)) * S ((dst_positive_code_swap_left) + (dst_positive_scale_swap_left)) + ((dst_positive_scale_swap_left) + (dst_positive_scale_swap_left))) + (((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) * S ((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) + ((dst_negative_scale_swap_left) + (dst_negative_scale_swap_left)))) * S ((((dst_positive_code_swap_left) + (dst_positive_scale_swap_left)) * S ((dst_positive_code_swap_left) + (dst_positive_scale_swap_left)) + ((dst_positive_scale_swap_left) + (dst_positive_scale_swap_left))) + (((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) * S ((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) + ((dst_negative_scale_swap_left) + (dst_negative_scale_swap_left)))) + ((((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) * S ((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) + ((dst_negative_scale_swap_left) + (dst_negative_scale_swap_left))) + (((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) * S ((dst_negative_code_swap_left) + (dst_negative_scale_swap_left)) + ((dst_negative_scale_swap_left) + (dst_negative_scale_swap_left)))))) /\ (forall dst_index_swap_left. (exists pvs_le_gap_swap_leftdomain. pvs_le_gap_swap_leftdomain + (dst_index_swap_left) = (N)) -> exists dst_positive_swap_left dst_negative_swap_left dst_value_swap_left. ((((exists ff_h_pvs_swap_leftentrypositive. ff_h_pvs_swap_leftentrypositive + S (dst_positive_swap_left) = S ((S (dst_index_swap_left)) * dst_positive_scale_swap_left)) /\ exists ff_q_pvs_swap_leftentrypositive. dst_positive_code_swap_left = ff_q_pvs_swap_leftentrypositive * S ((S (dst_index_swap_left)) * dst_positive_scale_swap_left) + (dst_positive_swap_left))) /\ (((((exists ff_h_pvs_swap_leftentrynegative. ff_h_pvs_swap_leftentrynegative + S (dst_negative_swap_left) = S ((S (dst_index_swap_left)) * dst_negative_scale_swap_left)) /\ exists ff_q_pvs_swap_leftentrynegative. dst_negative_code_swap_left = ff_q_pvs_swap_leftentrynegative * S ((S (dst_index_swap_left)) * dst_negative_scale_swap_left) + (dst_negative_swap_left))) /\ (exists ge_balance_positive_swap_leftentryvalue ge_balance_negative_swap_leftentryvalue. (((((dst_value_swap_left) = 2 * (ge_balance_positive_swap_leftentryvalue) /\ (ge_balance_negative_swap_leftentryvalue) = 0) \/ exists ge_signed_half_swap_leftentryvaluedecode. (((dst_value_swap_left) = 2 * ge_signed_half_swap_leftentryvaluedecode + 1 /\ (ge_balance_positive_swap_leftentryvalue) = 0) /\ (ge_balance_negative_swap_leftentryvalue) = S ge_signed_half_swap_leftentryvaluedecode))) /\ ((dst_positive_swap_left) + ge_balance_negative_swap_leftentryvalue = (dst_negative_swap_left) + ge_balance_positive_swap_leftentryvalue))))))))) -> (exists dst_positive_code_swap_right dst_positive_scale_swap_right dst_negative_code_swap_right dst_negative_scale_swap_right. (((G) = (((((dst_positive_code_swap_right) + (dst_positive_scale_swap_right)) * S ((dst_positive_code_swap_right) + (dst_positive_scale_swap_right)) + ((dst_positive_scale_swap_right) + (dst_positive_scale_swap_right))) + (((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) * S ((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) + ((dst_negative_scale_swap_right) + (dst_negative_scale_swap_right)))) * S ((((dst_positive_code_swap_right) + (dst_positive_scale_swap_right)) * S ((dst_positive_code_swap_right) + (dst_positive_scale_swap_right)) + ((dst_positive_scale_swap_right) + (dst_positive_scale_swap_right))) + (((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) * S ((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) + ((dst_negative_scale_swap_right) + (dst_negative_scale_swap_right)))) + ((((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) * S ((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) + ((dst_negative_scale_swap_right) + (dst_negative_scale_swap_right))) + (((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) * S ((dst_negative_code_swap_right) + (dst_negative_scale_swap_right)) + ((dst_negative_scale_swap_right) + (dst_negative_scale_swap_right)))))) /\ (forall dst_index_swap_right. (exists pvs_le_gap_swap_rightdomain. pvs_le_gap_swap_rightdomain + (dst_index_swap_right) = (N)) -> exists dst_positive_swap_right dst_negative_swap_right dst_value_swap_right. ((((exists ff_h_pvs_swap_rightentrypositive. ff_h_pvs_swap_rightentrypositive + S (dst_positive_swap_right) = S ((S (dst_index_swap_right)) * dst_positive_scale_swap_right)) /\ exists ff_q_pvs_swap_rightentrypositive. dst_positive_code_swap_right = ff_q_pvs_swap_rightentrypositive * S ((S (dst_index_swap_right)) * dst_positive_scale_swap_right) + (dst_positive_swap_right))) /\ (((((exists ff_h_pvs_swap_rightentrynegative. ff_h_pvs_swap_rightentrynegative + S (dst_negative_swap_right) = S ((S (dst_index_swap_right)) * dst_negative_scale_swap_right)) /\ exists ff_q_pvs_swap_rightentrynegative. dst_negative_code_swap_right = ff_q_pvs_swap_rightentrynegative * S ((S (dst_index_swap_right)) * dst_negative_scale_swap_right) + (dst_negative_swap_right))) /\ (exists ge_balance_positive_swap_rightentryvalue ge_balance_negative_swap_rightentryvalue. (((((dst_value_swap_right) = 2 * (ge_balance_positive_swap_rightentryvalue) /\ (ge_balance_negative_swap_rightentryvalue) = 0) \/ exists ge_signed_half_swap_rightentryvaluedecode. (((dst_value_swap_right) = 2 * ge_signed_half_swap_rightentryvaluedecode + 1 /\ (ge_balance_positive_swap_rightentryvalue) = 0) /\ (ge_balance_negative_swap_rightentryvalue) = S ge_signed_half_swap_rightentryvaluedecode))) /\ ((dst_positive_swap_right) + ge_balance_negative_swap_rightentryvalue = (dst_negative_swap_right) + ge_balance_positive_swap_rightentryvalue))))))))) -> (exists pvs_le_gap_swap_bound. pvs_le_gap_swap_bound + (n) = (N)) -> (((~((n)=0)) /\ (exists dc_mask_swap_given. ((((exists dst_positive_code_swap_givenmasktable dst_positive_scale_swap_givenmasktable dst_negative_code_swap_givenmasktable dst_negative_scale_swap_givenmasktable. (((dc_mask_swap_given) = (((((dst_positive_code_swap_givenmasktable) + (dst_positive_scale_swap_givenmasktable)) * S ((dst_positive_code_swap_givenmasktable) + (dst_positive_scale_swap_givenmasktable)) + ((dst_positive_scale_swap_givenmasktable) + (dst_positive_scale_swap_givenmasktable))) + (((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) * S ((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) + ((dst_negative_scale_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)))) * S ((((dst_positive_code_swap_givenmasktable) + (dst_positive_scale_swap_givenmasktable)) * S ((dst_positive_code_swap_givenmasktable) + (dst_positive_scale_swap_givenmasktable)) + ((dst_positive_scale_swap_givenmasktable) + (dst_positive_scale_swap_givenmasktable))) + (((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) * S ((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) + ((dst_negative_scale_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)))) + ((((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) * S ((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) + ((dst_negative_scale_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable))) + (((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) * S ((dst_negative_code_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)) + ((dst_negative_scale_swap_givenmasktable) + (dst_negative_scale_swap_givenmasktable)))))) /\ (forall dst_index_swap_givenmasktable. (exists pvs_le_gap_swap_givenmasktabledomain. pvs_le_gap_swap_givenmasktabledomain + (dst_index_swap_givenmasktable) = (n)) -> exists dst_positive_swap_givenmasktable dst_negative_swap_givenmasktable dst_value_swap_givenmasktable. ((((exists ff_h_pvs_swap_givenmasktableentrypositive. ff_h_pvs_swap_givenmasktableentrypositive + S (dst_positive_swap_givenmasktable) = S ((S (dst_index_swap_givenmasktable)) * dst_positive_scale_swap_givenmasktable)) /\ exists ff_q_pvs_swap_givenmasktableentrypositive. dst_positive_code_swap_givenmasktable = ff_q_pvs_swap_givenmasktableentrypositive * S ((S (dst_index_swap_givenmasktable)) * dst_positive_scale_swap_givenmasktable) + (dst_positive_swap_givenmasktable))) /\ (((((exists ff_h_pvs_swap_givenmasktableentrynegative. ff_h_pvs_swap_givenmasktableentrynegative + S (dst_negative_swap_givenmasktable) = S ((S (dst_index_swap_givenmasktable)) * dst_negative_scale_swap_givenmasktable)) /\ exists ff_q_pvs_swap_givenmasktableentrynegative. dst_negative_code_swap_givenmasktable = ff_q_pvs_swap_givenmasktableentrynegative * S ((S (dst_index_swap_givenmasktable)) * dst_negative_scale_swap_givenmasktable) + (dst_negative_swap_givenmasktable))) /\ (exists ge_balance_positive_swap_givenmasktableentryvalue ge_balance_negative_swap_givenmasktableentryvalue. (((((dst_value_swap_givenmasktable) = 2 * (ge_balance_positive_swap_givenmasktableentryvalue) /\ (ge_balance_negative_swap_givenmasktableentryvalue) = 0) \/ exists ge_signed_half_swap_givenmasktableentryvaluedecode. (((dst_value_swap_givenmasktable) = 2 * ge_signed_half_swap_givenmasktableentryvaluedecode + 1 /\ (ge_balance_positive_swap_givenmasktableentryvalue) = 0) /\ (ge_balance_negative_swap_givenmasktableentryvalue) = S ge_signed_half_swap_givenmasktableentryvaluedecode))) /\ ((dst_positive_swap_givenmasktable) + ge_balance_negative_swap_givenmasktableentryvalue = (dst_negative_swap_givenmasktable) + ge_balance_positive_swap_givenmasktableentryvalue))))))))) /\ (forall dc_index_swap_givenmask dc_value_swap_givenmask. (exists pvs_le_gap_swap_givenmaskdomain. pvs_le_gap_swap_givenmaskdomain + (dc_index_swap_givenmask) = (n)) -> (exists dst_positive_code_swap_givenmasklookup dst_positive_scale_swap_givenmasklookup dst_negative_code_swap_givenmasklookup dst_negative_scale_swap_givenmasklookup dst_positive_swap_givenmasklookup dst_negative_swap_givenmasklookup. (((dc_mask_swap_given) = (((((dst_positive_code_swap_givenmasklookup) + (dst_positive_scale_swap_givenmasklookup)) * S ((dst_positive_code_swap_givenmasklookup) + (dst_positive_scale_swap_givenmasklookup)) + ((dst_positive_scale_swap_givenmasklookup) + (dst_positive_scale_swap_givenmasklookup))) + (((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) * S ((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) + ((dst_negative_scale_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)))) * S ((((dst_positive_code_swap_givenmasklookup) + (dst_positive_scale_swap_givenmasklookup)) * S ((dst_positive_code_swap_givenmasklookup) + (dst_positive_scale_swap_givenmasklookup)) + ((dst_positive_scale_swap_givenmasklookup) + (dst_positive_scale_swap_givenmasklookup))) + (((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) * S ((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) + ((dst_negative_scale_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)))) + ((((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) * S ((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) + ((dst_negative_scale_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup))) + (((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) * S ((dst_negative_code_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)) + ((dst_negative_scale_swap_givenmasklookup) + (dst_negative_scale_swap_givenmasklookup)))))) /\ (((((exists ff_h_pvs_swap_givenmasklookuppositive. ff_h_pvs_swap_givenmasklookuppositive + S (dst_positive_swap_givenmasklookup) = S ((S (dc_index_swap_givenmask)) * dst_positive_scale_swap_givenmasklookup)) /\ exists ff_q_pvs_swap_givenmasklookuppositive. dst_positive_code_swap_givenmasklookup = ff_q_pvs_swap_givenmasklookuppositive * S ((S (dc_index_swap_givenmask)) * dst_positive_scale_swap_givenmasklookup) + (dst_positive_swap_givenmasklookup))) /\ (((((exists ff_h_pvs_swap_givenmasklookupnegative. ff_h_pvs_swap_givenmasklookupnegative + S (dst_negative_swap_givenmasklookup) = S ((S (dc_index_swap_givenmask)) * dst_negative_scale_swap_givenmasklookup)) /\ exists ff_q_pvs_swap_givenmasklookupnegative. dst_negative_code_swap_givenmasklookup = ff_q_pvs_swap_givenmasklookupnegative * S ((S (dc_index_swap_givenmask)) * dst_negative_scale_swap_givenmasklookup) + (dst_negative_swap_givenmasklookup))) /\ (exists ge_balance_positive_swap_givenmasklookupvalue ge_balance_negative_swap_givenmasklookupvalue. (((((dc_value_swap_givenmask) = 2 * (ge_balance_positive_swap_givenmasklookupvalue) /\ (ge_balance_negative_swap_givenmasklookupvalue) = 0) \/ exists ge_signed_half_swap_givenmasklookupvaluedecode. (((dc_value_swap_givenmask) = 2 * ge_signed_half_swap_givenmasklookupvaluedecode + 1 /\ (ge_balance_positive_swap_givenmasklookupvalue) = 0) /\ (ge_balance_negative_swap_givenmasklookupvalue) = S ge_signed_half_swap_givenmasklookupvaluedecode))) /\ ((dst_positive_swap_givenmasklookup) + ge_balance_negative_swap_givenmasklookupvalue = (dst_negative_swap_givenmasklookup) + ge_balance_positive_swap_givenmasklookupvalue))))))))) -> ((((~((dc_index_swap_givenmask)=0)) /\ (exists dc_quotient_swap_givenmaskentry dc_left_swap_givenmaskentry dc_right_swap_givenmaskentry. (((n)=(dc_index_swap_givenmask)*dc_quotient_swap_givenmaskentry) /\ (((exists dst_positive_code_swap_givenmaskentryleft dst_positive_scale_swap_givenmaskentryleft dst_negative_code_swap_givenmaskentryleft dst_negative_scale_swap_givenmaskentryleft dst_positive_swap_givenmaskentryleft dst_negative_swap_givenmaskentryleft. (((F) = (((((dst_positive_code_swap_givenmaskentryleft) + (dst_positive_scale_swap_givenmaskentryleft)) * S ((dst_positive_code_swap_givenmaskentryleft) + (dst_positive_scale_swap_givenmaskentryleft)) + ((dst_positive_scale_swap_givenmaskentryleft) + (dst_positive_scale_swap_givenmaskentryleft))) + (((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) * S ((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) + ((dst_negative_scale_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)))) * S ((((dst_positive_code_swap_givenmaskentryleft) + (dst_positive_scale_swap_givenmaskentryleft)) * S ((dst_positive_code_swap_givenmaskentryleft) + (dst_positive_scale_swap_givenmaskentryleft)) + ((dst_positive_scale_swap_givenmaskentryleft) + (dst_positive_scale_swap_givenmaskentryleft))) + (((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) * S ((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) + ((dst_negative_scale_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)))) + ((((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) * S ((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) + ((dst_negative_scale_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft))) + (((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) * S ((dst_negative_code_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)) + ((dst_negative_scale_swap_givenmaskentryleft) + (dst_negative_scale_swap_givenmaskentryleft)))))) /\ (((((exists ff_h_pvs_swap_givenmaskentryleftpositive. ff_h_pvs_swap_givenmaskentryleftpositive + S (dst_positive_swap_givenmaskentryleft) = S ((S (dc_index_swap_givenmask)) * dst_positive_scale_swap_givenmaskentryleft)) /\ exists ff_q_pvs_swap_givenmaskentryleftpositive. dst_positive_code_swap_givenmaskentryleft = ff_q_pvs_swap_givenmaskentryleftpositive * S ((S (dc_index_swap_givenmask)) * dst_positive_scale_swap_givenmaskentryleft) + (dst_positive_swap_givenmaskentryleft))) /\ (((((exists ff_h_pvs_swap_givenmaskentryleftnegative. ff_h_pvs_swap_givenmaskentryleftnegative + S (dst_negative_swap_givenmaskentryleft) = S ((S (dc_index_swap_givenmask)) * dst_negative_scale_swap_givenmaskentryleft)) /\ exists ff_q_pvs_swap_givenmaskentryleftnegative. dst_negative_code_swap_givenmaskentryleft = ff_q_pvs_swap_givenmaskentryleftnegative * S ((S (dc_index_swap_givenmask)) * dst_negative_scale_swap_givenmaskentryleft) + (dst_negative_swap_givenmaskentryleft))) /\ (exists ge_balance_positive_swap_givenmaskentryleftvalue ge_balance_negative_swap_givenmaskentryleftvalue. (((((dc_left_swap_givenmaskentry) = 2 * (ge_balance_positive_swap_givenmaskentryleftvalue) /\ (ge_balance_negative_swap_givenmaskentryleftvalue) = 0) \/ exists ge_signed_half_swap_givenmaskentryleftvaluedecode. (((dc_left_swap_givenmaskentry) = 2 * ge_signed_half_swap_givenmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_swap_givenmaskentryleftvalue) = 0) /\ (ge_balance_negative_swap_givenmaskentryleftvalue) = S ge_signed_half_swap_givenmaskentryleftvaluedecode))) /\ ((dst_positive_swap_givenmaskentryleft) + ge_balance_negative_swap_givenmaskentryleftvalue = (dst_negative_swap_givenmaskentryleft) + ge_balance_positive_swap_givenmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_swap_givenmaskentryright dst_positive_scale_swap_givenmaskentryright dst_negative_code_swap_givenmaskentryright dst_negative_scale_swap_givenmaskentryright dst_positive_swap_givenmaskentryright dst_negative_swap_givenmaskentryright. (((G) = (((((dst_positive_code_swap_givenmaskentryright) + (dst_positive_scale_swap_givenmaskentryright)) * S ((dst_positive_code_swap_givenmaskentryright) + (dst_positive_scale_swap_givenmaskentryright)) + ((dst_positive_scale_swap_givenmaskentryright) + (dst_positive_scale_swap_givenmaskentryright))) + (((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) * S ((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) + ((dst_negative_scale_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)))) * S ((((dst_positive_code_swap_givenmaskentryright) + (dst_positive_scale_swap_givenmaskentryright)) * S ((dst_positive_code_swap_givenmaskentryright) + (dst_positive_scale_swap_givenmaskentryright)) + ((dst_positive_scale_swap_givenmaskentryright) + (dst_positive_scale_swap_givenmaskentryright))) + (((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) * S ((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) + ((dst_negative_scale_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)))) + ((((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) * S ((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) + ((dst_negative_scale_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright))) + (((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) * S ((dst_negative_code_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)) + ((dst_negative_scale_swap_givenmaskentryright) + (dst_negative_scale_swap_givenmaskentryright)))))) /\ (((((exists ff_h_pvs_swap_givenmaskentryrightpositive. ff_h_pvs_swap_givenmaskentryrightpositive + S (dst_positive_swap_givenmaskentryright) = S ((S (dc_quotient_swap_givenmaskentry)) * dst_positive_scale_swap_givenmaskentryright)) /\ exists ff_q_pvs_swap_givenmaskentryrightpositive. dst_positive_code_swap_givenmaskentryright = ff_q_pvs_swap_givenmaskentryrightpositive * S ((S (dc_quotient_swap_givenmaskentry)) * dst_positive_scale_swap_givenmaskentryright) + (dst_positive_swap_givenmaskentryright))) /\ (((((exists ff_h_pvs_swap_givenmaskentryrightnegative. ff_h_pvs_swap_givenmaskentryrightnegative + S (dst_negative_swap_givenmaskentryright) = S ((S (dc_quotient_swap_givenmaskentry)) * dst_negative_scale_swap_givenmaskentryright)) /\ exists ff_q_pvs_swap_givenmaskentryrightnegative. dst_negative_code_swap_givenmaskentryright = ff_q_pvs_swap_givenmaskentryrightnegative * S ((S (dc_quotient_swap_givenmaskentry)) * dst_negative_scale_swap_givenmaskentryright) + (dst_negative_swap_givenmaskentryright))) /\ (exists ge_balance_positive_swap_givenmaskentryrightvalue ge_balance_negative_swap_givenmaskentryrightvalue. (((((dc_right_swap_givenmaskentry) = 2 * (ge_balance_positive_swap_givenmaskentryrightvalue) /\ (ge_balance_negative_swap_givenmaskentryrightvalue) = 0) \/ exists ge_signed_half_swap_givenmaskentryrightvaluedecode. (((dc_right_swap_givenmaskentry) = 2 * ge_signed_half_swap_givenmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_swap_givenmaskentryrightvalue) = 0) /\ (ge_balance_negative_swap_givenmaskentryrightvalue) = S ge_signed_half_swap_givenmaskentryrightvaluedecode))) /\ ((dst_positive_swap_givenmaskentryright) + ge_balance_negative_swap_givenmaskentryrightvalue = (dst_negative_swap_givenmaskentryright) + ge_balance_positive_swap_givenmaskentryrightvalue))))))))) /\ (exists sto_ap_swap_givenmaskentryproduct sto_an_swap_givenmaskentryproduct sto_bp_swap_givenmaskentryproduct sto_bn_swap_givenmaskentryproduct sto_cp_swap_givenmaskentryproduct sto_cn_swap_givenmaskentryproduct. (((((dc_left_swap_givenmaskentry) = 2 * (sto_ap_swap_givenmaskentryproduct) /\ (sto_an_swap_givenmaskentryproduct) = 0) \/ exists ge_signed_half_swap_givenmaskentryproductleft. (((dc_left_swap_givenmaskentry) = 2 * ge_signed_half_swap_givenmaskentryproductleft + 1 /\ (sto_ap_swap_givenmaskentryproduct) = 0) /\ (sto_an_swap_givenmaskentryproduct) = S ge_signed_half_swap_givenmaskentryproductleft))) /\ ((((((dc_right_swap_givenmaskentry) = 2 * (sto_bp_swap_givenmaskentryproduct) /\ (sto_bn_swap_givenmaskentryproduct) = 0) \/ exists ge_signed_half_swap_givenmaskentryproductright. (((dc_right_swap_givenmaskentry) = 2 * ge_signed_half_swap_givenmaskentryproductright + 1 /\ (sto_bp_swap_givenmaskentryproduct) = 0) /\ (sto_bn_swap_givenmaskentryproduct) = S ge_signed_half_swap_givenmaskentryproductright))) /\ ((((((dc_value_swap_givenmask) = 2 * (sto_cp_swap_givenmaskentryproduct) /\ (sto_cn_swap_givenmaskentryproduct) = 0) \/ exists ge_signed_half_swap_givenmaskentryproductoutput. (((dc_value_swap_givenmask) = 2 * ge_signed_half_swap_givenmaskentryproductoutput + 1 /\ (sto_cp_swap_givenmaskentryproduct) = 0) /\ (sto_cn_swap_givenmaskentryproduct) = S ge_signed_half_swap_givenmaskentryproductoutput))) /\ ((sto_ap_swap_givenmaskentryproduct * sto_bp_swap_givenmaskentryproduct + sto_an_swap_givenmaskentryproduct * sto_bn_swap_givenmaskentryproduct) + sto_cn_swap_givenmaskentryproduct = (sto_ap_swap_givenmaskentryproduct * sto_bn_swap_givenmaskentryproduct + sto_an_swap_givenmaskentryproduct * sto_bp_swap_givenmaskentryproduct) + sto_cp_swap_givenmaskentryproduct))))))))))))))) \/ ((((dc_index_swap_givenmask)=0 \/ ~(exists pvs_factor_swap_givenmaskentrynondivisor. (n) = (dc_index_swap_givenmask) * pvs_factor_swap_givenmaskentrynondivisor)) /\ ((dc_value_swap_givenmask)=0))))))) /\ (exists dst_positive_code_swap_givenfold dst_positive_scale_swap_givenfold dst_negative_code_swap_givenfold dst_negative_scale_swap_givenfold dst_positive_sum_swap_givenfold dst_negative_sum_swap_givenfold. (((dc_mask_swap_given) = (((((dst_positive_code_swap_givenfold) + (dst_positive_scale_swap_givenfold)) * S ((dst_positive_code_swap_givenfold) + (dst_positive_scale_swap_givenfold)) + ((dst_positive_scale_swap_givenfold) + (dst_positive_scale_swap_givenfold))) + (((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) * S ((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) + ((dst_negative_scale_swap_givenfold) + (dst_negative_scale_swap_givenfold)))) * S ((((dst_positive_code_swap_givenfold) + (dst_positive_scale_swap_givenfold)) * S ((dst_positive_code_swap_givenfold) + (dst_positive_scale_swap_givenfold)) + ((dst_positive_scale_swap_givenfold) + (dst_positive_scale_swap_givenfold))) + (((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) * S ((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) + ((dst_negative_scale_swap_givenfold) + (dst_negative_scale_swap_givenfold)))) + ((((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) * S ((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) + ((dst_negative_scale_swap_givenfold) + (dst_negative_scale_swap_givenfold))) + (((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) * S ((dst_negative_code_swap_givenfold) + (dst_negative_scale_swap_givenfold)) + ((dst_negative_scale_swap_givenfold) + (dst_negative_scale_swap_givenfold)))))) /\ (((exists fs_u_dst_swap_givenfoldpositive fs_v_dst_swap_givenfoldpositive. ((((exists fs_h_dst_swap_givenfoldpositive_body_start. fs_h_dst_swap_givenfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_swap_givenfoldpositive)) /\ exists fs_q_dst_swap_givenfoldpositive_body_start. fs_u_dst_swap_givenfoldpositive = fs_q_dst_swap_givenfoldpositive_body_start * S ((S (0)) * fs_v_dst_swap_givenfoldpositive) + (0))) /\ ((((exists fs_h_dst_swap_givenfoldpositive_body_terminal. fs_h_dst_swap_givenfoldpositive_body_terminal + S (dst_positive_sum_swap_givenfold) = S ((S (S (n))) * fs_v_dst_swap_givenfoldpositive)) /\ exists fs_q_dst_swap_givenfoldpositive_body_terminal. fs_u_dst_swap_givenfoldpositive = fs_q_dst_swap_givenfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_swap_givenfoldpositive) + (dst_positive_sum_swap_givenfold))) /\ forall fs_i_dst_swap_givenfoldpositive_body_steps. (exists fs_lt_dst_swap_givenfoldpositive_body_steps_bound. fs_lt_dst_swap_givenfoldpositive_body_steps_bound + S fs_i_dst_swap_givenfoldpositive_body_steps = S (n)) -> exists fs_a_dst_swap_givenfoldpositive_body_steps fs_r_dst_swap_givenfoldpositive_body_steps fs_s_dst_swap_givenfoldpositive_body_steps. ((((exists fs_h_dst_swap_givenfoldpositive_body_steps_summand. fs_h_dst_swap_givenfoldpositive_body_steps_summand + S (fs_a_dst_swap_givenfoldpositive_body_steps) = S ((S (fs_i_dst_swap_givenfoldpositive_body_steps)) * dst_positive_scale_swap_givenfold)) /\ exists fs_q_dst_swap_givenfoldpositive_body_steps_summand. dst_positive_code_swap_givenfold = fs_q_dst_swap_givenfoldpositive_body_steps_summand * S ((S (fs_i_dst_swap_givenfoldpositive_body_steps)) * dst_positive_scale_swap_givenfold) + (fs_a_dst_swap_givenfoldpositive_body_steps))) /\ ((((exists fs_h_dst_swap_givenfoldpositive_body_steps_partial. fs_h_dst_swap_givenfoldpositive_body_steps_partial + S (fs_r_dst_swap_givenfoldpositive_body_steps) = S ((S (fs_i_dst_swap_givenfoldpositive_body_steps)) * fs_v_dst_swap_givenfoldpositive)) /\ exists fs_q_dst_swap_givenfoldpositive_body_steps_partial. fs_u_dst_swap_givenfoldpositive = fs_q_dst_swap_givenfoldpositive_body_steps_partial * S ((S (fs_i_dst_swap_givenfoldpositive_body_steps)) * fs_v_dst_swap_givenfoldpositive) + (fs_r_dst_swap_givenfoldpositive_body_steps))) /\ ((((exists fs_h_dst_swap_givenfoldpositive_body_steps_successor. fs_h_dst_swap_givenfoldpositive_body_steps_successor + S (fs_s_dst_swap_givenfoldpositive_body_steps) = S ((S (S fs_i_dst_swap_givenfoldpositive_body_steps)) * fs_v_dst_swap_givenfoldpositive)) /\ exists fs_q_dst_swap_givenfoldpositive_body_steps_successor. fs_u_dst_swap_givenfoldpositive = fs_q_dst_swap_givenfoldpositive_body_steps_successor * S ((S (S fs_i_dst_swap_givenfoldpositive_body_steps)) * fs_v_dst_swap_givenfoldpositive) + (fs_s_dst_swap_givenfoldpositive_body_steps))) /\ fs_s_dst_swap_givenfoldpositive_body_steps = fs_r_dst_swap_givenfoldpositive_body_steps + fs_a_dst_swap_givenfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_swap_givenfoldnegative fs_v_dst_swap_givenfoldnegative. ((((exists fs_h_dst_swap_givenfoldnegative_body_start. fs_h_dst_swap_givenfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_swap_givenfoldnegative)) /\ exists fs_q_dst_swap_givenfoldnegative_body_start. fs_u_dst_swap_givenfoldnegative = fs_q_dst_swap_givenfoldnegative_body_start * S ((S (0)) * fs_v_dst_swap_givenfoldnegative) + (0))) /\ ((((exists fs_h_dst_swap_givenfoldnegative_body_terminal. fs_h_dst_swap_givenfoldnegative_body_terminal + S (dst_negative_sum_swap_givenfold) = S ((S (S (n))) * fs_v_dst_swap_givenfoldnegative)) /\ exists fs_q_dst_swap_givenfoldnegative_body_terminal. fs_u_dst_swap_givenfoldnegative = fs_q_dst_swap_givenfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_swap_givenfoldnegative) + (dst_negative_sum_swap_givenfold))) /\ forall fs_i_dst_swap_givenfoldnegative_body_steps. (exists fs_lt_dst_swap_givenfoldnegative_body_steps_bound. fs_lt_dst_swap_givenfoldnegative_body_steps_bound + S fs_i_dst_swap_givenfoldnegative_body_steps = S (n)) -> exists fs_a_dst_swap_givenfoldnegative_body_steps fs_r_dst_swap_givenfoldnegative_body_steps fs_s_dst_swap_givenfoldnegative_body_steps. ((((exists fs_h_dst_swap_givenfoldnegative_body_steps_summand. fs_h_dst_swap_givenfoldnegative_body_steps_summand + S (fs_a_dst_swap_givenfoldnegative_body_steps) = S ((S (fs_i_dst_swap_givenfoldnegative_body_steps)) * dst_negative_scale_swap_givenfold)) /\ exists fs_q_dst_swap_givenfoldnegative_body_steps_summand. dst_negative_code_swap_givenfold = fs_q_dst_swap_givenfoldnegative_body_steps_summand * S ((S (fs_i_dst_swap_givenfoldnegative_body_steps)) * dst_negative_scale_swap_givenfold) + (fs_a_dst_swap_givenfoldnegative_body_steps))) /\ ((((exists fs_h_dst_swap_givenfoldnegative_body_steps_partial. fs_h_dst_swap_givenfoldnegative_body_steps_partial + S (fs_r_dst_swap_givenfoldnegative_body_steps) = S ((S (fs_i_dst_swap_givenfoldnegative_body_steps)) * fs_v_dst_swap_givenfoldnegative)) /\ exists fs_q_dst_swap_givenfoldnegative_body_steps_partial. fs_u_dst_swap_givenfoldnegative = fs_q_dst_swap_givenfoldnegative_body_steps_partial * S ((S (fs_i_dst_swap_givenfoldnegative_body_steps)) * fs_v_dst_swap_givenfoldnegative) + (fs_r_dst_swap_givenfoldnegative_body_steps))) /\ ((((exists fs_h_dst_swap_givenfoldnegative_body_steps_successor. fs_h_dst_swap_givenfoldnegative_body_steps_successor + S (fs_s_dst_swap_givenfoldnegative_body_steps) = S ((S (S fs_i_dst_swap_givenfoldnegative_body_steps)) * fs_v_dst_swap_givenfoldnegative)) /\ exists fs_q_dst_swap_givenfoldnegative_body_steps_successor. fs_u_dst_swap_givenfoldnegative = fs_q_dst_swap_givenfoldnegative_body_steps_successor * S ((S (S fs_i_dst_swap_givenfoldnegative_body_steps)) * fs_v_dst_swap_givenfoldnegative) + (fs_s_dst_swap_givenfoldnegative_body_steps))) /\ fs_s_dst_swap_givenfoldnegative_body_steps = fs_r_dst_swap_givenfoldnegative_body_steps + fs_a_dst_swap_givenfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_swap_givenfoldresult ge_balance_negative_swap_givenfoldresult. (((((z) = 2 * (ge_balance_positive_swap_givenfoldresult) /\ (ge_balance_negative_swap_givenfoldresult) = 0) \/ exists ge_signed_half_swap_givenfoldresultdecode. (((z) = 2 * ge_signed_half_swap_givenfoldresultdecode + 1 /\ (ge_balance_positive_swap_givenfoldresult) = 0) /\ (ge_balance_negative_swap_givenfoldresult) = S ge_signed_half_swap_givenfoldresultdecode))) /\ ((dst_positive_sum_swap_givenfold) + ge_balance_negative_swap_givenfoldresult = (dst_negative_sum_swap_givenfold) + ge_balance_positive_swap_givenfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dc_mask_swap_result. ((((exists dst_positive_code_swap_resultmasktable dst_positive_scale_swap_resultmasktable dst_negative_code_swap_resultmasktable dst_negative_scale_swap_resultmasktable. (((dc_mask_swap_result) = (((((dst_positive_code_swap_resultmasktable) + (dst_positive_scale_swap_resultmasktable)) * S ((dst_positive_code_swap_resultmasktable) + (dst_positive_scale_swap_resultmasktable)) + ((dst_positive_scale_swap_resultmasktable) + (dst_positive_scale_swap_resultmasktable))) + (((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) * S ((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) + ((dst_negative_scale_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)))) * S ((((dst_positive_code_swap_resultmasktable) + (dst_positive_scale_swap_resultmasktable)) * S ((dst_positive_code_swap_resultmasktable) + (dst_positive_scale_swap_resultmasktable)) + ((dst_positive_scale_swap_resultmasktable) + (dst_positive_scale_swap_resultmasktable))) + (((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) * S ((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) + ((dst_negative_scale_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)))) + ((((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) * S ((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) + ((dst_negative_scale_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable))) + (((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) * S ((dst_negative_code_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)) + ((dst_negative_scale_swap_resultmasktable) + (dst_negative_scale_swap_resultmasktable)))))) /\ (forall dst_index_swap_resultmasktable. (exists pvs_le_gap_swap_resultmasktabledomain. pvs_le_gap_swap_resultmasktabledomain + (dst_index_swap_resultmasktable) = (n)) -> exists dst_positive_swap_resultmasktable dst_negative_swap_resultmasktable dst_value_swap_resultmasktable. ((((exists ff_h_pvs_swap_resultmasktableentrypositive. ff_h_pvs_swap_resultmasktableentrypositive + S (dst_positive_swap_resultmasktable) = S ((S (dst_index_swap_resultmasktable)) * dst_positive_scale_swap_resultmasktable)) /\ exists ff_q_pvs_swap_resultmasktableentrypositive. dst_positive_code_swap_resultmasktable = ff_q_pvs_swap_resultmasktableentrypositive * S ((S (dst_index_swap_resultmasktable)) * dst_positive_scale_swap_resultmasktable) + (dst_positive_swap_resultmasktable))) /\ (((((exists ff_h_pvs_swap_resultmasktableentrynegative. ff_h_pvs_swap_resultmasktableentrynegative + S (dst_negative_swap_resultmasktable) = S ((S (dst_index_swap_resultmasktable)) * dst_negative_scale_swap_resultmasktable)) /\ exists ff_q_pvs_swap_resultmasktableentrynegative. dst_negative_code_swap_resultmasktable = ff_q_pvs_swap_resultmasktableentrynegative * S ((S (dst_index_swap_resultmasktable)) * dst_negative_scale_swap_resultmasktable) + (dst_negative_swap_resultmasktable))) /\ (exists ge_balance_positive_swap_resultmasktableentryvalue ge_balance_negative_swap_resultmasktableentryvalue. (((((dst_value_swap_resultmasktable) = 2 * (ge_balance_positive_swap_resultmasktableentryvalue) /\ (ge_balance_negative_swap_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_swap_resultmasktableentryvaluedecode. (((dst_value_swap_resultmasktable) = 2 * ge_signed_half_swap_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_swap_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_swap_resultmasktableentryvalue) = S ge_signed_half_swap_resultmasktableentryvaluedecode))) /\ ((dst_positive_swap_resultmasktable) + ge_balance_negative_swap_resultmasktableentryvalue = (dst_negative_swap_resultmasktable) + ge_balance_positive_swap_resultmasktableentryvalue))))))))) /\ (forall dc_index_swap_resultmask dc_value_swap_resultmask. (exists pvs_le_gap_swap_resultmaskdomain. pvs_le_gap_swap_resultmaskdomain + (dc_index_swap_resultmask) = (n)) -> (exists dst_positive_code_swap_resultmasklookup dst_positive_scale_swap_resultmasklookup dst_negative_code_swap_resultmasklookup dst_negative_scale_swap_resultmasklookup dst_positive_swap_resultmasklookup dst_negative_swap_resultmasklookup. (((dc_mask_swap_result) = (((((dst_positive_code_swap_resultmasklookup) + (dst_positive_scale_swap_resultmasklookup)) * S ((dst_positive_code_swap_resultmasklookup) + (dst_positive_scale_swap_resultmasklookup)) + ((dst_positive_scale_swap_resultmasklookup) + (dst_positive_scale_swap_resultmasklookup))) + (((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) * S ((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) + ((dst_negative_scale_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)))) * S ((((dst_positive_code_swap_resultmasklookup) + (dst_positive_scale_swap_resultmasklookup)) * S ((dst_positive_code_swap_resultmasklookup) + (dst_positive_scale_swap_resultmasklookup)) + ((dst_positive_scale_swap_resultmasklookup) + (dst_positive_scale_swap_resultmasklookup))) + (((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) * S ((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) + ((dst_negative_scale_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)))) + ((((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) * S ((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) + ((dst_negative_scale_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup))) + (((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) * S ((dst_negative_code_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)) + ((dst_negative_scale_swap_resultmasklookup) + (dst_negative_scale_swap_resultmasklookup)))))) /\ (((((exists ff_h_pvs_swap_resultmasklookuppositive. ff_h_pvs_swap_resultmasklookuppositive + S (dst_positive_swap_resultmasklookup) = S ((S (dc_index_swap_resultmask)) * dst_positive_scale_swap_resultmasklookup)) /\ exists ff_q_pvs_swap_resultmasklookuppositive. dst_positive_code_swap_resultmasklookup = ff_q_pvs_swap_resultmasklookuppositive * S ((S (dc_index_swap_resultmask)) * dst_positive_scale_swap_resultmasklookup) + (dst_positive_swap_resultmasklookup))) /\ (((((exists ff_h_pvs_swap_resultmasklookupnegative. ff_h_pvs_swap_resultmasklookupnegative + S (dst_negative_swap_resultmasklookup) = S ((S (dc_index_swap_resultmask)) * dst_negative_scale_swap_resultmasklookup)) /\ exists ff_q_pvs_swap_resultmasklookupnegative. dst_negative_code_swap_resultmasklookup = ff_q_pvs_swap_resultmasklookupnegative * S ((S (dc_index_swap_resultmask)) * dst_negative_scale_swap_resultmasklookup) + (dst_negative_swap_resultmasklookup))) /\ (exists ge_balance_positive_swap_resultmasklookupvalue ge_balance_negative_swap_resultmasklookupvalue. (((((dc_value_swap_resultmask) = 2 * (ge_balance_positive_swap_resultmasklookupvalue) /\ (ge_balance_negative_swap_resultmasklookupvalue) = 0) \/ exists ge_signed_half_swap_resultmasklookupvaluedecode. (((dc_value_swap_resultmask) = 2 * ge_signed_half_swap_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_swap_resultmasklookupvalue) = 0) /\ (ge_balance_negative_swap_resultmasklookupvalue) = S ge_signed_half_swap_resultmasklookupvaluedecode))) /\ ((dst_positive_swap_resultmasklookup) + ge_balance_negative_swap_resultmasklookupvalue = (dst_negative_swap_resultmasklookup) + ge_balance_positive_swap_resultmasklookupvalue))))))))) -> ((((~((dc_index_swap_resultmask)=0)) /\ (exists dc_quotient_swap_resultmaskentry dc_left_swap_resultmaskentry dc_right_swap_resultmaskentry. (((n)=(dc_index_swap_resultmask)*dc_quotient_swap_resultmaskentry) /\ (((exists dst_positive_code_swap_resultmaskentryleft dst_positive_scale_swap_resultmaskentryleft dst_negative_code_swap_resultmaskentryleft dst_negative_scale_swap_resultmaskentryleft dst_positive_swap_resultmaskentryleft dst_negative_swap_resultmaskentryleft. (((G) = (((((dst_positive_code_swap_resultmaskentryleft) + (dst_positive_scale_swap_resultmaskentryleft)) * S ((dst_positive_code_swap_resultmaskentryleft) + (dst_positive_scale_swap_resultmaskentryleft)) + ((dst_positive_scale_swap_resultmaskentryleft) + (dst_positive_scale_swap_resultmaskentryleft))) + (((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) * S ((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) + ((dst_negative_scale_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)))) * S ((((dst_positive_code_swap_resultmaskentryleft) + (dst_positive_scale_swap_resultmaskentryleft)) * S ((dst_positive_code_swap_resultmaskentryleft) + (dst_positive_scale_swap_resultmaskentryleft)) + ((dst_positive_scale_swap_resultmaskentryleft) + (dst_positive_scale_swap_resultmaskentryleft))) + (((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) * S ((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) + ((dst_negative_scale_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)))) + ((((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) * S ((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) + ((dst_negative_scale_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft))) + (((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) * S ((dst_negative_code_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)) + ((dst_negative_scale_swap_resultmaskentryleft) + (dst_negative_scale_swap_resultmaskentryleft)))))) /\ (((((exists ff_h_pvs_swap_resultmaskentryleftpositive. ff_h_pvs_swap_resultmaskentryleftpositive + S (dst_positive_swap_resultmaskentryleft) = S ((S (dc_index_swap_resultmask)) * dst_positive_scale_swap_resultmaskentryleft)) /\ exists ff_q_pvs_swap_resultmaskentryleftpositive. dst_positive_code_swap_resultmaskentryleft = ff_q_pvs_swap_resultmaskentryleftpositive * S ((S (dc_index_swap_resultmask)) * dst_positive_scale_swap_resultmaskentryleft) + (dst_positive_swap_resultmaskentryleft))) /\ (((((exists ff_h_pvs_swap_resultmaskentryleftnegative. ff_h_pvs_swap_resultmaskentryleftnegative + S (dst_negative_swap_resultmaskentryleft) = S ((S (dc_index_swap_resultmask)) * dst_negative_scale_swap_resultmaskentryleft)) /\ exists ff_q_pvs_swap_resultmaskentryleftnegative. dst_negative_code_swap_resultmaskentryleft = ff_q_pvs_swap_resultmaskentryleftnegative * S ((S (dc_index_swap_resultmask)) * dst_negative_scale_swap_resultmaskentryleft) + (dst_negative_swap_resultmaskentryleft))) /\ (exists ge_balance_positive_swap_resultmaskentryleftvalue ge_balance_negative_swap_resultmaskentryleftvalue. (((((dc_left_swap_resultmaskentry) = 2 * (ge_balance_positive_swap_resultmaskentryleftvalue) /\ (ge_balance_negative_swap_resultmaskentryleftvalue) = 0) \/ exists ge_signed_half_swap_resultmaskentryleftvaluedecode. (((dc_left_swap_resultmaskentry) = 2 * ge_signed_half_swap_resultmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_swap_resultmaskentryleftvalue) = 0) /\ (ge_balance_negative_swap_resultmaskentryleftvalue) = S ge_signed_half_swap_resultmaskentryleftvaluedecode))) /\ ((dst_positive_swap_resultmaskentryleft) + ge_balance_negative_swap_resultmaskentryleftvalue = (dst_negative_swap_resultmaskentryleft) + ge_balance_positive_swap_resultmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_swap_resultmaskentryright dst_positive_scale_swap_resultmaskentryright dst_negative_code_swap_resultmaskentryright dst_negative_scale_swap_resultmaskentryright dst_positive_swap_resultmaskentryright dst_negative_swap_resultmaskentryright. (((F) = (((((dst_positive_code_swap_resultmaskentryright) + (dst_positive_scale_swap_resultmaskentryright)) * S ((dst_positive_code_swap_resultmaskentryright) + (dst_positive_scale_swap_resultmaskentryright)) + ((dst_positive_scale_swap_resultmaskentryright) + (dst_positive_scale_swap_resultmaskentryright))) + (((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) * S ((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) + ((dst_negative_scale_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)))) * S ((((dst_positive_code_swap_resultmaskentryright) + (dst_positive_scale_swap_resultmaskentryright)) * S ((dst_positive_code_swap_resultmaskentryright) + (dst_positive_scale_swap_resultmaskentryright)) + ((dst_positive_scale_swap_resultmaskentryright) + (dst_positive_scale_swap_resultmaskentryright))) + (((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) * S ((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) + ((dst_negative_scale_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)))) + ((((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) * S ((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) + ((dst_negative_scale_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright))) + (((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) * S ((dst_negative_code_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)) + ((dst_negative_scale_swap_resultmaskentryright) + (dst_negative_scale_swap_resultmaskentryright)))))) /\ (((((exists ff_h_pvs_swap_resultmaskentryrightpositive. ff_h_pvs_swap_resultmaskentryrightpositive + S (dst_positive_swap_resultmaskentryright) = S ((S (dc_quotient_swap_resultmaskentry)) * dst_positive_scale_swap_resultmaskentryright)) /\ exists ff_q_pvs_swap_resultmaskentryrightpositive. dst_positive_code_swap_resultmaskentryright = ff_q_pvs_swap_resultmaskentryrightpositive * S ((S (dc_quotient_swap_resultmaskentry)) * dst_positive_scale_swap_resultmaskentryright) + (dst_positive_swap_resultmaskentryright))) /\ (((((exists ff_h_pvs_swap_resultmaskentryrightnegative. ff_h_pvs_swap_resultmaskentryrightnegative + S (dst_negative_swap_resultmaskentryright) = S ((S (dc_quotient_swap_resultmaskentry)) * dst_negative_scale_swap_resultmaskentryright)) /\ exists ff_q_pvs_swap_resultmaskentryrightnegative. dst_negative_code_swap_resultmaskentryright = ff_q_pvs_swap_resultmaskentryrightnegative * S ((S (dc_quotient_swap_resultmaskentry)) * dst_negative_scale_swap_resultmaskentryright) + (dst_negative_swap_resultmaskentryright))) /\ (exists ge_balance_positive_swap_resultmaskentryrightvalue ge_balance_negative_swap_resultmaskentryrightvalue. (((((dc_right_swap_resultmaskentry) = 2 * (ge_balance_positive_swap_resultmaskentryrightvalue) /\ (ge_balance_negative_swap_resultmaskentryrightvalue) = 0) \/ exists ge_signed_half_swap_resultmaskentryrightvaluedecode. (((dc_right_swap_resultmaskentry) = 2 * ge_signed_half_swap_resultmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_swap_resultmaskentryrightvalue) = 0) /\ (ge_balance_negative_swap_resultmaskentryrightvalue) = S ge_signed_half_swap_resultmaskentryrightvaluedecode))) /\ ((dst_positive_swap_resultmaskentryright) + ge_balance_negative_swap_resultmaskentryrightvalue = (dst_negative_swap_resultmaskentryright) + ge_balance_positive_swap_resultmaskentryrightvalue))))))))) /\ (exists sto_ap_swap_resultmaskentryproduct sto_an_swap_resultmaskentryproduct sto_bp_swap_resultmaskentryproduct sto_bn_swap_resultmaskentryproduct sto_cp_swap_resultmaskentryproduct sto_cn_swap_resultmaskentryproduct. (((((dc_left_swap_resultmaskentry) = 2 * (sto_ap_swap_resultmaskentryproduct) /\ (sto_an_swap_resultmaskentryproduct) = 0) \/ exists ge_signed_half_swap_resultmaskentryproductleft. (((dc_left_swap_resultmaskentry) = 2 * ge_signed_half_swap_resultmaskentryproductleft + 1 /\ (sto_ap_swap_resultmaskentryproduct) = 0) /\ (sto_an_swap_resultmaskentryproduct) = S ge_signed_half_swap_resultmaskentryproductleft))) /\ ((((((dc_right_swap_resultmaskentry) = 2 * (sto_bp_swap_resultmaskentryproduct) /\ (sto_bn_swap_resultmaskentryproduct) = 0) \/ exists ge_signed_half_swap_resultmaskentryproductright. (((dc_right_swap_resultmaskentry) = 2 * ge_signed_half_swap_resultmaskentryproductright + 1 /\ (sto_bp_swap_resultmaskentryproduct) = 0) /\ (sto_bn_swap_resultmaskentryproduct) = S ge_signed_half_swap_resultmaskentryproductright))) /\ ((((((dc_value_swap_resultmask) = 2 * (sto_cp_swap_resultmaskentryproduct) /\ (sto_cn_swap_resultmaskentryproduct) = 0) \/ exists ge_signed_half_swap_resultmaskentryproductoutput. (((dc_value_swap_resultmask) = 2 * ge_signed_half_swap_resultmaskentryproductoutput + 1 /\ (sto_cp_swap_resultmaskentryproduct) = 0) /\ (sto_cn_swap_resultmaskentryproduct) = S ge_signed_half_swap_resultmaskentryproductoutput))) /\ ((sto_ap_swap_resultmaskentryproduct * sto_bp_swap_resultmaskentryproduct + sto_an_swap_resultmaskentryproduct * sto_bn_swap_resultmaskentryproduct) + sto_cn_swap_resultmaskentryproduct = (sto_ap_swap_resultmaskentryproduct * sto_bn_swap_resultmaskentryproduct + sto_an_swap_resultmaskentryproduct * sto_bp_swap_resultmaskentryproduct) + sto_cp_swap_resultmaskentryproduct))))))))))))))) \/ ((((dc_index_swap_resultmask)=0 \/ ~(exists pvs_factor_swap_resultmaskentrynondivisor. (n) = (dc_index_swap_resultmask) * pvs_factor_swap_resultmaskentrynondivisor)) /\ ((dc_value_swap_resultmask)=0))))))) /\ (exists dst_positive_code_swap_resultfold dst_positive_scale_swap_resultfold dst_negative_code_swap_resultfold dst_negative_scale_swap_resultfold dst_positive_sum_swap_resultfold dst_negative_sum_swap_resultfold. (((dc_mask_swap_result) = (((((dst_positive_code_swap_resultfold) + (dst_positive_scale_swap_resultfold)) * S ((dst_positive_code_swap_resultfold) + (dst_positive_scale_swap_resultfold)) + ((dst_positive_scale_swap_resultfold) + (dst_positive_scale_swap_resultfold))) + (((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) * S ((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) + ((dst_negative_scale_swap_resultfold) + (dst_negative_scale_swap_resultfold)))) * S ((((dst_positive_code_swap_resultfold) + (dst_positive_scale_swap_resultfold)) * S ((dst_positive_code_swap_resultfold) + (dst_positive_scale_swap_resultfold)) + ((dst_positive_scale_swap_resultfold) + (dst_positive_scale_swap_resultfold))) + (((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) * S ((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) + ((dst_negative_scale_swap_resultfold) + (dst_negative_scale_swap_resultfold)))) + ((((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) * S ((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) + ((dst_negative_scale_swap_resultfold) + (dst_negative_scale_swap_resultfold))) + (((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) * S ((dst_negative_code_swap_resultfold) + (dst_negative_scale_swap_resultfold)) + ((dst_negative_scale_swap_resultfold) + (dst_negative_scale_swap_resultfold)))))) /\ (((exists fs_u_dst_swap_resultfoldpositive fs_v_dst_swap_resultfoldpositive. ((((exists fs_h_dst_swap_resultfoldpositive_body_start. fs_h_dst_swap_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_swap_resultfoldpositive)) /\ exists fs_q_dst_swap_resultfoldpositive_body_start. fs_u_dst_swap_resultfoldpositive = fs_q_dst_swap_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_swap_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_swap_resultfoldpositive_body_terminal. fs_h_dst_swap_resultfoldpositive_body_terminal + S (dst_positive_sum_swap_resultfold) = S ((S (S (n))) * fs_v_dst_swap_resultfoldpositive)) /\ exists fs_q_dst_swap_resultfoldpositive_body_terminal. fs_u_dst_swap_resultfoldpositive = fs_q_dst_swap_resultfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_swap_resultfoldpositive) + (dst_positive_sum_swap_resultfold))) /\ forall fs_i_dst_swap_resultfoldpositive_body_steps. (exists fs_lt_dst_swap_resultfoldpositive_body_steps_bound. fs_lt_dst_swap_resultfoldpositive_body_steps_bound + S fs_i_dst_swap_resultfoldpositive_body_steps = S (n)) -> exists fs_a_dst_swap_resultfoldpositive_body_steps fs_r_dst_swap_resultfoldpositive_body_steps fs_s_dst_swap_resultfoldpositive_body_steps. ((((exists fs_h_dst_swap_resultfoldpositive_body_steps_summand. fs_h_dst_swap_resultfoldpositive_body_steps_summand + S (fs_a_dst_swap_resultfoldpositive_body_steps) = S ((S (fs_i_dst_swap_resultfoldpositive_body_steps)) * dst_positive_scale_swap_resultfold)) /\ exists fs_q_dst_swap_resultfoldpositive_body_steps_summand. dst_positive_code_swap_resultfold = fs_q_dst_swap_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_swap_resultfoldpositive_body_steps)) * dst_positive_scale_swap_resultfold) + (fs_a_dst_swap_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_swap_resultfoldpositive_body_steps_partial. fs_h_dst_swap_resultfoldpositive_body_steps_partial + S (fs_r_dst_swap_resultfoldpositive_body_steps) = S ((S (fs_i_dst_swap_resultfoldpositive_body_steps)) * fs_v_dst_swap_resultfoldpositive)) /\ exists fs_q_dst_swap_resultfoldpositive_body_steps_partial. fs_u_dst_swap_resultfoldpositive = fs_q_dst_swap_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_swap_resultfoldpositive_body_steps)) * fs_v_dst_swap_resultfoldpositive) + (fs_r_dst_swap_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_swap_resultfoldpositive_body_steps_successor. fs_h_dst_swap_resultfoldpositive_body_steps_successor + S (fs_s_dst_swap_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_swap_resultfoldpositive_body_steps)) * fs_v_dst_swap_resultfoldpositive)) /\ exists fs_q_dst_swap_resultfoldpositive_body_steps_successor. fs_u_dst_swap_resultfoldpositive = fs_q_dst_swap_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_swap_resultfoldpositive_body_steps)) * fs_v_dst_swap_resultfoldpositive) + (fs_s_dst_swap_resultfoldpositive_body_steps))) /\ fs_s_dst_swap_resultfoldpositive_body_steps = fs_r_dst_swap_resultfoldpositive_body_steps + fs_a_dst_swap_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_swap_resultfoldnegative fs_v_dst_swap_resultfoldnegative. ((((exists fs_h_dst_swap_resultfoldnegative_body_start. fs_h_dst_swap_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_swap_resultfoldnegative)) /\ exists fs_q_dst_swap_resultfoldnegative_body_start. fs_u_dst_swap_resultfoldnegative = fs_q_dst_swap_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_swap_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_swap_resultfoldnegative_body_terminal. fs_h_dst_swap_resultfoldnegative_body_terminal + S (dst_negative_sum_swap_resultfold) = S ((S (S (n))) * fs_v_dst_swap_resultfoldnegative)) /\ exists fs_q_dst_swap_resultfoldnegative_body_terminal. fs_u_dst_swap_resultfoldnegative = fs_q_dst_swap_resultfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_swap_resultfoldnegative) + (dst_negative_sum_swap_resultfold))) /\ forall fs_i_dst_swap_resultfoldnegative_body_steps. (exists fs_lt_dst_swap_resultfoldnegative_body_steps_bound. fs_lt_dst_swap_resultfoldnegative_body_steps_bound + S fs_i_dst_swap_resultfoldnegative_body_steps = S (n)) -> exists fs_a_dst_swap_resultfoldnegative_body_steps fs_r_dst_swap_resultfoldnegative_body_steps fs_s_dst_swap_resultfoldnegative_body_steps. ((((exists fs_h_dst_swap_resultfoldnegative_body_steps_summand. fs_h_dst_swap_resultfoldnegative_body_steps_summand + S (fs_a_dst_swap_resultfoldnegative_body_steps) = S ((S (fs_i_dst_swap_resultfoldnegative_body_steps)) * dst_negative_scale_swap_resultfold)) /\ exists fs_q_dst_swap_resultfoldnegative_body_steps_summand. dst_negative_code_swap_resultfold = fs_q_dst_swap_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_swap_resultfoldnegative_body_steps)) * dst_negative_scale_swap_resultfold) + (fs_a_dst_swap_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_swap_resultfoldnegative_body_steps_partial. fs_h_dst_swap_resultfoldnegative_body_steps_partial + S (fs_r_dst_swap_resultfoldnegative_body_steps) = S ((S (fs_i_dst_swap_resultfoldnegative_body_steps)) * fs_v_dst_swap_resultfoldnegative)) /\ exists fs_q_dst_swap_resultfoldnegative_body_steps_partial. fs_u_dst_swap_resultfoldnegative = fs_q_dst_swap_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_swap_resultfoldnegative_body_steps)) * fs_v_dst_swap_resultfoldnegative) + (fs_r_dst_swap_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_swap_resultfoldnegative_body_steps_successor. fs_h_dst_swap_resultfoldnegative_body_steps_successor + S (fs_s_dst_swap_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_swap_resultfoldnegative_body_steps)) * fs_v_dst_swap_resultfoldnegative)) /\ exists fs_q_dst_swap_resultfoldnegative_body_steps_successor. fs_u_dst_swap_resultfoldnegative = fs_q_dst_swap_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_swap_resultfoldnegative_body_steps)) * fs_v_dst_swap_resultfoldnegative) + (fs_s_dst_swap_resultfoldnegative_body_steps))) /\ fs_s_dst_swap_resultfoldnegative_body_steps = fs_r_dst_swap_resultfoldnegative_body_steps + fs_a_dst_swap_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_swap_resultfoldresult ge_balance_negative_swap_resultfoldresult. (((((z) = 2 * (ge_balance_positive_swap_resultfoldresult) /\ (ge_balance_negative_swap_resultfoldresult) = 0) \/ exists ge_signed_half_swap_resultfoldresultdecode. (((z) = 2 * ge_signed_half_swap_resultfoldresultdecode + 1 /\ (ge_balance_positive_swap_resultfoldresult) = 0) /\ (ge_balance_negative_swap_resultfoldresult) = S ge_signed_half_swap_resultfoldresultdecode))) /\ ((dst_positive_sum_swap_resultfold) + ge_balance_negative_swap_resultfoldresult = (dst_negative_sum_swap_resultfold) + ge_balance_positive_swap_resultfoldresult)))))))))))))

dirichlet_convolution_table_commutative · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F G H. (((exists dst_positive_code_table_commutative_sourceleft dst_positive_scale_table_commutative_sourceleft dst_negative_code_table_commutative_sourceleft dst_negative_scale_table_commutative_sourceleft. (((F) = (((((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) * S ((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) + ((dst_positive_scale_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft))) + (((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)))) * S ((((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) * S ((dst_positive_code_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft)) + ((dst_positive_scale_table_commutative_sourceleft) + (dst_positive_scale_table_commutative_sourceleft))) + (((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)))) + ((((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft))) + (((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) * S ((dst_negative_code_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)) + ((dst_negative_scale_table_commutative_sourceleft) + (dst_negative_scale_table_commutative_sourceleft)))))) /\ (forall dst_index_table_commutative_sourceleft. (exists pvs_le_gap_table_commutative_sourceleftdomain. pvs_le_gap_table_commutative_sourceleftdomain + (dst_index_table_commutative_sourceleft) = (N)) -> exists dst_positive_table_commutative_sourceleft dst_negative_table_commutative_sourceleft dst_value_table_commutative_sourceleft. ((((exists ff_h_pvs_table_commutative_sourceleftentrypositive. ff_h_pvs_table_commutative_sourceleftentrypositive + S (dst_positive_table_commutative_sourceleft) = S ((S (dst_index_table_commutative_sourceleft)) * dst_positive_scale_table_commutative_sourceleft)) /\ exists ff_q_pvs_table_commutative_sourceleftentrypositive. dst_positive_code_table_commutative_sourceleft = ff_q_pvs_table_commutative_sourceleftentrypositive * S ((S (dst_index_table_commutative_sourceleft)) * dst_positive_scale_table_commutative_sourceleft) + (dst_positive_table_commutative_sourceleft))) /\ (((((exists ff_h_pvs_table_commutative_sourceleftentrynegative. ff_h_pvs_table_commutative_sourceleftentrynegative + S (dst_negative_table_commutative_sourceleft) = S ((S (dst_index_table_commutative_sourceleft)) * dst_negative_scale_table_commutative_sourceleft)) /\ exists ff_q_pvs_table_commutative_sourceleftentrynegative. dst_negative_code_table_commutative_sourceleft = ff_q_pvs_table_commutative_sourceleftentrynegative * S ((S (dst_index_table_commutative_sourceleft)) * dst_negative_scale_table_commutative_sourceleft) + (dst_negative_table_commutative_sourceleft))) /\ (exists ge_balance_positive_table_commutative_sourceleftentryvalue ge_balance_negative_table_commutative_sourceleftentryvalue. (((((dst_value_table_commutative_sourceleft) = 2 * (ge_balance_positive_table_commutative_sourceleftentryvalue) /\ (ge_balance_negative_table_commutative_sourceleftentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourceleftentryvaluedecode. (((dst_value_table_commutative_sourceleft) = 2 * ge_signed_half_table_commutative_sourceleftentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourceleftentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourceleftentryvalue) = S ge_signed_half_table_commutative_sourceleftentryvaluedecode))) /\ ((dst_positive_table_commutative_sourceleft) + ge_balance_negative_table_commutative_sourceleftentryvalue = (dst_negative_table_commutative_sourceleft) + ge_balance_positive_table_commutative_sourceleftentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_sourceright dst_positive_scale_table_commutative_sourceright dst_negative_code_table_commutative_sourceright dst_negative_scale_table_commutative_sourceright. (((G) = (((((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) * S ((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) + ((dst_positive_scale_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright))) + (((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)))) * S ((((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) * S ((dst_positive_code_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright)) + ((dst_positive_scale_table_commutative_sourceright) + (dst_positive_scale_table_commutative_sourceright))) + (((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)))) + ((((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright))) + (((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) * S ((dst_negative_code_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)) + ((dst_negative_scale_table_commutative_sourceright) + (dst_negative_scale_table_commutative_sourceright)))))) /\ (forall dst_index_table_commutative_sourceright. (exists pvs_le_gap_table_commutative_sourcerightdomain. pvs_le_gap_table_commutative_sourcerightdomain + (dst_index_table_commutative_sourceright) = (N)) -> exists dst_positive_table_commutative_sourceright dst_negative_table_commutative_sourceright dst_value_table_commutative_sourceright. ((((exists ff_h_pvs_table_commutative_sourcerightentrypositive. ff_h_pvs_table_commutative_sourcerightentrypositive + S (dst_positive_table_commutative_sourceright) = S ((S (dst_index_table_commutative_sourceright)) * dst_positive_scale_table_commutative_sourceright)) /\ exists ff_q_pvs_table_commutative_sourcerightentrypositive. dst_positive_code_table_commutative_sourceright = ff_q_pvs_table_commutative_sourcerightentrypositive * S ((S (dst_index_table_commutative_sourceright)) * dst_positive_scale_table_commutative_sourceright) + (dst_positive_table_commutative_sourceright))) /\ (((((exists ff_h_pvs_table_commutative_sourcerightentrynegative. ff_h_pvs_table_commutative_sourcerightentrynegative + S (dst_negative_table_commutative_sourceright) = S ((S (dst_index_table_commutative_sourceright)) * dst_negative_scale_table_commutative_sourceright)) /\ exists ff_q_pvs_table_commutative_sourcerightentrynegative. dst_negative_code_table_commutative_sourceright = ff_q_pvs_table_commutative_sourcerightentrynegative * S ((S (dst_index_table_commutative_sourceright)) * dst_negative_scale_table_commutative_sourceright) + (dst_negative_table_commutative_sourceright))) /\ (exists ge_balance_positive_table_commutative_sourcerightentryvalue ge_balance_negative_table_commutative_sourcerightentryvalue. (((((dst_value_table_commutative_sourceright) = 2 * (ge_balance_positive_table_commutative_sourcerightentryvalue) /\ (ge_balance_negative_table_commutative_sourcerightentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcerightentryvaluedecode. (((dst_value_table_commutative_sourceright) = 2 * ge_signed_half_table_commutative_sourcerightentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcerightentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcerightentryvalue) = S ge_signed_half_table_commutative_sourcerightentryvaluedecode))) /\ ((dst_positive_table_commutative_sourceright) + ge_balance_negative_table_commutative_sourcerightentryvalue = (dst_negative_table_commutative_sourceright) + ge_balance_positive_table_commutative_sourcerightentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_sourcetable dst_positive_scale_table_commutative_sourcetable dst_negative_code_table_commutative_sourcetable dst_negative_scale_table_commutative_sourcetable. (((H) = (((((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) * S ((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) + ((dst_positive_scale_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable))) + (((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)))) * S ((((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) * S ((dst_positive_code_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable)) + ((dst_positive_scale_table_commutative_sourcetable) + (dst_positive_scale_table_commutative_sourcetable))) + (((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)))) + ((((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable))) + (((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) * S ((dst_negative_code_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)) + ((dst_negative_scale_table_commutative_sourcetable) + (dst_negative_scale_table_commutative_sourcetable)))))) /\ (forall dst_index_table_commutative_sourcetable. (exists pvs_le_gap_table_commutative_sourcetabledomain. pvs_le_gap_table_commutative_sourcetabledomain + (dst_index_table_commutative_sourcetable) = (N)) -> exists dst_positive_table_commutative_sourcetable dst_negative_table_commutative_sourcetable dst_value_table_commutative_sourcetable. ((((exists ff_h_pvs_table_commutative_sourcetableentrypositive. ff_h_pvs_table_commutative_sourcetableentrypositive + S (dst_positive_table_commutative_sourcetable) = S ((S (dst_index_table_commutative_sourcetable)) * dst_positive_scale_table_commutative_sourcetable)) /\ exists ff_q_pvs_table_commutative_sourcetableentrypositive. dst_positive_code_table_commutative_sourcetable = ff_q_pvs_table_commutative_sourcetableentrypositive * S ((S (dst_index_table_commutative_sourcetable)) * dst_positive_scale_table_commutative_sourcetable) + (dst_positive_table_commutative_sourcetable))) /\ (((((exists ff_h_pvs_table_commutative_sourcetableentrynegative. ff_h_pvs_table_commutative_sourcetableentrynegative + S (dst_negative_table_commutative_sourcetable) = S ((S (dst_index_table_commutative_sourcetable)) * dst_negative_scale_table_commutative_sourcetable)) /\ exists ff_q_pvs_table_commutative_sourcetableentrynegative. dst_negative_code_table_commutative_sourcetable = ff_q_pvs_table_commutative_sourcetableentrynegative * S ((S (dst_index_table_commutative_sourcetable)) * dst_negative_scale_table_commutative_sourcetable) + (dst_negative_table_commutative_sourcetable))) /\ (exists ge_balance_positive_table_commutative_sourcetableentryvalue ge_balance_negative_table_commutative_sourcetableentryvalue. (((((dst_value_table_commutative_sourcetable) = 2 * (ge_balance_positive_table_commutative_sourcetableentryvalue) /\ (ge_balance_negative_table_commutative_sourcetableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcetableentryvaluedecode. (((dst_value_table_commutative_sourcetable) = 2 * ge_signed_half_table_commutative_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcetableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcetableentryvalue) = S ge_signed_half_table_commutative_sourcetableentryvaluedecode))) /\ ((dst_positive_table_commutative_sourcetable) + ge_balance_negative_table_commutative_sourcetableentryvalue = (dst_negative_table_commutative_sourcetable) + ge_balance_positive_table_commutative_sourcetableentryvalue))))))))) /\ (forall dc_input_table_commutative_source dc_output_table_commutative_source. ~(dc_input_table_commutative_source=0) -> (exists pvs_le_gap_table_commutative_sourcedomain. pvs_le_gap_table_commutative_sourcedomain + (dc_input_table_commutative_source) = (N)) -> (exists dst_positive_code_table_commutative_sourcelookup dst_positive_scale_table_commutative_sourcelookup dst_negative_code_table_commutative_sourcelookup dst_negative_scale_table_commutative_sourcelookup dst_positive_table_commutative_sourcelookup dst_negative_table_commutative_sourcelookup. (((H) = (((((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) * S ((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) + ((dst_positive_scale_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup))) + (((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)))) * S ((((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) * S ((dst_positive_code_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup)) + ((dst_positive_scale_table_commutative_sourcelookup) + (dst_positive_scale_table_commutative_sourcelookup))) + (((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)))) + ((((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup))) + (((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) * S ((dst_negative_code_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)) + ((dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_scale_table_commutative_sourcelookup)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcelookuppositive. ff_h_pvs_table_commutative_sourcelookuppositive + S (dst_positive_table_commutative_sourcelookup) = S ((S (dc_input_table_commutative_source)) * dst_positive_scale_table_commutative_sourcelookup)) /\ exists ff_q_pvs_table_commutative_sourcelookuppositive. dst_positive_code_table_commutative_sourcelookup = ff_q_pvs_table_commutative_sourcelookuppositive * S ((S (dc_input_table_commutative_source)) * dst_positive_scale_table_commutative_sourcelookup) + (dst_positive_table_commutative_sourcelookup))) /\ (((((exists ff_h_pvs_table_commutative_sourcelookupnegative. ff_h_pvs_table_commutative_sourcelookupnegative + S (dst_negative_table_commutative_sourcelookup) = S ((S (dc_input_table_commutative_source)) * dst_negative_scale_table_commutative_sourcelookup)) /\ exists ff_q_pvs_table_commutative_sourcelookupnegative. dst_negative_code_table_commutative_sourcelookup = ff_q_pvs_table_commutative_sourcelookupnegative * S ((S (dc_input_table_commutative_source)) * dst_negative_scale_table_commutative_sourcelookup) + (dst_negative_table_commutative_sourcelookup))) /\ (exists ge_balance_positive_table_commutative_sourcelookupvalue ge_balance_negative_table_commutative_sourcelookupvalue. (((((dc_output_table_commutative_source) = 2 * (ge_balance_positive_table_commutative_sourcelookupvalue) /\ (ge_balance_negative_table_commutative_sourcelookupvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcelookupvaluedecode. (((dc_output_table_commutative_source) = 2 * ge_signed_half_table_commutative_sourcelookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcelookupvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcelookupvalue) = S ge_signed_half_table_commutative_sourcelookupvaluedecode))) /\ ((dst_positive_table_commutative_sourcelookup) + ge_balance_negative_table_commutative_sourcelookupvalue = (dst_negative_table_commutative_sourcelookup) + ge_balance_positive_table_commutative_sourcelookupvalue))))))))) -> (((~((dc_input_table_commutative_source)=0)) /\ (exists dc_mask_table_commutative_sourcevalue. ((((exists dst_positive_code_table_commutative_sourcevaluemasktable dst_positive_scale_table_commutative_sourcevaluemasktable dst_negative_code_table_commutative_sourcevaluemasktable dst_negative_scale_table_commutative_sourcevaluemasktable. (((dc_mask_table_commutative_sourcevalue) = (((((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) * S ((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) + ((dst_positive_scale_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable))) + (((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)))) * S ((((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) * S ((dst_positive_code_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable)) + ((dst_positive_scale_table_commutative_sourcevaluemasktable) + (dst_positive_scale_table_commutative_sourcevaluemasktable))) + (((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)))) + ((((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable))) + (((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) * S ((dst_negative_code_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)) + ((dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_scale_table_commutative_sourcevaluemasktable)))))) /\ (forall dst_index_table_commutative_sourcevaluemasktable. (exists pvs_le_gap_table_commutative_sourcevaluemasktabledomain. pvs_le_gap_table_commutative_sourcevaluemasktabledomain + (dst_index_table_commutative_sourcevaluemasktable) = (dc_input_table_commutative_source)) -> exists dst_positive_table_commutative_sourcevaluemasktable dst_negative_table_commutative_sourcevaluemasktable dst_value_table_commutative_sourcevaluemasktable. ((((exists ff_h_pvs_table_commutative_sourcevaluemasktableentrypositive. ff_h_pvs_table_commutative_sourcevaluemasktableentrypositive + S (dst_positive_table_commutative_sourcevaluemasktable) = S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_positive_scale_table_commutative_sourcevaluemasktable)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasktableentrypositive. dst_positive_code_table_commutative_sourcevaluemasktable = ff_q_pvs_table_commutative_sourcevaluemasktableentrypositive * S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_positive_scale_table_commutative_sourcevaluemasktable) + (dst_positive_table_commutative_sourcevaluemasktable))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemasktableentrynegative. ff_h_pvs_table_commutative_sourcevaluemasktableentrynegative + S (dst_negative_table_commutative_sourcevaluemasktable) = S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_negative_scale_table_commutative_sourcevaluemasktable)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasktableentrynegative. dst_negative_code_table_commutative_sourcevaluemasktable = ff_q_pvs_table_commutative_sourcevaluemasktableentrynegative * S ((S (dst_index_table_commutative_sourcevaluemasktable)) * dst_negative_scale_table_commutative_sourcevaluemasktable) + (dst_negative_table_commutative_sourcevaluemasktable))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue. (((((dst_value_table_commutative_sourcevaluemasktable) = 2 * (ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemasktableentryvaluedecode. (((dst_value_table_commutative_sourcevaluemasktable) = 2 * ge_signed_half_table_commutative_sourcevaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue) = S ge_signed_half_table_commutative_sourcevaluemasktableentryvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemasktable) + ge_balance_negative_table_commutative_sourcevaluemasktableentryvalue = (dst_negative_table_commutative_sourcevaluemasktable) + ge_balance_positive_table_commutative_sourcevaluemasktableentryvalue))))))))) /\ (forall dc_index_table_commutative_sourcevaluemask dc_value_table_commutative_sourcevaluemask. (exists pvs_le_gap_table_commutative_sourcevaluemaskdomain. pvs_le_gap_table_commutative_sourcevaluemaskdomain + (dc_index_table_commutative_sourcevaluemask) = (dc_input_table_commutative_source)) -> (exists dst_positive_code_table_commutative_sourcevaluemasklookup dst_positive_scale_table_commutative_sourcevaluemasklookup dst_negative_code_table_commutative_sourcevaluemasklookup dst_negative_scale_table_commutative_sourcevaluemasklookup dst_positive_table_commutative_sourcevaluemasklookup dst_negative_table_commutative_sourcevaluemasklookup. (((dc_mask_table_commutative_sourcevalue) = (((((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) + ((dst_positive_scale_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup))) + (((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)))) * S ((((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_positive_code_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup)) + ((dst_positive_scale_table_commutative_sourcevaluemasklookup) + (dst_positive_scale_table_commutative_sourcevaluemasklookup))) + (((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)))) + ((((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup))) + (((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) * S ((dst_negative_code_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)) + ((dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_scale_table_commutative_sourcevaluemasklookup)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemasklookuppositive. ff_h_pvs_table_commutative_sourcevaluemasklookuppositive + S (dst_positive_table_commutative_sourcevaluemasklookup) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasklookuppositive. dst_positive_code_table_commutative_sourcevaluemasklookup = ff_q_pvs_table_commutative_sourcevaluemasklookuppositive * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemasklookup) + (dst_positive_table_commutative_sourcevaluemasklookup))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemasklookupnegative. ff_h_pvs_table_commutative_sourcevaluemasklookupnegative + S (dst_negative_table_commutative_sourcevaluemasklookup) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_commutative_sourcevaluemasklookupnegative. dst_negative_code_table_commutative_sourcevaluemasklookup = ff_q_pvs_table_commutative_sourcevaluemasklookupnegative * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemasklookup) + (dst_negative_table_commutative_sourcevaluemasklookup))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemasklookupvalue ge_balance_negative_table_commutative_sourcevaluemasklookupvalue. (((((dc_value_table_commutative_sourcevaluemask) = 2 * (ge_balance_positive_table_commutative_sourcevaluemasklookupvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemasklookupvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemasklookupvaluedecode. (((dc_value_table_commutative_sourcevaluemask) = 2 * ge_signed_half_table_commutative_sourcevaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemasklookupvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemasklookupvalue) = S ge_signed_half_table_commutative_sourcevaluemasklookupvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemasklookup) + ge_balance_negative_table_commutative_sourcevaluemasklookupvalue = (dst_negative_table_commutative_sourcevaluemasklookup) + ge_balance_positive_table_commutative_sourcevaluemasklookupvalue))))))))) -> ((((~((dc_index_table_commutative_sourcevaluemask)=0)) /\ (exists dc_quotient_table_commutative_sourcevaluemaskentry dc_left_table_commutative_sourcevaluemaskentry dc_right_table_commutative_sourcevaluemaskentry. (((dc_input_table_commutative_source)=(dc_index_table_commutative_sourcevaluemask)*dc_quotient_table_commutative_sourcevaluemaskentry) /\ (((exists dst_positive_code_table_commutative_sourcevaluemaskentryleft dst_positive_scale_table_commutative_sourcevaluemaskentryleft dst_negative_code_table_commutative_sourcevaluemaskentryleft dst_negative_scale_table_commutative_sourcevaluemaskentryleft dst_positive_table_commutative_sourcevaluemaskentryleft dst_negative_table_commutative_sourcevaluemaskentryleft. (((F) = (((((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)))) * S ((((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryleft) + (dst_positive_scale_table_commutative_sourcevaluemaskentryleft))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)))) + ((((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_scale_table_commutative_sourcevaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryleftpositive. ff_h_pvs_table_commutative_sourcevaluemaskentryleftpositive + S (dst_positive_table_commutative_sourcevaluemaskentryleft) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryleftpositive. dst_positive_code_table_commutative_sourcevaluemaskentryleft = ff_q_pvs_table_commutative_sourcevaluemaskentryleftpositive * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_positive_scale_table_commutative_sourcevaluemaskentryleft) + (dst_positive_table_commutative_sourcevaluemaskentryleft))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryleftnegative. ff_h_pvs_table_commutative_sourcevaluemaskentryleftnegative + S (dst_negative_table_commutative_sourcevaluemaskentryleft) = S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryleftnegative. dst_negative_code_table_commutative_sourcevaluemaskentryleft = ff_q_pvs_table_commutative_sourcevaluemaskentryleftnegative * S ((S (dc_index_table_commutative_sourcevaluemask)) * dst_negative_scale_table_commutative_sourcevaluemaskentryleft) + (dst_negative_table_commutative_sourcevaluemaskentryleft))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue. (((((dc_left_table_commutative_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryleftvaluedecode. (((dc_left_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue) = S ge_signed_half_table_commutative_sourcevaluemaskentryleftvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemaskentryleft) + ge_balance_negative_table_commutative_sourcevaluemaskentryleftvalue = (dst_negative_table_commutative_sourcevaluemaskentryleft) + ge_balance_positive_table_commutative_sourcevaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_commutative_sourcevaluemaskentryright dst_positive_scale_table_commutative_sourcevaluemaskentryright dst_negative_code_table_commutative_sourcevaluemaskentryright dst_negative_scale_table_commutative_sourcevaluemaskentryright dst_positive_table_commutative_sourcevaluemaskentryright dst_negative_table_commutative_sourcevaluemaskentryright. (((G) = (((((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)))) * S ((((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_positive_code_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_positive_scale_table_commutative_sourcevaluemaskentryright) + (dst_positive_scale_table_commutative_sourcevaluemaskentryright))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)))) + ((((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright))) + (((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) * S ((dst_negative_code_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)) + ((dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_scale_table_commutative_sourcevaluemaskentryright)))))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryrightpositive. ff_h_pvs_table_commutative_sourcevaluemaskentryrightpositive + S (dst_positive_table_commutative_sourcevaluemaskentryright) = S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_positive_scale_table_commutative_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryrightpositive. dst_positive_code_table_commutative_sourcevaluemaskentryright = ff_q_pvs_table_commutative_sourcevaluemaskentryrightpositive * S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_positive_scale_table_commutative_sourcevaluemaskentryright) + (dst_positive_table_commutative_sourcevaluemaskentryright))) /\ (((((exists ff_h_pvs_table_commutative_sourcevaluemaskentryrightnegative. ff_h_pvs_table_commutative_sourcevaluemaskentryrightnegative + S (dst_negative_table_commutative_sourcevaluemaskentryright) = S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_negative_scale_table_commutative_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_sourcevaluemaskentryrightnegative. dst_negative_code_table_commutative_sourcevaluemaskentryright = ff_q_pvs_table_commutative_sourcevaluemaskentryrightnegative * S ((S (dc_quotient_table_commutative_sourcevaluemaskentry)) * dst_negative_scale_table_commutative_sourcevaluemaskentryright) + (dst_negative_table_commutative_sourcevaluemaskentryright))) /\ (exists ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue. (((((dc_right_table_commutative_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryrightvaluedecode. (((dc_right_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue) = S ge_signed_half_table_commutative_sourcevaluemaskentryrightvaluedecode))) /\ ((dst_positive_table_commutative_sourcevaluemaskentryright) + ge_balance_negative_table_commutative_sourcevaluemaskentryrightvalue = (dst_negative_table_commutative_sourcevaluemaskentryright) + ge_balance_positive_table_commutative_sourcevaluemaskentryrightvalue))))))))) /\ (exists sto_ap_table_commutative_sourcevaluemaskentryproduct sto_an_table_commutative_sourcevaluemaskentryproduct sto_bp_table_commutative_sourcevaluemaskentryproduct sto_bn_table_commutative_sourcevaluemaskentryproduct sto_cp_table_commutative_sourcevaluemaskentryproduct sto_cn_table_commutative_sourcevaluemaskentryproduct. (((((dc_left_table_commutative_sourcevaluemaskentry) = 2 * (sto_ap_table_commutative_sourcevaluemaskentryproduct) /\ (sto_an_table_commutative_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryproductleft. (((dc_left_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryproductleft + 1 /\ (sto_ap_table_commutative_sourcevaluemaskentryproduct) = 0) /\ (sto_an_table_commutative_sourcevaluemaskentryproduct) = S ge_signed_half_table_commutative_sourcevaluemaskentryproductleft))) /\ ((((((dc_right_table_commutative_sourcevaluemaskentry) = 2 * (sto_bp_table_commutative_sourcevaluemaskentryproduct) /\ (sto_bn_table_commutative_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryproductright. (((dc_right_table_commutative_sourcevaluemaskentry) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryproductright + 1 /\ (sto_bp_table_commutative_sourcevaluemaskentryproduct) = 0) /\ (sto_bn_table_commutative_sourcevaluemaskentryproduct) = S ge_signed_half_table_commutative_sourcevaluemaskentryproductright))) /\ ((((((dc_value_table_commutative_sourcevaluemask) = 2 * (sto_cp_table_commutative_sourcevaluemaskentryproduct) /\ (sto_cn_table_commutative_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluemaskentryproductoutput. (((dc_value_table_commutative_sourcevaluemask) = 2 * ge_signed_half_table_commutative_sourcevaluemaskentryproductoutput + 1 /\ (sto_cp_table_commutative_sourcevaluemaskentryproduct) = 0) /\ (sto_cn_table_commutative_sourcevaluemaskentryproduct) = S ge_signed_half_table_commutative_sourcevaluemaskentryproductoutput))) /\ ((sto_ap_table_commutative_sourcevaluemaskentryproduct * sto_bp_table_commutative_sourcevaluemaskentryproduct + sto_an_table_commutative_sourcevaluemaskentryproduct * sto_bn_table_commutative_sourcevaluemaskentryproduct) + sto_cn_table_commutative_sourcevaluemaskentryproduct = (sto_ap_table_commutative_sourcevaluemaskentryproduct * sto_bn_table_commutative_sourcevaluemaskentryproduct + sto_an_table_commutative_sourcevaluemaskentryproduct * sto_bp_table_commutative_sourcevaluemaskentryproduct) + sto_cp_table_commutative_sourcevaluemaskentryproduct))))))))))))))) \/ ((((dc_index_table_commutative_sourcevaluemask)=0 \/ ~(exists pvs_factor_table_commutative_sourcevaluemaskentrynondivisor. (dc_input_table_commutative_source) = (dc_index_table_commutative_sourcevaluemask) * pvs_factor_table_commutative_sourcevaluemaskentrynondivisor)) /\ ((dc_value_table_commutative_sourcevaluemask)=0))))))) /\ (exists dst_positive_code_table_commutative_sourcevaluefold dst_positive_scale_table_commutative_sourcevaluefold dst_negative_code_table_commutative_sourcevaluefold dst_negative_scale_table_commutative_sourcevaluefold dst_positive_sum_table_commutative_sourcevaluefold dst_negative_sum_table_commutative_sourcevaluefold. (((dc_mask_table_commutative_sourcevalue) = (((((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) * S ((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) + ((dst_positive_scale_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold))) + (((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)))) * S ((((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) * S ((dst_positive_code_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold)) + ((dst_positive_scale_table_commutative_sourcevaluefold) + (dst_positive_scale_table_commutative_sourcevaluefold))) + (((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)))) + ((((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold))) + (((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) * S ((dst_negative_code_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)) + ((dst_negative_scale_table_commutative_sourcevaluefold) + (dst_negative_scale_table_commutative_sourcevaluefold)))))) /\ (((exists fs_u_dst_table_commutative_sourcevaluefoldpositive fs_v_dst_table_commutative_sourcevaluefoldpositive. ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_start. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_start. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_terminal. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_terminal + S (dst_positive_sum_table_commutative_sourcevaluefold) = S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_terminal. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_terminal * S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (dst_positive_sum_table_commutative_sourcevaluefold))) /\ forall fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps. (exists fs_lt_dst_table_commutative_sourcevaluefoldpositive_body_steps_bound. fs_lt_dst_table_commutative_sourcevaluefoldpositive_body_steps_bound + S fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps = S (dc_input_table_commutative_source)) -> exists fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps. ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand + S (fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_sourcevaluefold)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand. dst_positive_code_table_commutative_sourcevaluefold = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_sourcevaluefold) + (fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial + S (fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor. fs_h_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor + S (fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps) = S ((S (S fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor. fs_u_dst_table_commutative_sourcevaluefoldpositive = fs_q_dst_table_commutative_sourcevaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_commutative_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldpositive) + (fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps))) /\ fs_s_dst_table_commutative_sourcevaluefoldpositive_body_steps = fs_r_dst_table_commutative_sourcevaluefoldpositive_body_steps + fs_a_dst_table_commutative_sourcevaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_commutative_sourcevaluefoldnegative fs_v_dst_table_commutative_sourcevaluefoldnegative. ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_start. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_start. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_terminal. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_terminal + S (dst_negative_sum_table_commutative_sourcevaluefold) = S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_terminal. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_terminal * S ((S (S (dc_input_table_commutative_source))) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (dst_negative_sum_table_commutative_sourcevaluefold))) /\ forall fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps. (exists fs_lt_dst_table_commutative_sourcevaluefoldnegative_body_steps_bound. fs_lt_dst_table_commutative_sourcevaluefoldnegative_body_steps_bound + S fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps = S (dc_input_table_commutative_source)) -> exists fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps. ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand + S (fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_sourcevaluefold)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand. dst_negative_code_table_commutative_sourcevaluefold = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_sourcevaluefold) + (fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial + S (fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor. fs_h_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor + S (fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps) = S ((S (S fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor. fs_u_dst_table_commutative_sourcevaluefoldnegative = fs_q_dst_table_commutative_sourcevaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_commutative_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_sourcevaluefoldnegative) + (fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps))) /\ fs_s_dst_table_commutative_sourcevaluefoldnegative_body_steps = fs_r_dst_table_commutative_sourcevaluefoldnegative_body_steps + fs_a_dst_table_commutative_sourcevaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_commutative_sourcevaluefoldresult ge_balance_negative_table_commutative_sourcevaluefoldresult. (((((dc_output_table_commutative_source) = 2 * (ge_balance_positive_table_commutative_sourcevaluefoldresult) /\ (ge_balance_negative_table_commutative_sourcevaluefoldresult) = 0) \/ exists ge_signed_half_table_commutative_sourcevaluefoldresultdecode. (((dc_output_table_commutative_source) = 2 * ge_signed_half_table_commutative_sourcevaluefoldresultdecode + 1 /\ (ge_balance_positive_table_commutative_sourcevaluefoldresult) = 0) /\ (ge_balance_negative_table_commutative_sourcevaluefoldresult) = S ge_signed_half_table_commutative_sourcevaluefoldresultdecode))) /\ ((dst_positive_sum_table_commutative_sourcevaluefold) + ge_balance_negative_table_commutative_sourcevaluefoldresult = (dst_negative_sum_table_commutative_sourcevaluefold) + ge_balance_positive_table_commutative_sourcevaluefoldresult)))))))))))))))))))) -> (((exists dst_positive_code_table_commutative_resultleft dst_positive_scale_table_commutative_resultleft dst_negative_code_table_commutative_resultleft dst_negative_scale_table_commutative_resultleft. (((G) = (((((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) * S ((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) + ((dst_positive_scale_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft))) + (((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)))) * S ((((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) * S ((dst_positive_code_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft)) + ((dst_positive_scale_table_commutative_resultleft) + (dst_positive_scale_table_commutative_resultleft))) + (((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)))) + ((((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft))) + (((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) * S ((dst_negative_code_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)) + ((dst_negative_scale_table_commutative_resultleft) + (dst_negative_scale_table_commutative_resultleft)))))) /\ (forall dst_index_table_commutative_resultleft. (exists pvs_le_gap_table_commutative_resultleftdomain. pvs_le_gap_table_commutative_resultleftdomain + (dst_index_table_commutative_resultleft) = (N)) -> exists dst_positive_table_commutative_resultleft dst_negative_table_commutative_resultleft dst_value_table_commutative_resultleft. ((((exists ff_h_pvs_table_commutative_resultleftentrypositive. ff_h_pvs_table_commutative_resultleftentrypositive + S (dst_positive_table_commutative_resultleft) = S ((S (dst_index_table_commutative_resultleft)) * dst_positive_scale_table_commutative_resultleft)) /\ exists ff_q_pvs_table_commutative_resultleftentrypositive. dst_positive_code_table_commutative_resultleft = ff_q_pvs_table_commutative_resultleftentrypositive * S ((S (dst_index_table_commutative_resultleft)) * dst_positive_scale_table_commutative_resultleft) + (dst_positive_table_commutative_resultleft))) /\ (((((exists ff_h_pvs_table_commutative_resultleftentrynegative. ff_h_pvs_table_commutative_resultleftentrynegative + S (dst_negative_table_commutative_resultleft) = S ((S (dst_index_table_commutative_resultleft)) * dst_negative_scale_table_commutative_resultleft)) /\ exists ff_q_pvs_table_commutative_resultleftentrynegative. dst_negative_code_table_commutative_resultleft = ff_q_pvs_table_commutative_resultleftentrynegative * S ((S (dst_index_table_commutative_resultleft)) * dst_negative_scale_table_commutative_resultleft) + (dst_negative_table_commutative_resultleft))) /\ (exists ge_balance_positive_table_commutative_resultleftentryvalue ge_balance_negative_table_commutative_resultleftentryvalue. (((((dst_value_table_commutative_resultleft) = 2 * (ge_balance_positive_table_commutative_resultleftentryvalue) /\ (ge_balance_negative_table_commutative_resultleftentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resultleftentryvaluedecode. (((dst_value_table_commutative_resultleft) = 2 * ge_signed_half_table_commutative_resultleftentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultleftentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resultleftentryvalue) = S ge_signed_half_table_commutative_resultleftentryvaluedecode))) /\ ((dst_positive_table_commutative_resultleft) + ge_balance_negative_table_commutative_resultleftentryvalue = (dst_negative_table_commutative_resultleft) + ge_balance_positive_table_commutative_resultleftentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_resultright dst_positive_scale_table_commutative_resultright dst_negative_code_table_commutative_resultright dst_negative_scale_table_commutative_resultright. (((F) = (((((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) * S ((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) + ((dst_positive_scale_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright))) + (((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)))) * S ((((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) * S ((dst_positive_code_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright)) + ((dst_positive_scale_table_commutative_resultright) + (dst_positive_scale_table_commutative_resultright))) + (((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)))) + ((((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright))) + (((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) * S ((dst_negative_code_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)) + ((dst_negative_scale_table_commutative_resultright) + (dst_negative_scale_table_commutative_resultright)))))) /\ (forall dst_index_table_commutative_resultright. (exists pvs_le_gap_table_commutative_resultrightdomain. pvs_le_gap_table_commutative_resultrightdomain + (dst_index_table_commutative_resultright) = (N)) -> exists dst_positive_table_commutative_resultright dst_negative_table_commutative_resultright dst_value_table_commutative_resultright. ((((exists ff_h_pvs_table_commutative_resultrightentrypositive. ff_h_pvs_table_commutative_resultrightentrypositive + S (dst_positive_table_commutative_resultright) = S ((S (dst_index_table_commutative_resultright)) * dst_positive_scale_table_commutative_resultright)) /\ exists ff_q_pvs_table_commutative_resultrightentrypositive. dst_positive_code_table_commutative_resultright = ff_q_pvs_table_commutative_resultrightentrypositive * S ((S (dst_index_table_commutative_resultright)) * dst_positive_scale_table_commutative_resultright) + (dst_positive_table_commutative_resultright))) /\ (((((exists ff_h_pvs_table_commutative_resultrightentrynegative. ff_h_pvs_table_commutative_resultrightentrynegative + S (dst_negative_table_commutative_resultright) = S ((S (dst_index_table_commutative_resultright)) * dst_negative_scale_table_commutative_resultright)) /\ exists ff_q_pvs_table_commutative_resultrightentrynegative. dst_negative_code_table_commutative_resultright = ff_q_pvs_table_commutative_resultrightentrynegative * S ((S (dst_index_table_commutative_resultright)) * dst_negative_scale_table_commutative_resultright) + (dst_negative_table_commutative_resultright))) /\ (exists ge_balance_positive_table_commutative_resultrightentryvalue ge_balance_negative_table_commutative_resultrightentryvalue. (((((dst_value_table_commutative_resultright) = 2 * (ge_balance_positive_table_commutative_resultrightentryvalue) /\ (ge_balance_negative_table_commutative_resultrightentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resultrightentryvaluedecode. (((dst_value_table_commutative_resultright) = 2 * ge_signed_half_table_commutative_resultrightentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultrightentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resultrightentryvalue) = S ge_signed_half_table_commutative_resultrightentryvaluedecode))) /\ ((dst_positive_table_commutative_resultright) + ge_balance_negative_table_commutative_resultrightentryvalue = (dst_negative_table_commutative_resultright) + ge_balance_positive_table_commutative_resultrightentryvalue))))))))) /\ (((exists dst_positive_code_table_commutative_resulttable dst_positive_scale_table_commutative_resulttable dst_negative_code_table_commutative_resulttable dst_negative_scale_table_commutative_resulttable. (((H) = (((((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) * S ((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) + ((dst_positive_scale_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable))) + (((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)))) * S ((((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) * S ((dst_positive_code_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable)) + ((dst_positive_scale_table_commutative_resulttable) + (dst_positive_scale_table_commutative_resulttable))) + (((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)))) + ((((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable))) + (((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) * S ((dst_negative_code_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)) + ((dst_negative_scale_table_commutative_resulttable) + (dst_negative_scale_table_commutative_resulttable)))))) /\ (forall dst_index_table_commutative_resulttable. (exists pvs_le_gap_table_commutative_resulttabledomain. pvs_le_gap_table_commutative_resulttabledomain + (dst_index_table_commutative_resulttable) = (N)) -> exists dst_positive_table_commutative_resulttable dst_negative_table_commutative_resulttable dst_value_table_commutative_resulttable. ((((exists ff_h_pvs_table_commutative_resulttableentrypositive. ff_h_pvs_table_commutative_resulttableentrypositive + S (dst_positive_table_commutative_resulttable) = S ((S (dst_index_table_commutative_resulttable)) * dst_positive_scale_table_commutative_resulttable)) /\ exists ff_q_pvs_table_commutative_resulttableentrypositive. dst_positive_code_table_commutative_resulttable = ff_q_pvs_table_commutative_resulttableentrypositive * S ((S (dst_index_table_commutative_resulttable)) * dst_positive_scale_table_commutative_resulttable) + (dst_positive_table_commutative_resulttable))) /\ (((((exists ff_h_pvs_table_commutative_resulttableentrynegative. ff_h_pvs_table_commutative_resulttableentrynegative + S (dst_negative_table_commutative_resulttable) = S ((S (dst_index_table_commutative_resulttable)) * dst_negative_scale_table_commutative_resulttable)) /\ exists ff_q_pvs_table_commutative_resulttableentrynegative. dst_negative_code_table_commutative_resulttable = ff_q_pvs_table_commutative_resulttableentrynegative * S ((S (dst_index_table_commutative_resulttable)) * dst_negative_scale_table_commutative_resulttable) + (dst_negative_table_commutative_resulttable))) /\ (exists ge_balance_positive_table_commutative_resulttableentryvalue ge_balance_negative_table_commutative_resulttableentryvalue. (((((dst_value_table_commutative_resulttable) = 2 * (ge_balance_positive_table_commutative_resulttableentryvalue) /\ (ge_balance_negative_table_commutative_resulttableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resulttableentryvaluedecode. (((dst_value_table_commutative_resulttable) = 2 * ge_signed_half_table_commutative_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resulttableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resulttableentryvalue) = S ge_signed_half_table_commutative_resulttableentryvaluedecode))) /\ ((dst_positive_table_commutative_resulttable) + ge_balance_negative_table_commutative_resulttableentryvalue = (dst_negative_table_commutative_resulttable) + ge_balance_positive_table_commutative_resulttableentryvalue))))))))) /\ (forall dc_input_table_commutative_result dc_output_table_commutative_result. ~(dc_input_table_commutative_result=0) -> (exists pvs_le_gap_table_commutative_resultdomain. pvs_le_gap_table_commutative_resultdomain + (dc_input_table_commutative_result) = (N)) -> (exists dst_positive_code_table_commutative_resultlookup dst_positive_scale_table_commutative_resultlookup dst_negative_code_table_commutative_resultlookup dst_negative_scale_table_commutative_resultlookup dst_positive_table_commutative_resultlookup dst_negative_table_commutative_resultlookup. (((H) = (((((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) * S ((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) + ((dst_positive_scale_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup))) + (((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)))) * S ((((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) * S ((dst_positive_code_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup)) + ((dst_positive_scale_table_commutative_resultlookup) + (dst_positive_scale_table_commutative_resultlookup))) + (((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)))) + ((((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup))) + (((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) * S ((dst_negative_code_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)) + ((dst_negative_scale_table_commutative_resultlookup) + (dst_negative_scale_table_commutative_resultlookup)))))) /\ (((((exists ff_h_pvs_table_commutative_resultlookuppositive. ff_h_pvs_table_commutative_resultlookuppositive + S (dst_positive_table_commutative_resultlookup) = S ((S (dc_input_table_commutative_result)) * dst_positive_scale_table_commutative_resultlookup)) /\ exists ff_q_pvs_table_commutative_resultlookuppositive. dst_positive_code_table_commutative_resultlookup = ff_q_pvs_table_commutative_resultlookuppositive * S ((S (dc_input_table_commutative_result)) * dst_positive_scale_table_commutative_resultlookup) + (dst_positive_table_commutative_resultlookup))) /\ (((((exists ff_h_pvs_table_commutative_resultlookupnegative. ff_h_pvs_table_commutative_resultlookupnegative + S (dst_negative_table_commutative_resultlookup) = S ((S (dc_input_table_commutative_result)) * dst_negative_scale_table_commutative_resultlookup)) /\ exists ff_q_pvs_table_commutative_resultlookupnegative. dst_negative_code_table_commutative_resultlookup = ff_q_pvs_table_commutative_resultlookupnegative * S ((S (dc_input_table_commutative_result)) * dst_negative_scale_table_commutative_resultlookup) + (dst_negative_table_commutative_resultlookup))) /\ (exists ge_balance_positive_table_commutative_resultlookupvalue ge_balance_negative_table_commutative_resultlookupvalue. (((((dc_output_table_commutative_result) = 2 * (ge_balance_positive_table_commutative_resultlookupvalue) /\ (ge_balance_negative_table_commutative_resultlookupvalue) = 0) \/ exists ge_signed_half_table_commutative_resultlookupvaluedecode. (((dc_output_table_commutative_result) = 2 * ge_signed_half_table_commutative_resultlookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultlookupvalue) = 0) /\ (ge_balance_negative_table_commutative_resultlookupvalue) = S ge_signed_half_table_commutative_resultlookupvaluedecode))) /\ ((dst_positive_table_commutative_resultlookup) + ge_balance_negative_table_commutative_resultlookupvalue = (dst_negative_table_commutative_resultlookup) + ge_balance_positive_table_commutative_resultlookupvalue))))))))) -> (((~((dc_input_table_commutative_result)=0)) /\ (exists dc_mask_table_commutative_resultvalue. ((((exists dst_positive_code_table_commutative_resultvaluemasktable dst_positive_scale_table_commutative_resultvaluemasktable dst_negative_code_table_commutative_resultvaluemasktable dst_negative_scale_table_commutative_resultvaluemasktable. (((dc_mask_table_commutative_resultvalue) = (((((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) * S ((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) + ((dst_positive_scale_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable))) + (((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)))) * S ((((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) * S ((dst_positive_code_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable)) + ((dst_positive_scale_table_commutative_resultvaluemasktable) + (dst_positive_scale_table_commutative_resultvaluemasktable))) + (((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)))) + ((((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable))) + (((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) * S ((dst_negative_code_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)) + ((dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_scale_table_commutative_resultvaluemasktable)))))) /\ (forall dst_index_table_commutative_resultvaluemasktable. (exists pvs_le_gap_table_commutative_resultvaluemasktabledomain. pvs_le_gap_table_commutative_resultvaluemasktabledomain + (dst_index_table_commutative_resultvaluemasktable) = (dc_input_table_commutative_result)) -> exists dst_positive_table_commutative_resultvaluemasktable dst_negative_table_commutative_resultvaluemasktable dst_value_table_commutative_resultvaluemasktable. ((((exists ff_h_pvs_table_commutative_resultvaluemasktableentrypositive. ff_h_pvs_table_commutative_resultvaluemasktableentrypositive + S (dst_positive_table_commutative_resultvaluemasktable) = S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_positive_scale_table_commutative_resultvaluemasktable)) /\ exists ff_q_pvs_table_commutative_resultvaluemasktableentrypositive. dst_positive_code_table_commutative_resultvaluemasktable = ff_q_pvs_table_commutative_resultvaluemasktableentrypositive * S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_positive_scale_table_commutative_resultvaluemasktable) + (dst_positive_table_commutative_resultvaluemasktable))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemasktableentrynegative. ff_h_pvs_table_commutative_resultvaluemasktableentrynegative + S (dst_negative_table_commutative_resultvaluemasktable) = S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_negative_scale_table_commutative_resultvaluemasktable)) /\ exists ff_q_pvs_table_commutative_resultvaluemasktableentrynegative. dst_negative_code_table_commutative_resultvaluemasktable = ff_q_pvs_table_commutative_resultvaluemasktableentrynegative * S ((S (dst_index_table_commutative_resultvaluemasktable)) * dst_negative_scale_table_commutative_resultvaluemasktable) + (dst_negative_table_commutative_resultvaluemasktable))) /\ (exists ge_balance_positive_table_commutative_resultvaluemasktableentryvalue ge_balance_negative_table_commutative_resultvaluemasktableentryvalue. (((((dst_value_table_commutative_resultvaluemasktable) = 2 * (ge_balance_positive_table_commutative_resultvaluemasktableentryvalue) /\ (ge_balance_negative_table_commutative_resultvaluemasktableentryvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemasktableentryvaluedecode. (((dst_value_table_commutative_resultvaluemasktable) = 2 * ge_signed_half_table_commutative_resultvaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemasktableentryvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemasktableentryvalue) = S ge_signed_half_table_commutative_resultvaluemasktableentryvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemasktable) + ge_balance_negative_table_commutative_resultvaluemasktableentryvalue = (dst_negative_table_commutative_resultvaluemasktable) + ge_balance_positive_table_commutative_resultvaluemasktableentryvalue))))))))) /\ (forall dc_index_table_commutative_resultvaluemask dc_value_table_commutative_resultvaluemask. (exists pvs_le_gap_table_commutative_resultvaluemaskdomain. pvs_le_gap_table_commutative_resultvaluemaskdomain + (dc_index_table_commutative_resultvaluemask) = (dc_input_table_commutative_result)) -> (exists dst_positive_code_table_commutative_resultvaluemasklookup dst_positive_scale_table_commutative_resultvaluemasklookup dst_negative_code_table_commutative_resultvaluemasklookup dst_negative_scale_table_commutative_resultvaluemasklookup dst_positive_table_commutative_resultvaluemasklookup dst_negative_table_commutative_resultvaluemasklookup. (((dc_mask_table_commutative_resultvalue) = (((((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) * S ((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) + ((dst_positive_scale_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup))) + (((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)))) * S ((((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) * S ((dst_positive_code_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup)) + ((dst_positive_scale_table_commutative_resultvaluemasklookup) + (dst_positive_scale_table_commutative_resultvaluemasklookup))) + (((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)))) + ((((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup))) + (((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) * S ((dst_negative_code_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)) + ((dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_scale_table_commutative_resultvaluemasklookup)))))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemasklookuppositive. ff_h_pvs_table_commutative_resultvaluemasklookuppositive + S (dst_positive_table_commutative_resultvaluemasklookup) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemasklookup)) /\ exists ff_q_pvs_table_commutative_resultvaluemasklookuppositive. dst_positive_code_table_commutative_resultvaluemasklookup = ff_q_pvs_table_commutative_resultvaluemasklookuppositive * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemasklookup) + (dst_positive_table_commutative_resultvaluemasklookup))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemasklookupnegative. ff_h_pvs_table_commutative_resultvaluemasklookupnegative + S (dst_negative_table_commutative_resultvaluemasklookup) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemasklookup)) /\ exists ff_q_pvs_table_commutative_resultvaluemasklookupnegative. dst_negative_code_table_commutative_resultvaluemasklookup = ff_q_pvs_table_commutative_resultvaluemasklookupnegative * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemasklookup) + (dst_negative_table_commutative_resultvaluemasklookup))) /\ (exists ge_balance_positive_table_commutative_resultvaluemasklookupvalue ge_balance_negative_table_commutative_resultvaluemasklookupvalue. (((((dc_value_table_commutative_resultvaluemask) = 2 * (ge_balance_positive_table_commutative_resultvaluemasklookupvalue) /\ (ge_balance_negative_table_commutative_resultvaluemasklookupvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemasklookupvaluedecode. (((dc_value_table_commutative_resultvaluemask) = 2 * ge_signed_half_table_commutative_resultvaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemasklookupvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemasklookupvalue) = S ge_signed_half_table_commutative_resultvaluemasklookupvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemasklookup) + ge_balance_negative_table_commutative_resultvaluemasklookupvalue = (dst_negative_table_commutative_resultvaluemasklookup) + ge_balance_positive_table_commutative_resultvaluemasklookupvalue))))))))) -> ((((~((dc_index_table_commutative_resultvaluemask)=0)) /\ (exists dc_quotient_table_commutative_resultvaluemaskentry dc_left_table_commutative_resultvaluemaskentry dc_right_table_commutative_resultvaluemaskentry. (((dc_input_table_commutative_result)=(dc_index_table_commutative_resultvaluemask)*dc_quotient_table_commutative_resultvaluemaskentry) /\ (((exists dst_positive_code_table_commutative_resultvaluemaskentryleft dst_positive_scale_table_commutative_resultvaluemaskentryleft dst_negative_code_table_commutative_resultvaluemaskentryleft dst_negative_scale_table_commutative_resultvaluemaskentryleft dst_positive_table_commutative_resultvaluemaskentryleft dst_negative_table_commutative_resultvaluemaskentryleft. (((G) = (((((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft))) + (((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)))) * S ((((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryleft) + (dst_positive_scale_table_commutative_resultvaluemaskentryleft))) + (((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)))) + ((((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft))) + (((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_scale_table_commutative_resultvaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryleftpositive. ff_h_pvs_table_commutative_resultvaluemaskentryleftpositive + S (dst_positive_table_commutative_resultvaluemaskentryleft) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryleftpositive. dst_positive_code_table_commutative_resultvaluemaskentryleft = ff_q_pvs_table_commutative_resultvaluemaskentryleftpositive * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_positive_scale_table_commutative_resultvaluemaskentryleft) + (dst_positive_table_commutative_resultvaluemaskentryleft))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryleftnegative. ff_h_pvs_table_commutative_resultvaluemaskentryleftnegative + S (dst_negative_table_commutative_resultvaluemaskentryleft) = S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemaskentryleft)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryleftnegative. dst_negative_code_table_commutative_resultvaluemaskentryleft = ff_q_pvs_table_commutative_resultvaluemaskentryleftnegative * S ((S (dc_index_table_commutative_resultvaluemask)) * dst_negative_scale_table_commutative_resultvaluemaskentryleft) + (dst_negative_table_commutative_resultvaluemaskentryleft))) /\ (exists ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue. (((((dc_left_table_commutative_resultvaluemaskentry) = 2 * (ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryleftvaluedecode. (((dc_left_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue) = S ge_signed_half_table_commutative_resultvaluemaskentryleftvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemaskentryleft) + ge_balance_negative_table_commutative_resultvaluemaskentryleftvalue = (dst_negative_table_commutative_resultvaluemaskentryleft) + ge_balance_positive_table_commutative_resultvaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_commutative_resultvaluemaskentryright dst_positive_scale_table_commutative_resultvaluemaskentryright dst_negative_code_table_commutative_resultvaluemaskentryright dst_negative_scale_table_commutative_resultvaluemaskentryright dst_positive_table_commutative_resultvaluemaskentryright dst_negative_table_commutative_resultvaluemaskentryright. (((F) = (((((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright))) + (((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)))) * S ((((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_positive_code_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright)) + ((dst_positive_scale_table_commutative_resultvaluemaskentryright) + (dst_positive_scale_table_commutative_resultvaluemaskentryright))) + (((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)))) + ((((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright))) + (((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) * S ((dst_negative_code_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)) + ((dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_scale_table_commutative_resultvaluemaskentryright)))))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryrightpositive. ff_h_pvs_table_commutative_resultvaluemaskentryrightpositive + S (dst_positive_table_commutative_resultvaluemaskentryright) = S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_positive_scale_table_commutative_resultvaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryrightpositive. dst_positive_code_table_commutative_resultvaluemaskentryright = ff_q_pvs_table_commutative_resultvaluemaskentryrightpositive * S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_positive_scale_table_commutative_resultvaluemaskentryright) + (dst_positive_table_commutative_resultvaluemaskentryright))) /\ (((((exists ff_h_pvs_table_commutative_resultvaluemaskentryrightnegative. ff_h_pvs_table_commutative_resultvaluemaskentryrightnegative + S (dst_negative_table_commutative_resultvaluemaskentryright) = S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_negative_scale_table_commutative_resultvaluemaskentryright)) /\ exists ff_q_pvs_table_commutative_resultvaluemaskentryrightnegative. dst_negative_code_table_commutative_resultvaluemaskentryright = ff_q_pvs_table_commutative_resultvaluemaskentryrightnegative * S ((S (dc_quotient_table_commutative_resultvaluemaskentry)) * dst_negative_scale_table_commutative_resultvaluemaskentryright) + (dst_negative_table_commutative_resultvaluemaskentryright))) /\ (exists ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue. (((((dc_right_table_commutative_resultvaluemaskentry) = 2 * (ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryrightvaluedecode. (((dc_right_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue) = S ge_signed_half_table_commutative_resultvaluemaskentryrightvaluedecode))) /\ ((dst_positive_table_commutative_resultvaluemaskentryright) + ge_balance_negative_table_commutative_resultvaluemaskentryrightvalue = (dst_negative_table_commutative_resultvaluemaskentryright) + ge_balance_positive_table_commutative_resultvaluemaskentryrightvalue))))))))) /\ (exists sto_ap_table_commutative_resultvaluemaskentryproduct sto_an_table_commutative_resultvaluemaskentryproduct sto_bp_table_commutative_resultvaluemaskentryproduct sto_bn_table_commutative_resultvaluemaskentryproduct sto_cp_table_commutative_resultvaluemaskentryproduct sto_cn_table_commutative_resultvaluemaskentryproduct. (((((dc_left_table_commutative_resultvaluemaskentry) = 2 * (sto_ap_table_commutative_resultvaluemaskentryproduct) /\ (sto_an_table_commutative_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryproductleft. (((dc_left_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryproductleft + 1 /\ (sto_ap_table_commutative_resultvaluemaskentryproduct) = 0) /\ (sto_an_table_commutative_resultvaluemaskentryproduct) = S ge_signed_half_table_commutative_resultvaluemaskentryproductleft))) /\ ((((((dc_right_table_commutative_resultvaluemaskentry) = 2 * (sto_bp_table_commutative_resultvaluemaskentryproduct) /\ (sto_bn_table_commutative_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryproductright. (((dc_right_table_commutative_resultvaluemaskentry) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryproductright + 1 /\ (sto_bp_table_commutative_resultvaluemaskentryproduct) = 0) /\ (sto_bn_table_commutative_resultvaluemaskentryproduct) = S ge_signed_half_table_commutative_resultvaluemaskentryproductright))) /\ ((((((dc_value_table_commutative_resultvaluemask) = 2 * (sto_cp_table_commutative_resultvaluemaskentryproduct) /\ (sto_cn_table_commutative_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_commutative_resultvaluemaskentryproductoutput. (((dc_value_table_commutative_resultvaluemask) = 2 * ge_signed_half_table_commutative_resultvaluemaskentryproductoutput + 1 /\ (sto_cp_table_commutative_resultvaluemaskentryproduct) = 0) /\ (sto_cn_table_commutative_resultvaluemaskentryproduct) = S ge_signed_half_table_commutative_resultvaluemaskentryproductoutput))) /\ ((sto_ap_table_commutative_resultvaluemaskentryproduct * sto_bp_table_commutative_resultvaluemaskentryproduct + sto_an_table_commutative_resultvaluemaskentryproduct * sto_bn_table_commutative_resultvaluemaskentryproduct) + sto_cn_table_commutative_resultvaluemaskentryproduct = (sto_ap_table_commutative_resultvaluemaskentryproduct * sto_bn_table_commutative_resultvaluemaskentryproduct + sto_an_table_commutative_resultvaluemaskentryproduct * sto_bp_table_commutative_resultvaluemaskentryproduct) + sto_cp_table_commutative_resultvaluemaskentryproduct))))))))))))))) \/ ((((dc_index_table_commutative_resultvaluemask)=0 \/ ~(exists pvs_factor_table_commutative_resultvaluemaskentrynondivisor. (dc_input_table_commutative_result) = (dc_index_table_commutative_resultvaluemask) * pvs_factor_table_commutative_resultvaluemaskentrynondivisor)) /\ ((dc_value_table_commutative_resultvaluemask)=0))))))) /\ (exists dst_positive_code_table_commutative_resultvaluefold dst_positive_scale_table_commutative_resultvaluefold dst_negative_code_table_commutative_resultvaluefold dst_negative_scale_table_commutative_resultvaluefold dst_positive_sum_table_commutative_resultvaluefold dst_negative_sum_table_commutative_resultvaluefold. (((dc_mask_table_commutative_resultvalue) = (((((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) * S ((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) + ((dst_positive_scale_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold))) + (((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)))) * S ((((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) * S ((dst_positive_code_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold)) + ((dst_positive_scale_table_commutative_resultvaluefold) + (dst_positive_scale_table_commutative_resultvaluefold))) + (((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)))) + ((((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold))) + (((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) * S ((dst_negative_code_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)) + ((dst_negative_scale_table_commutative_resultvaluefold) + (dst_negative_scale_table_commutative_resultvaluefold)))))) /\ (((exists fs_u_dst_table_commutative_resultvaluefoldpositive fs_v_dst_table_commutative_resultvaluefoldpositive. ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_start. fs_h_dst_table_commutative_resultvaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_start. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_terminal. fs_h_dst_table_commutative_resultvaluefoldpositive_body_terminal + S (dst_positive_sum_table_commutative_resultvaluefold) = S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_terminal. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_terminal * S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (dst_positive_sum_table_commutative_resultvaluefold))) /\ forall fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps. (exists fs_lt_dst_table_commutative_resultvaluefoldpositive_body_steps_bound. fs_lt_dst_table_commutative_resultvaluefoldpositive_body_steps_bound + S fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps = S (dc_input_table_commutative_result)) -> exists fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps. ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_summand. fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_summand + S (fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_resultvaluefold)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_summand. dst_positive_code_table_commutative_resultvaluefold = fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * dst_positive_scale_table_commutative_resultvaluefold) + (fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_partial. fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_partial + S (fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_partial. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_successor. fs_h_dst_table_commutative_resultvaluefoldpositive_body_steps_successor + S (fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps) = S ((S (S fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive)) /\ exists fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_successor. fs_u_dst_table_commutative_resultvaluefoldpositive = fs_q_dst_table_commutative_resultvaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_commutative_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldpositive) + (fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps))) /\ fs_s_dst_table_commutative_resultvaluefoldpositive_body_steps = fs_r_dst_table_commutative_resultvaluefoldpositive_body_steps + fs_a_dst_table_commutative_resultvaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_commutative_resultvaluefoldnegative fs_v_dst_table_commutative_resultvaluefoldnegative. ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_start. fs_h_dst_table_commutative_resultvaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_start. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_terminal. fs_h_dst_table_commutative_resultvaluefoldnegative_body_terminal + S (dst_negative_sum_table_commutative_resultvaluefold) = S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_terminal. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_terminal * S ((S (S (dc_input_table_commutative_result))) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (dst_negative_sum_table_commutative_resultvaluefold))) /\ forall fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps. (exists fs_lt_dst_table_commutative_resultvaluefoldnegative_body_steps_bound. fs_lt_dst_table_commutative_resultvaluefoldnegative_body_steps_bound + S fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps = S (dc_input_table_commutative_result)) -> exists fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps. ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_summand. fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_summand + S (fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_resultvaluefold)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_summand. dst_negative_code_table_commutative_resultvaluefold = fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * dst_negative_scale_table_commutative_resultvaluefold) + (fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_partial. fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_partial + S (fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_partial. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_successor. fs_h_dst_table_commutative_resultvaluefoldnegative_body_steps_successor + S (fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps) = S ((S (S fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative)) /\ exists fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_successor. fs_u_dst_table_commutative_resultvaluefoldnegative = fs_q_dst_table_commutative_resultvaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_commutative_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_commutative_resultvaluefoldnegative) + (fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps))) /\ fs_s_dst_table_commutative_resultvaluefoldnegative_body_steps = fs_r_dst_table_commutative_resultvaluefoldnegative_body_steps + fs_a_dst_table_commutative_resultvaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_commutative_resultvaluefoldresult ge_balance_negative_table_commutative_resultvaluefoldresult. (((((dc_output_table_commutative_result) = 2 * (ge_balance_positive_table_commutative_resultvaluefoldresult) /\ (ge_balance_negative_table_commutative_resultvaluefoldresult) = 0) \/ exists ge_signed_half_table_commutative_resultvaluefoldresultdecode. (((dc_output_table_commutative_result) = 2 * ge_signed_half_table_commutative_resultvaluefoldresultdecode + 1 /\ (ge_balance_positive_table_commutative_resultvaluefoldresult) = 0) /\ (ge_balance_negative_table_commutative_resultvaluefoldresult) = S ge_signed_half_table_commutative_resultvaluefoldresultdecode))) /\ ((dst_positive_sum_table_commutative_resultvaluefold) + ge_balance_negative_table_commutative_resultvaluefoldresult = (dst_negative_sum_table_commutative_resultvaluefold) + ge_balance_positive_table_commutative_resultvaluefoldresult))))))))))))))))))))

dirichlet_convolution_table_exists · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F G. (exists dst_positive_code_table_exists_left dst_positive_scale_table_exists_left dst_negative_code_table_exists_left dst_negative_scale_table_exists_left. (((F) = (((((dst_positive_code_table_exists_left) + (dst_positive_scale_table_exists_left)) * S ((dst_positive_code_table_exists_left) + (dst_positive_scale_table_exists_left)) + ((dst_positive_scale_table_exists_left) + (dst_positive_scale_table_exists_left))) + (((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) * S ((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) + ((dst_negative_scale_table_exists_left) + (dst_negative_scale_table_exists_left)))) * S ((((dst_positive_code_table_exists_left) + (dst_positive_scale_table_exists_left)) * S ((dst_positive_code_table_exists_left) + (dst_positive_scale_table_exists_left)) + ((dst_positive_scale_table_exists_left) + (dst_positive_scale_table_exists_left))) + (((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) * S ((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) + ((dst_negative_scale_table_exists_left) + (dst_negative_scale_table_exists_left)))) + ((((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) * S ((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) + ((dst_negative_scale_table_exists_left) + (dst_negative_scale_table_exists_left))) + (((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) * S ((dst_negative_code_table_exists_left) + (dst_negative_scale_table_exists_left)) + ((dst_negative_scale_table_exists_left) + (dst_negative_scale_table_exists_left)))))) /\ (forall dst_index_table_exists_left. (exists pvs_le_gap_table_exists_leftdomain. pvs_le_gap_table_exists_leftdomain + (dst_index_table_exists_left) = (N)) -> exists dst_positive_table_exists_left dst_negative_table_exists_left dst_value_table_exists_left. ((((exists ff_h_pvs_table_exists_leftentrypositive. ff_h_pvs_table_exists_leftentrypositive + S (dst_positive_table_exists_left) = S ((S (dst_index_table_exists_left)) * dst_positive_scale_table_exists_left)) /\ exists ff_q_pvs_table_exists_leftentrypositive. dst_positive_code_table_exists_left = ff_q_pvs_table_exists_leftentrypositive * S ((S (dst_index_table_exists_left)) * dst_positive_scale_table_exists_left) + (dst_positive_table_exists_left))) /\ (((((exists ff_h_pvs_table_exists_leftentrynegative. ff_h_pvs_table_exists_leftentrynegative + S (dst_negative_table_exists_left) = S ((S (dst_index_table_exists_left)) * dst_negative_scale_table_exists_left)) /\ exists ff_q_pvs_table_exists_leftentrynegative. dst_negative_code_table_exists_left = ff_q_pvs_table_exists_leftentrynegative * S ((S (dst_index_table_exists_left)) * dst_negative_scale_table_exists_left) + (dst_negative_table_exists_left))) /\ (exists ge_balance_positive_table_exists_leftentryvalue ge_balance_negative_table_exists_leftentryvalue. (((((dst_value_table_exists_left) = 2 * (ge_balance_positive_table_exists_leftentryvalue) /\ (ge_balance_negative_table_exists_leftentryvalue) = 0) \/ exists ge_signed_half_table_exists_leftentryvaluedecode. (((dst_value_table_exists_left) = 2 * ge_signed_half_table_exists_leftentryvaluedecode + 1 /\ (ge_balance_positive_table_exists_leftentryvalue) = 0) /\ (ge_balance_negative_table_exists_leftentryvalue) = S ge_signed_half_table_exists_leftentryvaluedecode))) /\ ((dst_positive_table_exists_left) + ge_balance_negative_table_exists_leftentryvalue = (dst_negative_table_exists_left) + ge_balance_positive_table_exists_leftentryvalue))))))))) -> (exists dst_positive_code_table_exists_right dst_positive_scale_table_exists_right dst_negative_code_table_exists_right dst_negative_scale_table_exists_right. (((G) = (((((dst_positive_code_table_exists_right) + (dst_positive_scale_table_exists_right)) * S ((dst_positive_code_table_exists_right) + (dst_positive_scale_table_exists_right)) + ((dst_positive_scale_table_exists_right) + (dst_positive_scale_table_exists_right))) + (((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) * S ((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) + ((dst_negative_scale_table_exists_right) + (dst_negative_scale_table_exists_right)))) * S ((((dst_positive_code_table_exists_right) + (dst_positive_scale_table_exists_right)) * S ((dst_positive_code_table_exists_right) + (dst_positive_scale_table_exists_right)) + ((dst_positive_scale_table_exists_right) + (dst_positive_scale_table_exists_right))) + (((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) * S ((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) + ((dst_negative_scale_table_exists_right) + (dst_negative_scale_table_exists_right)))) + ((((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) * S ((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) + ((dst_negative_scale_table_exists_right) + (dst_negative_scale_table_exists_right))) + (((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) * S ((dst_negative_code_table_exists_right) + (dst_negative_scale_table_exists_right)) + ((dst_negative_scale_table_exists_right) + (dst_negative_scale_table_exists_right)))))) /\ (forall dst_index_table_exists_right. (exists pvs_le_gap_table_exists_rightdomain. pvs_le_gap_table_exists_rightdomain + (dst_index_table_exists_right) = (N)) -> exists dst_positive_table_exists_right dst_negative_table_exists_right dst_value_table_exists_right. ((((exists ff_h_pvs_table_exists_rightentrypositive. ff_h_pvs_table_exists_rightentrypositive + S (dst_positive_table_exists_right) = S ((S (dst_index_table_exists_right)) * dst_positive_scale_table_exists_right)) /\ exists ff_q_pvs_table_exists_rightentrypositive. dst_positive_code_table_exists_right = ff_q_pvs_table_exists_rightentrypositive * S ((S (dst_index_table_exists_right)) * dst_positive_scale_table_exists_right) + (dst_positive_table_exists_right))) /\ (((((exists ff_h_pvs_table_exists_rightentrynegative. ff_h_pvs_table_exists_rightentrynegative + S (dst_negative_table_exists_right) = S ((S (dst_index_table_exists_right)) * dst_negative_scale_table_exists_right)) /\ exists ff_q_pvs_table_exists_rightentrynegative. dst_negative_code_table_exists_right = ff_q_pvs_table_exists_rightentrynegative * S ((S (dst_index_table_exists_right)) * dst_negative_scale_table_exists_right) + (dst_negative_table_exists_right))) /\ (exists ge_balance_positive_table_exists_rightentryvalue ge_balance_negative_table_exists_rightentryvalue. (((((dst_value_table_exists_right) = 2 * (ge_balance_positive_table_exists_rightentryvalue) /\ (ge_balance_negative_table_exists_rightentryvalue) = 0) \/ exists ge_signed_half_table_exists_rightentryvaluedecode. (((dst_value_table_exists_right) = 2 * ge_signed_half_table_exists_rightentryvaluedecode + 1 /\ (ge_balance_positive_table_exists_rightentryvalue) = 0) /\ (ge_balance_negative_table_exists_rightentryvalue) = S ge_signed_half_table_exists_rightentryvaluedecode))) /\ ((dst_positive_table_exists_right) + ge_balance_negative_table_exists_rightentryvalue = (dst_negative_table_exists_right) + ge_balance_positive_table_exists_rightentryvalue))))))))) -> exists H. (((exists dst_positive_code_table_exists_resultleft dst_positive_scale_table_exists_resultleft dst_negative_code_table_exists_resultleft dst_negative_scale_table_exists_resultleft. (((F) = (((((dst_positive_code_table_exists_resultleft) + (dst_positive_scale_table_exists_resultleft)) * S ((dst_positive_code_table_exists_resultleft) + (dst_positive_scale_table_exists_resultleft)) + ((dst_positive_scale_table_exists_resultleft) + (dst_positive_scale_table_exists_resultleft))) + (((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) * S ((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) + ((dst_negative_scale_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)))) * S ((((dst_positive_code_table_exists_resultleft) + (dst_positive_scale_table_exists_resultleft)) * S ((dst_positive_code_table_exists_resultleft) + (dst_positive_scale_table_exists_resultleft)) + ((dst_positive_scale_table_exists_resultleft) + (dst_positive_scale_table_exists_resultleft))) + (((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) * S ((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) + ((dst_negative_scale_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)))) + ((((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) * S ((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) + ((dst_negative_scale_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft))) + (((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) * S ((dst_negative_code_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)) + ((dst_negative_scale_table_exists_resultleft) + (dst_negative_scale_table_exists_resultleft)))))) /\ (forall dst_index_table_exists_resultleft. (exists pvs_le_gap_table_exists_resultleftdomain. pvs_le_gap_table_exists_resultleftdomain + (dst_index_table_exists_resultleft) = (N)) -> exists dst_positive_table_exists_resultleft dst_negative_table_exists_resultleft dst_value_table_exists_resultleft. ((((exists ff_h_pvs_table_exists_resultleftentrypositive. ff_h_pvs_table_exists_resultleftentrypositive + S (dst_positive_table_exists_resultleft) = S ((S (dst_index_table_exists_resultleft)) * dst_positive_scale_table_exists_resultleft)) /\ exists ff_q_pvs_table_exists_resultleftentrypositive. dst_positive_code_table_exists_resultleft = ff_q_pvs_table_exists_resultleftentrypositive * S ((S (dst_index_table_exists_resultleft)) * dst_positive_scale_table_exists_resultleft) + (dst_positive_table_exists_resultleft))) /\ (((((exists ff_h_pvs_table_exists_resultleftentrynegative. ff_h_pvs_table_exists_resultleftentrynegative + S (dst_negative_table_exists_resultleft) = S ((S (dst_index_table_exists_resultleft)) * dst_negative_scale_table_exists_resultleft)) /\ exists ff_q_pvs_table_exists_resultleftentrynegative. dst_negative_code_table_exists_resultleft = ff_q_pvs_table_exists_resultleftentrynegative * S ((S (dst_index_table_exists_resultleft)) * dst_negative_scale_table_exists_resultleft) + (dst_negative_table_exists_resultleft))) /\ (exists ge_balance_positive_table_exists_resultleftentryvalue ge_balance_negative_table_exists_resultleftentryvalue. (((((dst_value_table_exists_resultleft) = 2 * (ge_balance_positive_table_exists_resultleftentryvalue) /\ (ge_balance_negative_table_exists_resultleftentryvalue) = 0) \/ exists ge_signed_half_table_exists_resultleftentryvaluedecode. (((dst_value_table_exists_resultleft) = 2 * ge_signed_half_table_exists_resultleftentryvaluedecode + 1 /\ (ge_balance_positive_table_exists_resultleftentryvalue) = 0) /\ (ge_balance_negative_table_exists_resultleftentryvalue) = S ge_signed_half_table_exists_resultleftentryvaluedecode))) /\ ((dst_positive_table_exists_resultleft) + ge_balance_negative_table_exists_resultleftentryvalue = (dst_negative_table_exists_resultleft) + ge_balance_positive_table_exists_resultleftentryvalue))))))))) /\ (((exists dst_positive_code_table_exists_resultright dst_positive_scale_table_exists_resultright dst_negative_code_table_exists_resultright dst_negative_scale_table_exists_resultright. (((G) = (((((dst_positive_code_table_exists_resultright) + (dst_positive_scale_table_exists_resultright)) * S ((dst_positive_code_table_exists_resultright) + (dst_positive_scale_table_exists_resultright)) + ((dst_positive_scale_table_exists_resultright) + (dst_positive_scale_table_exists_resultright))) + (((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) * S ((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) + ((dst_negative_scale_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)))) * S ((((dst_positive_code_table_exists_resultright) + (dst_positive_scale_table_exists_resultright)) * S ((dst_positive_code_table_exists_resultright) + (dst_positive_scale_table_exists_resultright)) + ((dst_positive_scale_table_exists_resultright) + (dst_positive_scale_table_exists_resultright))) + (((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) * S ((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) + ((dst_negative_scale_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)))) + ((((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) * S ((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) + ((dst_negative_scale_table_exists_resultright) + (dst_negative_scale_table_exists_resultright))) + (((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) * S ((dst_negative_code_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)) + ((dst_negative_scale_table_exists_resultright) + (dst_negative_scale_table_exists_resultright)))))) /\ (forall dst_index_table_exists_resultright. (exists pvs_le_gap_table_exists_resultrightdomain. pvs_le_gap_table_exists_resultrightdomain + (dst_index_table_exists_resultright) = (N)) -> exists dst_positive_table_exists_resultright dst_negative_table_exists_resultright dst_value_table_exists_resultright. ((((exists ff_h_pvs_table_exists_resultrightentrypositive. ff_h_pvs_table_exists_resultrightentrypositive + S (dst_positive_table_exists_resultright) = S ((S (dst_index_table_exists_resultright)) * dst_positive_scale_table_exists_resultright)) /\ exists ff_q_pvs_table_exists_resultrightentrypositive. dst_positive_code_table_exists_resultright = ff_q_pvs_table_exists_resultrightentrypositive * S ((S (dst_index_table_exists_resultright)) * dst_positive_scale_table_exists_resultright) + (dst_positive_table_exists_resultright))) /\ (((((exists ff_h_pvs_table_exists_resultrightentrynegative. ff_h_pvs_table_exists_resultrightentrynegative + S (dst_negative_table_exists_resultright) = S ((S (dst_index_table_exists_resultright)) * dst_negative_scale_table_exists_resultright)) /\ exists ff_q_pvs_table_exists_resultrightentrynegative. dst_negative_code_table_exists_resultright = ff_q_pvs_table_exists_resultrightentrynegative * S ((S (dst_index_table_exists_resultright)) * dst_negative_scale_table_exists_resultright) + (dst_negative_table_exists_resultright))) /\ (exists ge_balance_positive_table_exists_resultrightentryvalue ge_balance_negative_table_exists_resultrightentryvalue. (((((dst_value_table_exists_resultright) = 2 * (ge_balance_positive_table_exists_resultrightentryvalue) /\ (ge_balance_negative_table_exists_resultrightentryvalue) = 0) \/ exists ge_signed_half_table_exists_resultrightentryvaluedecode. (((dst_value_table_exists_resultright) = 2 * ge_signed_half_table_exists_resultrightentryvaluedecode + 1 /\ (ge_balance_positive_table_exists_resultrightentryvalue) = 0) /\ (ge_balance_negative_table_exists_resultrightentryvalue) = S ge_signed_half_table_exists_resultrightentryvaluedecode))) /\ ((dst_positive_table_exists_resultright) + ge_balance_negative_table_exists_resultrightentryvalue = (dst_negative_table_exists_resultright) + ge_balance_positive_table_exists_resultrightentryvalue))))))))) /\ (((exists dst_positive_code_table_exists_resulttable dst_positive_scale_table_exists_resulttable dst_negative_code_table_exists_resulttable dst_negative_scale_table_exists_resulttable. (((H) = (((((dst_positive_code_table_exists_resulttable) + (dst_positive_scale_table_exists_resulttable)) * S ((dst_positive_code_table_exists_resulttable) + (dst_positive_scale_table_exists_resulttable)) + ((dst_positive_scale_table_exists_resulttable) + (dst_positive_scale_table_exists_resulttable))) + (((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) * S ((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) + ((dst_negative_scale_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)))) * S ((((dst_positive_code_table_exists_resulttable) + (dst_positive_scale_table_exists_resulttable)) * S ((dst_positive_code_table_exists_resulttable) + (dst_positive_scale_table_exists_resulttable)) + ((dst_positive_scale_table_exists_resulttable) + (dst_positive_scale_table_exists_resulttable))) + (((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) * S ((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) + ((dst_negative_scale_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)))) + ((((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) * S ((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) + ((dst_negative_scale_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable))) + (((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) * S ((dst_negative_code_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)) + ((dst_negative_scale_table_exists_resulttable) + (dst_negative_scale_table_exists_resulttable)))))) /\ (forall dst_index_table_exists_resulttable. (exists pvs_le_gap_table_exists_resulttabledomain. pvs_le_gap_table_exists_resulttabledomain + (dst_index_table_exists_resulttable) = (N)) -> exists dst_positive_table_exists_resulttable dst_negative_table_exists_resulttable dst_value_table_exists_resulttable. ((((exists ff_h_pvs_table_exists_resulttableentrypositive. ff_h_pvs_table_exists_resulttableentrypositive + S (dst_positive_table_exists_resulttable) = S ((S (dst_index_table_exists_resulttable)) * dst_positive_scale_table_exists_resulttable)) /\ exists ff_q_pvs_table_exists_resulttableentrypositive. dst_positive_code_table_exists_resulttable = ff_q_pvs_table_exists_resulttableentrypositive * S ((S (dst_index_table_exists_resulttable)) * dst_positive_scale_table_exists_resulttable) + (dst_positive_table_exists_resulttable))) /\ (((((exists ff_h_pvs_table_exists_resulttableentrynegative. ff_h_pvs_table_exists_resulttableentrynegative + S (dst_negative_table_exists_resulttable) = S ((S (dst_index_table_exists_resulttable)) * dst_negative_scale_table_exists_resulttable)) /\ exists ff_q_pvs_table_exists_resulttableentrynegative. dst_negative_code_table_exists_resulttable = ff_q_pvs_table_exists_resulttableentrynegative * S ((S (dst_index_table_exists_resulttable)) * dst_negative_scale_table_exists_resulttable) + (dst_negative_table_exists_resulttable))) /\ (exists ge_balance_positive_table_exists_resulttableentryvalue ge_balance_negative_table_exists_resulttableentryvalue. (((((dst_value_table_exists_resulttable) = 2 * (ge_balance_positive_table_exists_resulttableentryvalue) /\ (ge_balance_negative_table_exists_resulttableentryvalue) = 0) \/ exists ge_signed_half_table_exists_resulttableentryvaluedecode. (((dst_value_table_exists_resulttable) = 2 * ge_signed_half_table_exists_resulttableentryvaluedecode + 1 /\ (ge_balance_positive_table_exists_resulttableentryvalue) = 0) /\ (ge_balance_negative_table_exists_resulttableentryvalue) = S ge_signed_half_table_exists_resulttableentryvaluedecode))) /\ ((dst_positive_table_exists_resulttable) + ge_balance_negative_table_exists_resulttableentryvalue = (dst_negative_table_exists_resulttable) + ge_balance_positive_table_exists_resulttableentryvalue))))))))) /\ (forall dc_input_table_exists_result dc_output_table_exists_result. ~(dc_input_table_exists_result=0) -> (exists pvs_le_gap_table_exists_resultdomain. pvs_le_gap_table_exists_resultdomain + (dc_input_table_exists_result) = (N)) -> (exists dst_positive_code_table_exists_resultlookup dst_positive_scale_table_exists_resultlookup dst_negative_code_table_exists_resultlookup dst_negative_scale_table_exists_resultlookup dst_positive_table_exists_resultlookup dst_negative_table_exists_resultlookup. (((H) = (((((dst_positive_code_table_exists_resultlookup) + (dst_positive_scale_table_exists_resultlookup)) * S ((dst_positive_code_table_exists_resultlookup) + (dst_positive_scale_table_exists_resultlookup)) + ((dst_positive_scale_table_exists_resultlookup) + (dst_positive_scale_table_exists_resultlookup))) + (((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) * S ((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) + ((dst_negative_scale_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)))) * S ((((dst_positive_code_table_exists_resultlookup) + (dst_positive_scale_table_exists_resultlookup)) * S ((dst_positive_code_table_exists_resultlookup) + (dst_positive_scale_table_exists_resultlookup)) + ((dst_positive_scale_table_exists_resultlookup) + (dst_positive_scale_table_exists_resultlookup))) + (((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) * S ((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) + ((dst_negative_scale_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)))) + ((((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) * S ((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) + ((dst_negative_scale_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup))) + (((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) * S ((dst_negative_code_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)) + ((dst_negative_scale_table_exists_resultlookup) + (dst_negative_scale_table_exists_resultlookup)))))) /\ (((((exists ff_h_pvs_table_exists_resultlookuppositive. ff_h_pvs_table_exists_resultlookuppositive + S (dst_positive_table_exists_resultlookup) = S ((S (dc_input_table_exists_result)) * dst_positive_scale_table_exists_resultlookup)) /\ exists ff_q_pvs_table_exists_resultlookuppositive. dst_positive_code_table_exists_resultlookup = ff_q_pvs_table_exists_resultlookuppositive * S ((S (dc_input_table_exists_result)) * dst_positive_scale_table_exists_resultlookup) + (dst_positive_table_exists_resultlookup))) /\ (((((exists ff_h_pvs_table_exists_resultlookupnegative. ff_h_pvs_table_exists_resultlookupnegative + S (dst_negative_table_exists_resultlookup) = S ((S (dc_input_table_exists_result)) * dst_negative_scale_table_exists_resultlookup)) /\ exists ff_q_pvs_table_exists_resultlookupnegative. dst_negative_code_table_exists_resultlookup = ff_q_pvs_table_exists_resultlookupnegative * S ((S (dc_input_table_exists_result)) * dst_negative_scale_table_exists_resultlookup) + (dst_negative_table_exists_resultlookup))) /\ (exists ge_balance_positive_table_exists_resultlookupvalue ge_balance_negative_table_exists_resultlookupvalue. (((((dc_output_table_exists_result) = 2 * (ge_balance_positive_table_exists_resultlookupvalue) /\ (ge_balance_negative_table_exists_resultlookupvalue) = 0) \/ exists ge_signed_half_table_exists_resultlookupvaluedecode. (((dc_output_table_exists_result) = 2 * ge_signed_half_table_exists_resultlookupvaluedecode + 1 /\ (ge_balance_positive_table_exists_resultlookupvalue) = 0) /\ (ge_balance_negative_table_exists_resultlookupvalue) = S ge_signed_half_table_exists_resultlookupvaluedecode))) /\ ((dst_positive_table_exists_resultlookup) + ge_balance_negative_table_exists_resultlookupvalue = (dst_negative_table_exists_resultlookup) + ge_balance_positive_table_exists_resultlookupvalue))))))))) -> (((~((dc_input_table_exists_result)=0)) /\ (exists dc_mask_table_exists_resultvalue. ((((exists dst_positive_code_table_exists_resultvaluemasktable dst_positive_scale_table_exists_resultvaluemasktable dst_negative_code_table_exists_resultvaluemasktable dst_negative_scale_table_exists_resultvaluemasktable. (((dc_mask_table_exists_resultvalue) = (((((dst_positive_code_table_exists_resultvaluemasktable) + (dst_positive_scale_table_exists_resultvaluemasktable)) * S ((dst_positive_code_table_exists_resultvaluemasktable) + (dst_positive_scale_table_exists_resultvaluemasktable)) + ((dst_positive_scale_table_exists_resultvaluemasktable) + (dst_positive_scale_table_exists_resultvaluemasktable))) + (((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) * S ((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) + ((dst_negative_scale_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)))) * S ((((dst_positive_code_table_exists_resultvaluemasktable) + (dst_positive_scale_table_exists_resultvaluemasktable)) * S ((dst_positive_code_table_exists_resultvaluemasktable) + (dst_positive_scale_table_exists_resultvaluemasktable)) + ((dst_positive_scale_table_exists_resultvaluemasktable) + (dst_positive_scale_table_exists_resultvaluemasktable))) + (((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) * S ((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) + ((dst_negative_scale_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)))) + ((((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) * S ((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) + ((dst_negative_scale_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable))) + (((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) * S ((dst_negative_code_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)) + ((dst_negative_scale_table_exists_resultvaluemasktable) + (dst_negative_scale_table_exists_resultvaluemasktable)))))) /\ (forall dst_index_table_exists_resultvaluemasktable. (exists pvs_le_gap_table_exists_resultvaluemasktabledomain. pvs_le_gap_table_exists_resultvaluemasktabledomain + (dst_index_table_exists_resultvaluemasktable) = (dc_input_table_exists_result)) -> exists dst_positive_table_exists_resultvaluemasktable dst_negative_table_exists_resultvaluemasktable dst_value_table_exists_resultvaluemasktable. ((((exists ff_h_pvs_table_exists_resultvaluemasktableentrypositive. ff_h_pvs_table_exists_resultvaluemasktableentrypositive + S (dst_positive_table_exists_resultvaluemasktable) = S ((S (dst_index_table_exists_resultvaluemasktable)) * dst_positive_scale_table_exists_resultvaluemasktable)) /\ exists ff_q_pvs_table_exists_resultvaluemasktableentrypositive. dst_positive_code_table_exists_resultvaluemasktable = ff_q_pvs_table_exists_resultvaluemasktableentrypositive * S ((S (dst_index_table_exists_resultvaluemasktable)) * dst_positive_scale_table_exists_resultvaluemasktable) + (dst_positive_table_exists_resultvaluemasktable))) /\ (((((exists ff_h_pvs_table_exists_resultvaluemasktableentrynegative. ff_h_pvs_table_exists_resultvaluemasktableentrynegative + S (dst_negative_table_exists_resultvaluemasktable) = S ((S (dst_index_table_exists_resultvaluemasktable)) * dst_negative_scale_table_exists_resultvaluemasktable)) /\ exists ff_q_pvs_table_exists_resultvaluemasktableentrynegative. dst_negative_code_table_exists_resultvaluemasktable = ff_q_pvs_table_exists_resultvaluemasktableentrynegative * S ((S (dst_index_table_exists_resultvaluemasktable)) * dst_negative_scale_table_exists_resultvaluemasktable) + (dst_negative_table_exists_resultvaluemasktable))) /\ (exists ge_balance_positive_table_exists_resultvaluemasktableentryvalue ge_balance_negative_table_exists_resultvaluemasktableentryvalue. (((((dst_value_table_exists_resultvaluemasktable) = 2 * (ge_balance_positive_table_exists_resultvaluemasktableentryvalue) /\ (ge_balance_negative_table_exists_resultvaluemasktableentryvalue) = 0) \/ exists ge_signed_half_table_exists_resultvaluemasktableentryvaluedecode. (((dst_value_table_exists_resultvaluemasktable) = 2 * ge_signed_half_table_exists_resultvaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_exists_resultvaluemasktableentryvalue) = 0) /\ (ge_balance_negative_table_exists_resultvaluemasktableentryvalue) = S ge_signed_half_table_exists_resultvaluemasktableentryvaluedecode))) /\ ((dst_positive_table_exists_resultvaluemasktable) + ge_balance_negative_table_exists_resultvaluemasktableentryvalue = (dst_negative_table_exists_resultvaluemasktable) + ge_balance_positive_table_exists_resultvaluemasktableentryvalue))))))))) /\ (forall dc_index_table_exists_resultvaluemask dc_value_table_exists_resultvaluemask. (exists pvs_le_gap_table_exists_resultvaluemaskdomain. pvs_le_gap_table_exists_resultvaluemaskdomain + (dc_index_table_exists_resultvaluemask) = (dc_input_table_exists_result)) -> (exists dst_positive_code_table_exists_resultvaluemasklookup dst_positive_scale_table_exists_resultvaluemasklookup dst_negative_code_table_exists_resultvaluemasklookup dst_negative_scale_table_exists_resultvaluemasklookup dst_positive_table_exists_resultvaluemasklookup dst_negative_table_exists_resultvaluemasklookup. (((dc_mask_table_exists_resultvalue) = (((((dst_positive_code_table_exists_resultvaluemasklookup) + (dst_positive_scale_table_exists_resultvaluemasklookup)) * S ((dst_positive_code_table_exists_resultvaluemasklookup) + (dst_positive_scale_table_exists_resultvaluemasklookup)) + ((dst_positive_scale_table_exists_resultvaluemasklookup) + (dst_positive_scale_table_exists_resultvaluemasklookup))) + (((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) * S ((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) + ((dst_negative_scale_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)))) * S ((((dst_positive_code_table_exists_resultvaluemasklookup) + (dst_positive_scale_table_exists_resultvaluemasklookup)) * S ((dst_positive_code_table_exists_resultvaluemasklookup) + (dst_positive_scale_table_exists_resultvaluemasklookup)) + ((dst_positive_scale_table_exists_resultvaluemasklookup) + (dst_positive_scale_table_exists_resultvaluemasklookup))) + (((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) * S ((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) + ((dst_negative_scale_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)))) + ((((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) * S ((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) + ((dst_negative_scale_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup))) + (((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) * S ((dst_negative_code_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)) + ((dst_negative_scale_table_exists_resultvaluemasklookup) + (dst_negative_scale_table_exists_resultvaluemasklookup)))))) /\ (((((exists ff_h_pvs_table_exists_resultvaluemasklookuppositive. ff_h_pvs_table_exists_resultvaluemasklookuppositive + S (dst_positive_table_exists_resultvaluemasklookup) = S ((S (dc_index_table_exists_resultvaluemask)) * dst_positive_scale_table_exists_resultvaluemasklookup)) /\ exists ff_q_pvs_table_exists_resultvaluemasklookuppositive. dst_positive_code_table_exists_resultvaluemasklookup = ff_q_pvs_table_exists_resultvaluemasklookuppositive * S ((S (dc_index_table_exists_resultvaluemask)) * dst_positive_scale_table_exists_resultvaluemasklookup) + (dst_positive_table_exists_resultvaluemasklookup))) /\ (((((exists ff_h_pvs_table_exists_resultvaluemasklookupnegative. ff_h_pvs_table_exists_resultvaluemasklookupnegative + S (dst_negative_table_exists_resultvaluemasklookup) = S ((S (dc_index_table_exists_resultvaluemask)) * dst_negative_scale_table_exists_resultvaluemasklookup)) /\ exists ff_q_pvs_table_exists_resultvaluemasklookupnegative. dst_negative_code_table_exists_resultvaluemasklookup = ff_q_pvs_table_exists_resultvaluemasklookupnegative * S ((S (dc_index_table_exists_resultvaluemask)) * dst_negative_scale_table_exists_resultvaluemasklookup) + (dst_negative_table_exists_resultvaluemasklookup))) /\ (exists ge_balance_positive_table_exists_resultvaluemasklookupvalue ge_balance_negative_table_exists_resultvaluemasklookupvalue. (((((dc_value_table_exists_resultvaluemask) = 2 * (ge_balance_positive_table_exists_resultvaluemasklookupvalue) /\ (ge_balance_negative_table_exists_resultvaluemasklookupvalue) = 0) \/ exists ge_signed_half_table_exists_resultvaluemasklookupvaluedecode. (((dc_value_table_exists_resultvaluemask) = 2 * ge_signed_half_table_exists_resultvaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_exists_resultvaluemasklookupvalue) = 0) /\ (ge_balance_negative_table_exists_resultvaluemasklookupvalue) = S ge_signed_half_table_exists_resultvaluemasklookupvaluedecode))) /\ ((dst_positive_table_exists_resultvaluemasklookup) + ge_balance_negative_table_exists_resultvaluemasklookupvalue = (dst_negative_table_exists_resultvaluemasklookup) + ge_balance_positive_table_exists_resultvaluemasklookupvalue))))))))) -> ((((~((dc_index_table_exists_resultvaluemask)=0)) /\ (exists dc_quotient_table_exists_resultvaluemaskentry dc_left_table_exists_resultvaluemaskentry dc_right_table_exists_resultvaluemaskentry. (((dc_input_table_exists_result)=(dc_index_table_exists_resultvaluemask)*dc_quotient_table_exists_resultvaluemaskentry) /\ (((exists dst_positive_code_table_exists_resultvaluemaskentryleft dst_positive_scale_table_exists_resultvaluemaskentryleft dst_negative_code_table_exists_resultvaluemaskentryleft dst_negative_scale_table_exists_resultvaluemaskentryleft dst_positive_table_exists_resultvaluemaskentryleft dst_negative_table_exists_resultvaluemaskentryleft. (((F) = (((((dst_positive_code_table_exists_resultvaluemaskentryleft) + (dst_positive_scale_table_exists_resultvaluemaskentryleft)) * S ((dst_positive_code_table_exists_resultvaluemaskentryleft) + (dst_positive_scale_table_exists_resultvaluemaskentryleft)) + ((dst_positive_scale_table_exists_resultvaluemaskentryleft) + (dst_positive_scale_table_exists_resultvaluemaskentryleft))) + (((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) * S ((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) + ((dst_negative_scale_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)))) * S ((((dst_positive_code_table_exists_resultvaluemaskentryleft) + (dst_positive_scale_table_exists_resultvaluemaskentryleft)) * S ((dst_positive_code_table_exists_resultvaluemaskentryleft) + (dst_positive_scale_table_exists_resultvaluemaskentryleft)) + ((dst_positive_scale_table_exists_resultvaluemaskentryleft) + (dst_positive_scale_table_exists_resultvaluemaskentryleft))) + (((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) * S ((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) + ((dst_negative_scale_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)))) + ((((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) * S ((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) + ((dst_negative_scale_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft))) + (((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) * S ((dst_negative_code_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)) + ((dst_negative_scale_table_exists_resultvaluemaskentryleft) + (dst_negative_scale_table_exists_resultvaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_exists_resultvaluemaskentryleftpositive. ff_h_pvs_table_exists_resultvaluemaskentryleftpositive + S (dst_positive_table_exists_resultvaluemaskentryleft) = S ((S (dc_index_table_exists_resultvaluemask)) * dst_positive_scale_table_exists_resultvaluemaskentryleft)) /\ exists ff_q_pvs_table_exists_resultvaluemaskentryleftpositive. dst_positive_code_table_exists_resultvaluemaskentryleft = ff_q_pvs_table_exists_resultvaluemaskentryleftpositive * S ((S (dc_index_table_exists_resultvaluemask)) * dst_positive_scale_table_exists_resultvaluemaskentryleft) + (dst_positive_table_exists_resultvaluemaskentryleft))) /\ (((((exists ff_h_pvs_table_exists_resultvaluemaskentryleftnegative. ff_h_pvs_table_exists_resultvaluemaskentryleftnegative + S (dst_negative_table_exists_resultvaluemaskentryleft) = S ((S (dc_index_table_exists_resultvaluemask)) * dst_negative_scale_table_exists_resultvaluemaskentryleft)) /\ exists ff_q_pvs_table_exists_resultvaluemaskentryleftnegative. dst_negative_code_table_exists_resultvaluemaskentryleft = ff_q_pvs_table_exists_resultvaluemaskentryleftnegative * S ((S (dc_index_table_exists_resultvaluemask)) * dst_negative_scale_table_exists_resultvaluemaskentryleft) + (dst_negative_table_exists_resultvaluemaskentryleft))) /\ (exists ge_balance_positive_table_exists_resultvaluemaskentryleftvalue ge_balance_negative_table_exists_resultvaluemaskentryleftvalue. (((((dc_left_table_exists_resultvaluemaskentry) = 2 * (ge_balance_positive_table_exists_resultvaluemaskentryleftvalue) /\ (ge_balance_negative_table_exists_resultvaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_exists_resultvaluemaskentryleftvaluedecode. (((dc_left_table_exists_resultvaluemaskentry) = 2 * ge_signed_half_table_exists_resultvaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_exists_resultvaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_exists_resultvaluemaskentryleftvalue) = S ge_signed_half_table_exists_resultvaluemaskentryleftvaluedecode))) /\ ((dst_positive_table_exists_resultvaluemaskentryleft) + ge_balance_negative_table_exists_resultvaluemaskentryleftvalue = (dst_negative_table_exists_resultvaluemaskentryleft) + ge_balance_positive_table_exists_resultvaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_exists_resultvaluemaskentryright dst_positive_scale_table_exists_resultvaluemaskentryright dst_negative_code_table_exists_resultvaluemaskentryright dst_negative_scale_table_exists_resultvaluemaskentryright dst_positive_table_exists_resultvaluemaskentryright dst_negative_table_exists_resultvaluemaskentryright. (((G) = (((((dst_positive_code_table_exists_resultvaluemaskentryright) + (dst_positive_scale_table_exists_resultvaluemaskentryright)) * S ((dst_positive_code_table_exists_resultvaluemaskentryright) + (dst_positive_scale_table_exists_resultvaluemaskentryright)) + ((dst_positive_scale_table_exists_resultvaluemaskentryright) + (dst_positive_scale_table_exists_resultvaluemaskentryright))) + (((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) * S ((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) + ((dst_negative_scale_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)))) * S ((((dst_positive_code_table_exists_resultvaluemaskentryright) + (dst_positive_scale_table_exists_resultvaluemaskentryright)) * S ((dst_positive_code_table_exists_resultvaluemaskentryright) + (dst_positive_scale_table_exists_resultvaluemaskentryright)) + ((dst_positive_scale_table_exists_resultvaluemaskentryright) + (dst_positive_scale_table_exists_resultvaluemaskentryright))) + (((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) * S ((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) + ((dst_negative_scale_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)))) + ((((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) * S ((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) + ((dst_negative_scale_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright))) + (((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) * S ((dst_negative_code_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)) + ((dst_negative_scale_table_exists_resultvaluemaskentryright) + (dst_negative_scale_table_exists_resultvaluemaskentryright)))))) /\ (((((exists ff_h_pvs_table_exists_resultvaluemaskentryrightpositive. ff_h_pvs_table_exists_resultvaluemaskentryrightpositive + S (dst_positive_table_exists_resultvaluemaskentryright) = S ((S (dc_quotient_table_exists_resultvaluemaskentry)) * dst_positive_scale_table_exists_resultvaluemaskentryright)) /\ exists ff_q_pvs_table_exists_resultvaluemaskentryrightpositive. dst_positive_code_table_exists_resultvaluemaskentryright = ff_q_pvs_table_exists_resultvaluemaskentryrightpositive * S ((S (dc_quotient_table_exists_resultvaluemaskentry)) * dst_positive_scale_table_exists_resultvaluemaskentryright) + (dst_positive_table_exists_resultvaluemaskentryright))) /\ (((((exists ff_h_pvs_table_exists_resultvaluemaskentryrightnegative. ff_h_pvs_table_exists_resultvaluemaskentryrightnegative + S (dst_negative_table_exists_resultvaluemaskentryright) = S ((S (dc_quotient_table_exists_resultvaluemaskentry)) * dst_negative_scale_table_exists_resultvaluemaskentryright)) /\ exists ff_q_pvs_table_exists_resultvaluemaskentryrightnegative. dst_negative_code_table_exists_resultvaluemaskentryright = ff_q_pvs_table_exists_resultvaluemaskentryrightnegative * S ((S (dc_quotient_table_exists_resultvaluemaskentry)) * dst_negative_scale_table_exists_resultvaluemaskentryright) + (dst_negative_table_exists_resultvaluemaskentryright))) /\ (exists ge_balance_positive_table_exists_resultvaluemaskentryrightvalue ge_balance_negative_table_exists_resultvaluemaskentryrightvalue. (((((dc_right_table_exists_resultvaluemaskentry) = 2 * (ge_balance_positive_table_exists_resultvaluemaskentryrightvalue) /\ (ge_balance_negative_table_exists_resultvaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_exists_resultvaluemaskentryrightvaluedecode. (((dc_right_table_exists_resultvaluemaskentry) = 2 * ge_signed_half_table_exists_resultvaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_exists_resultvaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_exists_resultvaluemaskentryrightvalue) = S ge_signed_half_table_exists_resultvaluemaskentryrightvaluedecode))) /\ ((dst_positive_table_exists_resultvaluemaskentryright) + ge_balance_negative_table_exists_resultvaluemaskentryrightvalue = (dst_negative_table_exists_resultvaluemaskentryright) + ge_balance_positive_table_exists_resultvaluemaskentryrightvalue))))))))) /\ (exists sto_ap_table_exists_resultvaluemaskentryproduct sto_an_table_exists_resultvaluemaskentryproduct sto_bp_table_exists_resultvaluemaskentryproduct sto_bn_table_exists_resultvaluemaskentryproduct sto_cp_table_exists_resultvaluemaskentryproduct sto_cn_table_exists_resultvaluemaskentryproduct. (((((dc_left_table_exists_resultvaluemaskentry) = 2 * (sto_ap_table_exists_resultvaluemaskentryproduct) /\ (sto_an_table_exists_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_exists_resultvaluemaskentryproductleft. (((dc_left_table_exists_resultvaluemaskentry) = 2 * ge_signed_half_table_exists_resultvaluemaskentryproductleft + 1 /\ (sto_ap_table_exists_resultvaluemaskentryproduct) = 0) /\ (sto_an_table_exists_resultvaluemaskentryproduct) = S ge_signed_half_table_exists_resultvaluemaskentryproductleft))) /\ ((((((dc_right_table_exists_resultvaluemaskentry) = 2 * (sto_bp_table_exists_resultvaluemaskentryproduct) /\ (sto_bn_table_exists_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_exists_resultvaluemaskentryproductright. (((dc_right_table_exists_resultvaluemaskentry) = 2 * ge_signed_half_table_exists_resultvaluemaskentryproductright + 1 /\ (sto_bp_table_exists_resultvaluemaskentryproduct) = 0) /\ (sto_bn_table_exists_resultvaluemaskentryproduct) = S ge_signed_half_table_exists_resultvaluemaskentryproductright))) /\ ((((((dc_value_table_exists_resultvaluemask) = 2 * (sto_cp_table_exists_resultvaluemaskentryproduct) /\ (sto_cn_table_exists_resultvaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_exists_resultvaluemaskentryproductoutput. (((dc_value_table_exists_resultvaluemask) = 2 * ge_signed_half_table_exists_resultvaluemaskentryproductoutput + 1 /\ (sto_cp_table_exists_resultvaluemaskentryproduct) = 0) /\ (sto_cn_table_exists_resultvaluemaskentryproduct) = S ge_signed_half_table_exists_resultvaluemaskentryproductoutput))) /\ ((sto_ap_table_exists_resultvaluemaskentryproduct * sto_bp_table_exists_resultvaluemaskentryproduct + sto_an_table_exists_resultvaluemaskentryproduct * sto_bn_table_exists_resultvaluemaskentryproduct) + sto_cn_table_exists_resultvaluemaskentryproduct = (sto_ap_table_exists_resultvaluemaskentryproduct * sto_bn_table_exists_resultvaluemaskentryproduct + sto_an_table_exists_resultvaluemaskentryproduct * sto_bp_table_exists_resultvaluemaskentryproduct) + sto_cp_table_exists_resultvaluemaskentryproduct))))))))))))))) \/ ((((dc_index_table_exists_resultvaluemask)=0 \/ ~(exists pvs_factor_table_exists_resultvaluemaskentrynondivisor. (dc_input_table_exists_result) = (dc_index_table_exists_resultvaluemask) * pvs_factor_table_exists_resultvaluemaskentrynondivisor)) /\ ((dc_value_table_exists_resultvaluemask)=0))))))) /\ (exists dst_positive_code_table_exists_resultvaluefold dst_positive_scale_table_exists_resultvaluefold dst_negative_code_table_exists_resultvaluefold dst_negative_scale_table_exists_resultvaluefold dst_positive_sum_table_exists_resultvaluefold dst_negative_sum_table_exists_resultvaluefold. (((dc_mask_table_exists_resultvalue) = (((((dst_positive_code_table_exists_resultvaluefold) + (dst_positive_scale_table_exists_resultvaluefold)) * S ((dst_positive_code_table_exists_resultvaluefold) + (dst_positive_scale_table_exists_resultvaluefold)) + ((dst_positive_scale_table_exists_resultvaluefold) + (dst_positive_scale_table_exists_resultvaluefold))) + (((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) * S ((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) + ((dst_negative_scale_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)))) * S ((((dst_positive_code_table_exists_resultvaluefold) + (dst_positive_scale_table_exists_resultvaluefold)) * S ((dst_positive_code_table_exists_resultvaluefold) + (dst_positive_scale_table_exists_resultvaluefold)) + ((dst_positive_scale_table_exists_resultvaluefold) + (dst_positive_scale_table_exists_resultvaluefold))) + (((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) * S ((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) + ((dst_negative_scale_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)))) + ((((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) * S ((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) + ((dst_negative_scale_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold))) + (((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) * S ((dst_negative_code_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)) + ((dst_negative_scale_table_exists_resultvaluefold) + (dst_negative_scale_table_exists_resultvaluefold)))))) /\ (((exists fs_u_dst_table_exists_resultvaluefoldpositive fs_v_dst_table_exists_resultvaluefoldpositive. ((((exists fs_h_dst_table_exists_resultvaluefoldpositive_body_start. fs_h_dst_table_exists_resultvaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_exists_resultvaluefoldpositive)) /\ exists fs_q_dst_table_exists_resultvaluefoldpositive_body_start. fs_u_dst_table_exists_resultvaluefoldpositive = fs_q_dst_table_exists_resultvaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_exists_resultvaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_exists_resultvaluefoldpositive_body_terminal. fs_h_dst_table_exists_resultvaluefoldpositive_body_terminal + S (dst_positive_sum_table_exists_resultvaluefold) = S ((S (S (dc_input_table_exists_result))) * fs_v_dst_table_exists_resultvaluefoldpositive)) /\ exists fs_q_dst_table_exists_resultvaluefoldpositive_body_terminal. fs_u_dst_table_exists_resultvaluefoldpositive = fs_q_dst_table_exists_resultvaluefoldpositive_body_terminal * S ((S (S (dc_input_table_exists_result))) * fs_v_dst_table_exists_resultvaluefoldpositive) + (dst_positive_sum_table_exists_resultvaluefold))) /\ forall fs_i_dst_table_exists_resultvaluefoldpositive_body_steps. (exists fs_lt_dst_table_exists_resultvaluefoldpositive_body_steps_bound. fs_lt_dst_table_exists_resultvaluefoldpositive_body_steps_bound + S fs_i_dst_table_exists_resultvaluefoldpositive_body_steps = S (dc_input_table_exists_result)) -> exists fs_a_dst_table_exists_resultvaluefoldpositive_body_steps fs_r_dst_table_exists_resultvaluefoldpositive_body_steps fs_s_dst_table_exists_resultvaluefoldpositive_body_steps. ((((exists fs_h_dst_table_exists_resultvaluefoldpositive_body_steps_summand. fs_h_dst_table_exists_resultvaluefoldpositive_body_steps_summand + S (fs_a_dst_table_exists_resultvaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_exists_resultvaluefoldpositive_body_steps)) * dst_positive_scale_table_exists_resultvaluefold)) /\ exists fs_q_dst_table_exists_resultvaluefoldpositive_body_steps_summand. dst_positive_code_table_exists_resultvaluefold = fs_q_dst_table_exists_resultvaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_exists_resultvaluefoldpositive_body_steps)) * dst_positive_scale_table_exists_resultvaluefold) + (fs_a_dst_table_exists_resultvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_exists_resultvaluefoldpositive_body_steps_partial. fs_h_dst_table_exists_resultvaluefoldpositive_body_steps_partial + S (fs_r_dst_table_exists_resultvaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_exists_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_exists_resultvaluefoldpositive)) /\ exists fs_q_dst_table_exists_resultvaluefoldpositive_body_steps_partial. fs_u_dst_table_exists_resultvaluefoldpositive = fs_q_dst_table_exists_resultvaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_exists_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_exists_resultvaluefoldpositive) + (fs_r_dst_table_exists_resultvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_exists_resultvaluefoldpositive_body_steps_successor. fs_h_dst_table_exists_resultvaluefoldpositive_body_steps_successor + S (fs_s_dst_table_exists_resultvaluefoldpositive_body_steps) = S ((S (S fs_i_dst_table_exists_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_exists_resultvaluefoldpositive)) /\ exists fs_q_dst_table_exists_resultvaluefoldpositive_body_steps_successor. fs_u_dst_table_exists_resultvaluefoldpositive = fs_q_dst_table_exists_resultvaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_exists_resultvaluefoldpositive_body_steps)) * fs_v_dst_table_exists_resultvaluefoldpositive) + (fs_s_dst_table_exists_resultvaluefoldpositive_body_steps))) /\ fs_s_dst_table_exists_resultvaluefoldpositive_body_steps = fs_r_dst_table_exists_resultvaluefoldpositive_body_steps + fs_a_dst_table_exists_resultvaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_exists_resultvaluefoldnegative fs_v_dst_table_exists_resultvaluefoldnegative. ((((exists fs_h_dst_table_exists_resultvaluefoldnegative_body_start. fs_h_dst_table_exists_resultvaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_exists_resultvaluefoldnegative)) /\ exists fs_q_dst_table_exists_resultvaluefoldnegative_body_start. fs_u_dst_table_exists_resultvaluefoldnegative = fs_q_dst_table_exists_resultvaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_exists_resultvaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_exists_resultvaluefoldnegative_body_terminal. fs_h_dst_table_exists_resultvaluefoldnegative_body_terminal + S (dst_negative_sum_table_exists_resultvaluefold) = S ((S (S (dc_input_table_exists_result))) * fs_v_dst_table_exists_resultvaluefoldnegative)) /\ exists fs_q_dst_table_exists_resultvaluefoldnegative_body_terminal. fs_u_dst_table_exists_resultvaluefoldnegative = fs_q_dst_table_exists_resultvaluefoldnegative_body_terminal * S ((S (S (dc_input_table_exists_result))) * fs_v_dst_table_exists_resultvaluefoldnegative) + (dst_negative_sum_table_exists_resultvaluefold))) /\ forall fs_i_dst_table_exists_resultvaluefoldnegative_body_steps. (exists fs_lt_dst_table_exists_resultvaluefoldnegative_body_steps_bound. fs_lt_dst_table_exists_resultvaluefoldnegative_body_steps_bound + S fs_i_dst_table_exists_resultvaluefoldnegative_body_steps = S (dc_input_table_exists_result)) -> exists fs_a_dst_table_exists_resultvaluefoldnegative_body_steps fs_r_dst_table_exists_resultvaluefoldnegative_body_steps fs_s_dst_table_exists_resultvaluefoldnegative_body_steps. ((((exists fs_h_dst_table_exists_resultvaluefoldnegative_body_steps_summand. fs_h_dst_table_exists_resultvaluefoldnegative_body_steps_summand + S (fs_a_dst_table_exists_resultvaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_exists_resultvaluefoldnegative_body_steps)) * dst_negative_scale_table_exists_resultvaluefold)) /\ exists fs_q_dst_table_exists_resultvaluefoldnegative_body_steps_summand. dst_negative_code_table_exists_resultvaluefold = fs_q_dst_table_exists_resultvaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_exists_resultvaluefoldnegative_body_steps)) * dst_negative_scale_table_exists_resultvaluefold) + (fs_a_dst_table_exists_resultvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_exists_resultvaluefoldnegative_body_steps_partial. fs_h_dst_table_exists_resultvaluefoldnegative_body_steps_partial + S (fs_r_dst_table_exists_resultvaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_exists_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_exists_resultvaluefoldnegative)) /\ exists fs_q_dst_table_exists_resultvaluefoldnegative_body_steps_partial. fs_u_dst_table_exists_resultvaluefoldnegative = fs_q_dst_table_exists_resultvaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_exists_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_exists_resultvaluefoldnegative) + (fs_r_dst_table_exists_resultvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_exists_resultvaluefoldnegative_body_steps_successor. fs_h_dst_table_exists_resultvaluefoldnegative_body_steps_successor + S (fs_s_dst_table_exists_resultvaluefoldnegative_body_steps) = S ((S (S fs_i_dst_table_exists_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_exists_resultvaluefoldnegative)) /\ exists fs_q_dst_table_exists_resultvaluefoldnegative_body_steps_successor. fs_u_dst_table_exists_resultvaluefoldnegative = fs_q_dst_table_exists_resultvaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_exists_resultvaluefoldnegative_body_steps)) * fs_v_dst_table_exists_resultvaluefoldnegative) + (fs_s_dst_table_exists_resultvaluefoldnegative_body_steps))) /\ fs_s_dst_table_exists_resultvaluefoldnegative_body_steps = fs_r_dst_table_exists_resultvaluefoldnegative_body_steps + fs_a_dst_table_exists_resultvaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_exists_resultvaluefoldresult ge_balance_negative_table_exists_resultvaluefoldresult. (((((dc_output_table_exists_result) = 2 * (ge_balance_positive_table_exists_resultvaluefoldresult) /\ (ge_balance_negative_table_exists_resultvaluefoldresult) = 0) \/ exists ge_signed_half_table_exists_resultvaluefoldresultdecode. (((dc_output_table_exists_result) = 2 * ge_signed_half_table_exists_resultvaluefoldresultdecode + 1 /\ (ge_balance_positive_table_exists_resultvaluefoldresult) = 0) /\ (ge_balance_negative_table_exists_resultvaluefoldresult) = S ge_signed_half_table_exists_resultvaluefoldresultdecode))) /\ ((dst_positive_sum_table_exists_resultvaluefold) + ge_balance_negative_table_exists_resultvaluefoldresult = (dst_negative_sum_table_exists_resultvaluefold) + ge_balance_positive_table_exists_resultvaluefoldresult))))))))))))))))))))

dirichlet_convolution_table_lookup · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F G H n. (((exists dst_positive_code_table_lookup_sourceleft dst_positive_scale_table_lookup_sourceleft dst_negative_code_table_lookup_sourceleft dst_negative_scale_table_lookup_sourceleft. (((F) = (((((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) * S ((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) + ((dst_positive_scale_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft))) + (((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)))) * S ((((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) * S ((dst_positive_code_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft)) + ((dst_positive_scale_table_lookup_sourceleft) + (dst_positive_scale_table_lookup_sourceleft))) + (((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)))) + ((((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft))) + (((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) * S ((dst_negative_code_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)) + ((dst_negative_scale_table_lookup_sourceleft) + (dst_negative_scale_table_lookup_sourceleft)))))) /\ (forall dst_index_table_lookup_sourceleft. (exists pvs_le_gap_table_lookup_sourceleftdomain. pvs_le_gap_table_lookup_sourceleftdomain + (dst_index_table_lookup_sourceleft) = (N)) -> exists dst_positive_table_lookup_sourceleft dst_negative_table_lookup_sourceleft dst_value_table_lookup_sourceleft. ((((exists ff_h_pvs_table_lookup_sourceleftentrypositive. ff_h_pvs_table_lookup_sourceleftentrypositive + S (dst_positive_table_lookup_sourceleft) = S ((S (dst_index_table_lookup_sourceleft)) * dst_positive_scale_table_lookup_sourceleft)) /\ exists ff_q_pvs_table_lookup_sourceleftentrypositive. dst_positive_code_table_lookup_sourceleft = ff_q_pvs_table_lookup_sourceleftentrypositive * S ((S (dst_index_table_lookup_sourceleft)) * dst_positive_scale_table_lookup_sourceleft) + (dst_positive_table_lookup_sourceleft))) /\ (((((exists ff_h_pvs_table_lookup_sourceleftentrynegative. ff_h_pvs_table_lookup_sourceleftentrynegative + S (dst_negative_table_lookup_sourceleft) = S ((S (dst_index_table_lookup_sourceleft)) * dst_negative_scale_table_lookup_sourceleft)) /\ exists ff_q_pvs_table_lookup_sourceleftentrynegative. dst_negative_code_table_lookup_sourceleft = ff_q_pvs_table_lookup_sourceleftentrynegative * S ((S (dst_index_table_lookup_sourceleft)) * dst_negative_scale_table_lookup_sourceleft) + (dst_negative_table_lookup_sourceleft))) /\ (exists ge_balance_positive_table_lookup_sourceleftentryvalue ge_balance_negative_table_lookup_sourceleftentryvalue. (((((dst_value_table_lookup_sourceleft) = 2 * (ge_balance_positive_table_lookup_sourceleftentryvalue) /\ (ge_balance_negative_table_lookup_sourceleftentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourceleftentryvaluedecode. (((dst_value_table_lookup_sourceleft) = 2 * ge_signed_half_table_lookup_sourceleftentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourceleftentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourceleftentryvalue) = S ge_signed_half_table_lookup_sourceleftentryvaluedecode))) /\ ((dst_positive_table_lookup_sourceleft) + ge_balance_negative_table_lookup_sourceleftentryvalue = (dst_negative_table_lookup_sourceleft) + ge_balance_positive_table_lookup_sourceleftentryvalue))))))))) /\ (((exists dst_positive_code_table_lookup_sourceright dst_positive_scale_table_lookup_sourceright dst_negative_code_table_lookup_sourceright dst_negative_scale_table_lookup_sourceright. (((G) = (((((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) * S ((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) + ((dst_positive_scale_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright))) + (((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)))) * S ((((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) * S ((dst_positive_code_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright)) + ((dst_positive_scale_table_lookup_sourceright) + (dst_positive_scale_table_lookup_sourceright))) + (((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)))) + ((((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright))) + (((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) * S ((dst_negative_code_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)) + ((dst_negative_scale_table_lookup_sourceright) + (dst_negative_scale_table_lookup_sourceright)))))) /\ (forall dst_index_table_lookup_sourceright. (exists pvs_le_gap_table_lookup_sourcerightdomain. pvs_le_gap_table_lookup_sourcerightdomain + (dst_index_table_lookup_sourceright) = (N)) -> exists dst_positive_table_lookup_sourceright dst_negative_table_lookup_sourceright dst_value_table_lookup_sourceright. ((((exists ff_h_pvs_table_lookup_sourcerightentrypositive. ff_h_pvs_table_lookup_sourcerightentrypositive + S (dst_positive_table_lookup_sourceright) = S ((S (dst_index_table_lookup_sourceright)) * dst_positive_scale_table_lookup_sourceright)) /\ exists ff_q_pvs_table_lookup_sourcerightentrypositive. dst_positive_code_table_lookup_sourceright = ff_q_pvs_table_lookup_sourcerightentrypositive * S ((S (dst_index_table_lookup_sourceright)) * dst_positive_scale_table_lookup_sourceright) + (dst_positive_table_lookup_sourceright))) /\ (((((exists ff_h_pvs_table_lookup_sourcerightentrynegative. ff_h_pvs_table_lookup_sourcerightentrynegative + S (dst_negative_table_lookup_sourceright) = S ((S (dst_index_table_lookup_sourceright)) * dst_negative_scale_table_lookup_sourceright)) /\ exists ff_q_pvs_table_lookup_sourcerightentrynegative. dst_negative_code_table_lookup_sourceright = ff_q_pvs_table_lookup_sourcerightentrynegative * S ((S (dst_index_table_lookup_sourceright)) * dst_negative_scale_table_lookup_sourceright) + (dst_negative_table_lookup_sourceright))) /\ (exists ge_balance_positive_table_lookup_sourcerightentryvalue ge_balance_negative_table_lookup_sourcerightentryvalue. (((((dst_value_table_lookup_sourceright) = 2 * (ge_balance_positive_table_lookup_sourcerightentryvalue) /\ (ge_balance_negative_table_lookup_sourcerightentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcerightentryvaluedecode. (((dst_value_table_lookup_sourceright) = 2 * ge_signed_half_table_lookup_sourcerightentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcerightentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcerightentryvalue) = S ge_signed_half_table_lookup_sourcerightentryvaluedecode))) /\ ((dst_positive_table_lookup_sourceright) + ge_balance_negative_table_lookup_sourcerightentryvalue = (dst_negative_table_lookup_sourceright) + ge_balance_positive_table_lookup_sourcerightentryvalue))))))))) /\ (((exists dst_positive_code_table_lookup_sourcetable dst_positive_scale_table_lookup_sourcetable dst_negative_code_table_lookup_sourcetable dst_negative_scale_table_lookup_sourcetable. (((H) = (((((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) * S ((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) + ((dst_positive_scale_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable))) + (((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)))) * S ((((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) * S ((dst_positive_code_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable)) + ((dst_positive_scale_table_lookup_sourcetable) + (dst_positive_scale_table_lookup_sourcetable))) + (((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)))) + ((((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable))) + (((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) * S ((dst_negative_code_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)) + ((dst_negative_scale_table_lookup_sourcetable) + (dst_negative_scale_table_lookup_sourcetable)))))) /\ (forall dst_index_table_lookup_sourcetable. (exists pvs_le_gap_table_lookup_sourcetabledomain. pvs_le_gap_table_lookup_sourcetabledomain + (dst_index_table_lookup_sourcetable) = (N)) -> exists dst_positive_table_lookup_sourcetable dst_negative_table_lookup_sourcetable dst_value_table_lookup_sourcetable. ((((exists ff_h_pvs_table_lookup_sourcetableentrypositive. ff_h_pvs_table_lookup_sourcetableentrypositive + S (dst_positive_table_lookup_sourcetable) = S ((S (dst_index_table_lookup_sourcetable)) * dst_positive_scale_table_lookup_sourcetable)) /\ exists ff_q_pvs_table_lookup_sourcetableentrypositive. dst_positive_code_table_lookup_sourcetable = ff_q_pvs_table_lookup_sourcetableentrypositive * S ((S (dst_index_table_lookup_sourcetable)) * dst_positive_scale_table_lookup_sourcetable) + (dst_positive_table_lookup_sourcetable))) /\ (((((exists ff_h_pvs_table_lookup_sourcetableentrynegative. ff_h_pvs_table_lookup_sourcetableentrynegative + S (dst_negative_table_lookup_sourcetable) = S ((S (dst_index_table_lookup_sourcetable)) * dst_negative_scale_table_lookup_sourcetable)) /\ exists ff_q_pvs_table_lookup_sourcetableentrynegative. dst_negative_code_table_lookup_sourcetable = ff_q_pvs_table_lookup_sourcetableentrynegative * S ((S (dst_index_table_lookup_sourcetable)) * dst_negative_scale_table_lookup_sourcetable) + (dst_negative_table_lookup_sourcetable))) /\ (exists ge_balance_positive_table_lookup_sourcetableentryvalue ge_balance_negative_table_lookup_sourcetableentryvalue. (((((dst_value_table_lookup_sourcetable) = 2 * (ge_balance_positive_table_lookup_sourcetableentryvalue) /\ (ge_balance_negative_table_lookup_sourcetableentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcetableentryvaluedecode. (((dst_value_table_lookup_sourcetable) = 2 * ge_signed_half_table_lookup_sourcetableentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcetableentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcetableentryvalue) = S ge_signed_half_table_lookup_sourcetableentryvaluedecode))) /\ ((dst_positive_table_lookup_sourcetable) + ge_balance_negative_table_lookup_sourcetableentryvalue = (dst_negative_table_lookup_sourcetable) + ge_balance_positive_table_lookup_sourcetableentryvalue))))))))) /\ (forall dc_input_table_lookup_source dc_output_table_lookup_source. ~(dc_input_table_lookup_source=0) -> (exists pvs_le_gap_table_lookup_sourcedomain. pvs_le_gap_table_lookup_sourcedomain + (dc_input_table_lookup_source) = (N)) -> (exists dst_positive_code_table_lookup_sourcelookup dst_positive_scale_table_lookup_sourcelookup dst_negative_code_table_lookup_sourcelookup dst_negative_scale_table_lookup_sourcelookup dst_positive_table_lookup_sourcelookup dst_negative_table_lookup_sourcelookup. (((H) = (((((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) * S ((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) + ((dst_positive_scale_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup))) + (((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)))) * S ((((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) * S ((dst_positive_code_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup)) + ((dst_positive_scale_table_lookup_sourcelookup) + (dst_positive_scale_table_lookup_sourcelookup))) + (((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)))) + ((((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup))) + (((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) * S ((dst_negative_code_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)) + ((dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_scale_table_lookup_sourcelookup)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcelookuppositive. ff_h_pvs_table_lookup_sourcelookuppositive + S (dst_positive_table_lookup_sourcelookup) = S ((S (dc_input_table_lookup_source)) * dst_positive_scale_table_lookup_sourcelookup)) /\ exists ff_q_pvs_table_lookup_sourcelookuppositive. dst_positive_code_table_lookup_sourcelookup = ff_q_pvs_table_lookup_sourcelookuppositive * S ((S (dc_input_table_lookup_source)) * dst_positive_scale_table_lookup_sourcelookup) + (dst_positive_table_lookup_sourcelookup))) /\ (((((exists ff_h_pvs_table_lookup_sourcelookupnegative. ff_h_pvs_table_lookup_sourcelookupnegative + S (dst_negative_table_lookup_sourcelookup) = S ((S (dc_input_table_lookup_source)) * dst_negative_scale_table_lookup_sourcelookup)) /\ exists ff_q_pvs_table_lookup_sourcelookupnegative. dst_negative_code_table_lookup_sourcelookup = ff_q_pvs_table_lookup_sourcelookupnegative * S ((S (dc_input_table_lookup_source)) * dst_negative_scale_table_lookup_sourcelookup) + (dst_negative_table_lookup_sourcelookup))) /\ (exists ge_balance_positive_table_lookup_sourcelookupvalue ge_balance_negative_table_lookup_sourcelookupvalue. (((((dc_output_table_lookup_source) = 2 * (ge_balance_positive_table_lookup_sourcelookupvalue) /\ (ge_balance_negative_table_lookup_sourcelookupvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcelookupvaluedecode. (((dc_output_table_lookup_source) = 2 * ge_signed_half_table_lookup_sourcelookupvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcelookupvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcelookupvalue) = S ge_signed_half_table_lookup_sourcelookupvaluedecode))) /\ ((dst_positive_table_lookup_sourcelookup) + ge_balance_negative_table_lookup_sourcelookupvalue = (dst_negative_table_lookup_sourcelookup) + ge_balance_positive_table_lookup_sourcelookupvalue))))))))) -> (((~((dc_input_table_lookup_source)=0)) /\ (exists dc_mask_table_lookup_sourcevalue. ((((exists dst_positive_code_table_lookup_sourcevaluemasktable dst_positive_scale_table_lookup_sourcevaluemasktable dst_negative_code_table_lookup_sourcevaluemasktable dst_negative_scale_table_lookup_sourcevaluemasktable. (((dc_mask_table_lookup_sourcevalue) = (((((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) * S ((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) + ((dst_positive_scale_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable))) + (((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)))) * S ((((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) * S ((dst_positive_code_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable)) + ((dst_positive_scale_table_lookup_sourcevaluemasktable) + (dst_positive_scale_table_lookup_sourcevaluemasktable))) + (((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)))) + ((((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable))) + (((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) * S ((dst_negative_code_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)) + ((dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_scale_table_lookup_sourcevaluemasktable)))))) /\ (forall dst_index_table_lookup_sourcevaluemasktable. (exists pvs_le_gap_table_lookup_sourcevaluemasktabledomain. pvs_le_gap_table_lookup_sourcevaluemasktabledomain + (dst_index_table_lookup_sourcevaluemasktable) = (dc_input_table_lookup_source)) -> exists dst_positive_table_lookup_sourcevaluemasktable dst_negative_table_lookup_sourcevaluemasktable dst_value_table_lookup_sourcevaluemasktable. ((((exists ff_h_pvs_table_lookup_sourcevaluemasktableentrypositive. ff_h_pvs_table_lookup_sourcevaluemasktableentrypositive + S (dst_positive_table_lookup_sourcevaluemasktable) = S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_positive_scale_table_lookup_sourcevaluemasktable)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasktableentrypositive. dst_positive_code_table_lookup_sourcevaluemasktable = ff_q_pvs_table_lookup_sourcevaluemasktableentrypositive * S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_positive_scale_table_lookup_sourcevaluemasktable) + (dst_positive_table_lookup_sourcevaluemasktable))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemasktableentrynegative. ff_h_pvs_table_lookup_sourcevaluemasktableentrynegative + S (dst_negative_table_lookup_sourcevaluemasktable) = S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_negative_scale_table_lookup_sourcevaluemasktable)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasktableentrynegative. dst_negative_code_table_lookup_sourcevaluemasktable = ff_q_pvs_table_lookup_sourcevaluemasktableentrynegative * S ((S (dst_index_table_lookup_sourcevaluemasktable)) * dst_negative_scale_table_lookup_sourcevaluemasktable) + (dst_negative_table_lookup_sourcevaluemasktable))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue. (((((dst_value_table_lookup_sourcevaluemasktable) = 2 * (ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemasktableentryvaluedecode. (((dst_value_table_lookup_sourcevaluemasktable) = 2 * ge_signed_half_table_lookup_sourcevaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue) = S ge_signed_half_table_lookup_sourcevaluemasktableentryvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemasktable) + ge_balance_negative_table_lookup_sourcevaluemasktableentryvalue = (dst_negative_table_lookup_sourcevaluemasktable) + ge_balance_positive_table_lookup_sourcevaluemasktableentryvalue))))))))) /\ (forall dc_index_table_lookup_sourcevaluemask dc_value_table_lookup_sourcevaluemask. (exists pvs_le_gap_table_lookup_sourcevaluemaskdomain. pvs_le_gap_table_lookup_sourcevaluemaskdomain + (dc_index_table_lookup_sourcevaluemask) = (dc_input_table_lookup_source)) -> (exists dst_positive_code_table_lookup_sourcevaluemasklookup dst_positive_scale_table_lookup_sourcevaluemasklookup dst_negative_code_table_lookup_sourcevaluemasklookup dst_negative_scale_table_lookup_sourcevaluemasklookup dst_positive_table_lookup_sourcevaluemasklookup dst_negative_table_lookup_sourcevaluemasklookup. (((dc_mask_table_lookup_sourcevalue) = (((((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) + ((dst_positive_scale_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup))) + (((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)))) * S ((((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_positive_code_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup)) + ((dst_positive_scale_table_lookup_sourcevaluemasklookup) + (dst_positive_scale_table_lookup_sourcevaluemasklookup))) + (((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)))) + ((((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup))) + (((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) * S ((dst_negative_code_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)) + ((dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_scale_table_lookup_sourcevaluemasklookup)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemasklookuppositive. ff_h_pvs_table_lookup_sourcevaluemasklookuppositive + S (dst_positive_table_lookup_sourcevaluemasklookup) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasklookuppositive. dst_positive_code_table_lookup_sourcevaluemasklookup = ff_q_pvs_table_lookup_sourcevaluemasklookuppositive * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemasklookup) + (dst_positive_table_lookup_sourcevaluemasklookup))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemasklookupnegative. ff_h_pvs_table_lookup_sourcevaluemasklookupnegative + S (dst_negative_table_lookup_sourcevaluemasklookup) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemasklookup)) /\ exists ff_q_pvs_table_lookup_sourcevaluemasklookupnegative. dst_negative_code_table_lookup_sourcevaluemasklookup = ff_q_pvs_table_lookup_sourcevaluemasklookupnegative * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemasklookup) + (dst_negative_table_lookup_sourcevaluemasklookup))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemasklookupvalue ge_balance_negative_table_lookup_sourcevaluemasklookupvalue. (((((dc_value_table_lookup_sourcevaluemask) = 2 * (ge_balance_positive_table_lookup_sourcevaluemasklookupvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemasklookupvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemasklookupvaluedecode. (((dc_value_table_lookup_sourcevaluemask) = 2 * ge_signed_half_table_lookup_sourcevaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemasklookupvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemasklookupvalue) = S ge_signed_half_table_lookup_sourcevaluemasklookupvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemasklookup) + ge_balance_negative_table_lookup_sourcevaluemasklookupvalue = (dst_negative_table_lookup_sourcevaluemasklookup) + ge_balance_positive_table_lookup_sourcevaluemasklookupvalue))))))))) -> ((((~((dc_index_table_lookup_sourcevaluemask)=0)) /\ (exists dc_quotient_table_lookup_sourcevaluemaskentry dc_left_table_lookup_sourcevaluemaskentry dc_right_table_lookup_sourcevaluemaskentry. (((dc_input_table_lookup_source)=(dc_index_table_lookup_sourcevaluemask)*dc_quotient_table_lookup_sourcevaluemaskentry) /\ (((exists dst_positive_code_table_lookup_sourcevaluemaskentryleft dst_positive_scale_table_lookup_sourcevaluemaskentryleft dst_negative_code_table_lookup_sourcevaluemaskentryleft dst_negative_scale_table_lookup_sourcevaluemaskentryleft dst_positive_table_lookup_sourcevaluemaskentryleft dst_negative_table_lookup_sourcevaluemaskentryleft. (((F) = (((((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)))) * S ((((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryleft) + (dst_positive_scale_table_lookup_sourcevaluemaskentryleft))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)))) + ((((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_scale_table_lookup_sourcevaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryleftpositive. ff_h_pvs_table_lookup_sourcevaluemaskentryleftpositive + S (dst_positive_table_lookup_sourcevaluemaskentryleft) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryleftpositive. dst_positive_code_table_lookup_sourcevaluemaskentryleft = ff_q_pvs_table_lookup_sourcevaluemaskentryleftpositive * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_positive_scale_table_lookup_sourcevaluemaskentryleft) + (dst_positive_table_lookup_sourcevaluemaskentryleft))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryleftnegative. ff_h_pvs_table_lookup_sourcevaluemaskentryleftnegative + S (dst_negative_table_lookup_sourcevaluemaskentryleft) = S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemaskentryleft)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryleftnegative. dst_negative_code_table_lookup_sourcevaluemaskentryleft = ff_q_pvs_table_lookup_sourcevaluemaskentryleftnegative * S ((S (dc_index_table_lookup_sourcevaluemask)) * dst_negative_scale_table_lookup_sourcevaluemaskentryleft) + (dst_negative_table_lookup_sourcevaluemaskentryleft))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue. (((((dc_left_table_lookup_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryleftvaluedecode. (((dc_left_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue) = S ge_signed_half_table_lookup_sourcevaluemaskentryleftvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemaskentryleft) + ge_balance_negative_table_lookup_sourcevaluemaskentryleftvalue = (dst_negative_table_lookup_sourcevaluemaskentryleft) + ge_balance_positive_table_lookup_sourcevaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_lookup_sourcevaluemaskentryright dst_positive_scale_table_lookup_sourcevaluemaskentryright dst_negative_code_table_lookup_sourcevaluemaskentryright dst_negative_scale_table_lookup_sourcevaluemaskentryright dst_positive_table_lookup_sourcevaluemaskentryright dst_negative_table_lookup_sourcevaluemaskentryright. (((G) = (((((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)))) * S ((((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_positive_code_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_positive_scale_table_lookup_sourcevaluemaskentryright) + (dst_positive_scale_table_lookup_sourcevaluemaskentryright))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)))) + ((((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright))) + (((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) * S ((dst_negative_code_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)) + ((dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_scale_table_lookup_sourcevaluemaskentryright)))))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryrightpositive. ff_h_pvs_table_lookup_sourcevaluemaskentryrightpositive + S (dst_positive_table_lookup_sourcevaluemaskentryright) = S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_positive_scale_table_lookup_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryrightpositive. dst_positive_code_table_lookup_sourcevaluemaskentryright = ff_q_pvs_table_lookup_sourcevaluemaskentryrightpositive * S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_positive_scale_table_lookup_sourcevaluemaskentryright) + (dst_positive_table_lookup_sourcevaluemaskentryright))) /\ (((((exists ff_h_pvs_table_lookup_sourcevaluemaskentryrightnegative. ff_h_pvs_table_lookup_sourcevaluemaskentryrightnegative + S (dst_negative_table_lookup_sourcevaluemaskentryright) = S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_negative_scale_table_lookup_sourcevaluemaskentryright)) /\ exists ff_q_pvs_table_lookup_sourcevaluemaskentryrightnegative. dst_negative_code_table_lookup_sourcevaluemaskentryright = ff_q_pvs_table_lookup_sourcevaluemaskentryrightnegative * S ((S (dc_quotient_table_lookup_sourcevaluemaskentry)) * dst_negative_scale_table_lookup_sourcevaluemaskentryright) + (dst_negative_table_lookup_sourcevaluemaskentryright))) /\ (exists ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue. (((((dc_right_table_lookup_sourcevaluemaskentry) = 2 * (ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryrightvaluedecode. (((dc_right_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue) = S ge_signed_half_table_lookup_sourcevaluemaskentryrightvaluedecode))) /\ ((dst_positive_table_lookup_sourcevaluemaskentryright) + ge_balance_negative_table_lookup_sourcevaluemaskentryrightvalue = (dst_negative_table_lookup_sourcevaluemaskentryright) + ge_balance_positive_table_lookup_sourcevaluemaskentryrightvalue))))))))) /\ (exists sto_ap_table_lookup_sourcevaluemaskentryproduct sto_an_table_lookup_sourcevaluemaskentryproduct sto_bp_table_lookup_sourcevaluemaskentryproduct sto_bn_table_lookup_sourcevaluemaskentryproduct sto_cp_table_lookup_sourcevaluemaskentryproduct sto_cn_table_lookup_sourcevaluemaskentryproduct. (((((dc_left_table_lookup_sourcevaluemaskentry) = 2 * (sto_ap_table_lookup_sourcevaluemaskentryproduct) /\ (sto_an_table_lookup_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryproductleft. (((dc_left_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryproductleft + 1 /\ (sto_ap_table_lookup_sourcevaluemaskentryproduct) = 0) /\ (sto_an_table_lookup_sourcevaluemaskentryproduct) = S ge_signed_half_table_lookup_sourcevaluemaskentryproductleft))) /\ ((((((dc_right_table_lookup_sourcevaluemaskentry) = 2 * (sto_bp_table_lookup_sourcevaluemaskentryproduct) /\ (sto_bn_table_lookup_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryproductright. (((dc_right_table_lookup_sourcevaluemaskentry) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryproductright + 1 /\ (sto_bp_table_lookup_sourcevaluemaskentryproduct) = 0) /\ (sto_bn_table_lookup_sourcevaluemaskentryproduct) = S ge_signed_half_table_lookup_sourcevaluemaskentryproductright))) /\ ((((((dc_value_table_lookup_sourcevaluemask) = 2 * (sto_cp_table_lookup_sourcevaluemaskentryproduct) /\ (sto_cn_table_lookup_sourcevaluemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluemaskentryproductoutput. (((dc_value_table_lookup_sourcevaluemask) = 2 * ge_signed_half_table_lookup_sourcevaluemaskentryproductoutput + 1 /\ (sto_cp_table_lookup_sourcevaluemaskentryproduct) = 0) /\ (sto_cn_table_lookup_sourcevaluemaskentryproduct) = S ge_signed_half_table_lookup_sourcevaluemaskentryproductoutput))) /\ ((sto_ap_table_lookup_sourcevaluemaskentryproduct * sto_bp_table_lookup_sourcevaluemaskentryproduct + sto_an_table_lookup_sourcevaluemaskentryproduct * sto_bn_table_lookup_sourcevaluemaskentryproduct) + sto_cn_table_lookup_sourcevaluemaskentryproduct = (sto_ap_table_lookup_sourcevaluemaskentryproduct * sto_bn_table_lookup_sourcevaluemaskentryproduct + sto_an_table_lookup_sourcevaluemaskentryproduct * sto_bp_table_lookup_sourcevaluemaskentryproduct) + sto_cp_table_lookup_sourcevaluemaskentryproduct))))))))))))))) \/ ((((dc_index_table_lookup_sourcevaluemask)=0 \/ ~(exists pvs_factor_table_lookup_sourcevaluemaskentrynondivisor. (dc_input_table_lookup_source) = (dc_index_table_lookup_sourcevaluemask) * pvs_factor_table_lookup_sourcevaluemaskentrynondivisor)) /\ ((dc_value_table_lookup_sourcevaluemask)=0))))))) /\ (exists dst_positive_code_table_lookup_sourcevaluefold dst_positive_scale_table_lookup_sourcevaluefold dst_negative_code_table_lookup_sourcevaluefold dst_negative_scale_table_lookup_sourcevaluefold dst_positive_sum_table_lookup_sourcevaluefold dst_negative_sum_table_lookup_sourcevaluefold. (((dc_mask_table_lookup_sourcevalue) = (((((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) * S ((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) + ((dst_positive_scale_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold))) + (((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)))) * S ((((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) * S ((dst_positive_code_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold)) + ((dst_positive_scale_table_lookup_sourcevaluefold) + (dst_positive_scale_table_lookup_sourcevaluefold))) + (((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)))) + ((((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold))) + (((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) * S ((dst_negative_code_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)) + ((dst_negative_scale_table_lookup_sourcevaluefold) + (dst_negative_scale_table_lookup_sourcevaluefold)))))) /\ (((exists fs_u_dst_table_lookup_sourcevaluefoldpositive fs_v_dst_table_lookup_sourcevaluefoldpositive. ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_start. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_start. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_terminal. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_terminal + S (dst_positive_sum_table_lookup_sourcevaluefold) = S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_terminal. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_terminal * S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (dst_positive_sum_table_lookup_sourcevaluefold))) /\ forall fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps. (exists fs_lt_dst_table_lookup_sourcevaluefoldpositive_body_steps_bound. fs_lt_dst_table_lookup_sourcevaluefoldpositive_body_steps_bound + S fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps = S (dc_input_table_lookup_source)) -> exists fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps. ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand + S (fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_lookup_sourcevaluefold)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand. dst_positive_code_table_lookup_sourcevaluefold = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * dst_positive_scale_table_lookup_sourcevaluefold) + (fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial + S (fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor. fs_h_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor + S (fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps) = S ((S (S fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor. fs_u_dst_table_lookup_sourcevaluefoldpositive = fs_q_dst_table_lookup_sourcevaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_lookup_sourcevaluefoldpositive_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldpositive) + (fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps))) /\ fs_s_dst_table_lookup_sourcevaluefoldpositive_body_steps = fs_r_dst_table_lookup_sourcevaluefoldpositive_body_steps + fs_a_dst_table_lookup_sourcevaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_lookup_sourcevaluefoldnegative fs_v_dst_table_lookup_sourcevaluefoldnegative. ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_start. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_start. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_terminal. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_terminal + S (dst_negative_sum_table_lookup_sourcevaluefold) = S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_terminal. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_terminal * S ((S (S (dc_input_table_lookup_source))) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (dst_negative_sum_table_lookup_sourcevaluefold))) /\ forall fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps. (exists fs_lt_dst_table_lookup_sourcevaluefoldnegative_body_steps_bound. fs_lt_dst_table_lookup_sourcevaluefoldnegative_body_steps_bound + S fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps = S (dc_input_table_lookup_source)) -> exists fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps. ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand + S (fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_lookup_sourcevaluefold)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand. dst_negative_code_table_lookup_sourcevaluefold = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * dst_negative_scale_table_lookup_sourcevaluefold) + (fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial + S (fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor. fs_h_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor + S (fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps) = S ((S (S fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative)) /\ exists fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor. fs_u_dst_table_lookup_sourcevaluefoldnegative = fs_q_dst_table_lookup_sourcevaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_lookup_sourcevaluefoldnegative_body_steps)) * fs_v_dst_table_lookup_sourcevaluefoldnegative) + (fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps))) /\ fs_s_dst_table_lookup_sourcevaluefoldnegative_body_steps = fs_r_dst_table_lookup_sourcevaluefoldnegative_body_steps + fs_a_dst_table_lookup_sourcevaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_lookup_sourcevaluefoldresult ge_balance_negative_table_lookup_sourcevaluefoldresult. (((((dc_output_table_lookup_source) = 2 * (ge_balance_positive_table_lookup_sourcevaluefoldresult) /\ (ge_balance_negative_table_lookup_sourcevaluefoldresult) = 0) \/ exists ge_signed_half_table_lookup_sourcevaluefoldresultdecode. (((dc_output_table_lookup_source) = 2 * ge_signed_half_table_lookup_sourcevaluefoldresultdecode + 1 /\ (ge_balance_positive_table_lookup_sourcevaluefoldresult) = 0) /\ (ge_balance_negative_table_lookup_sourcevaluefoldresult) = S ge_signed_half_table_lookup_sourcevaluefoldresultdecode))) /\ ((dst_positive_sum_table_lookup_sourcevaluefold) + ge_balance_negative_table_lookup_sourcevaluefoldresult = (dst_negative_sum_table_lookup_sourcevaluefold) + ge_balance_positive_table_lookup_sourcevaluefoldresult)))))))))))))))))))) -> ~(n=0) -> (exists pvs_le_gap_table_lookup_bound. pvs_le_gap_table_lookup_bound + (n) = (N)) -> exists z. (exists dst_positive_code_table_lookup_entry dst_positive_scale_table_lookup_entry dst_negative_code_table_lookup_entry dst_negative_scale_table_lookup_entry dst_positive_table_lookup_entry dst_negative_table_lookup_entry. (((H) = (((((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) * S ((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) + ((dst_positive_scale_table_lookup_entry) + (dst_positive_scale_table_lookup_entry))) + (((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)))) * S ((((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) * S ((dst_positive_code_table_lookup_entry) + (dst_positive_scale_table_lookup_entry)) + ((dst_positive_scale_table_lookup_entry) + (dst_positive_scale_table_lookup_entry))) + (((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)))) + ((((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry))) + (((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) * S ((dst_negative_code_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)) + ((dst_negative_scale_table_lookup_entry) + (dst_negative_scale_table_lookup_entry)))))) /\ (((((exists ff_h_pvs_table_lookup_entrypositive. ff_h_pvs_table_lookup_entrypositive + S (dst_positive_table_lookup_entry) = S ((S (n)) * dst_positive_scale_table_lookup_entry)) /\ exists ff_q_pvs_table_lookup_entrypositive. dst_positive_code_table_lookup_entry = ff_q_pvs_table_lookup_entrypositive * S ((S (n)) * dst_positive_scale_table_lookup_entry) + (dst_positive_table_lookup_entry))) /\ (((((exists ff_h_pvs_table_lookup_entrynegative. ff_h_pvs_table_lookup_entrynegative + S (dst_negative_table_lookup_entry) = S ((S (n)) * dst_negative_scale_table_lookup_entry)) /\ exists ff_q_pvs_table_lookup_entrynegative. dst_negative_code_table_lookup_entry = ff_q_pvs_table_lookup_entrynegative * S ((S (n)) * dst_negative_scale_table_lookup_entry) + (dst_negative_table_lookup_entry))) /\ (exists ge_balance_positive_table_lookup_entryvalue ge_balance_negative_table_lookup_entryvalue. (((((z) = 2 * (ge_balance_positive_table_lookup_entryvalue) /\ (ge_balance_negative_table_lookup_entryvalue) = 0) \/ exists ge_signed_half_table_lookup_entryvaluedecode. (((z) = 2 * ge_signed_half_table_lookup_entryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_entryvalue) = 0) /\ (ge_balance_negative_table_lookup_entryvalue) = S ge_signed_half_table_lookup_entryvaluedecode))) /\ ((dst_positive_table_lookup_entry) + ge_balance_negative_table_lookup_entryvalue = (dst_negative_table_lookup_entry) + ge_balance_positive_table_lookup_entryvalue))))))))) /\ (((~((n)=0)) /\ (exists dc_mask_table_lookup_value. ((((exists dst_positive_code_table_lookup_valuemasktable dst_positive_scale_table_lookup_valuemasktable dst_negative_code_table_lookup_valuemasktable dst_negative_scale_table_lookup_valuemasktable. (((dc_mask_table_lookup_value) = (((((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) * S ((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) + ((dst_positive_scale_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable))) + (((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)))) * S ((((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) * S ((dst_positive_code_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable)) + ((dst_positive_scale_table_lookup_valuemasktable) + (dst_positive_scale_table_lookup_valuemasktable))) + (((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)))) + ((((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable))) + (((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) * S ((dst_negative_code_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)) + ((dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_scale_table_lookup_valuemasktable)))))) /\ (forall dst_index_table_lookup_valuemasktable. (exists pvs_le_gap_table_lookup_valuemasktabledomain. pvs_le_gap_table_lookup_valuemasktabledomain + (dst_index_table_lookup_valuemasktable) = (n)) -> exists dst_positive_table_lookup_valuemasktable dst_negative_table_lookup_valuemasktable dst_value_table_lookup_valuemasktable. ((((exists ff_h_pvs_table_lookup_valuemasktableentrypositive. ff_h_pvs_table_lookup_valuemasktableentrypositive + S (dst_positive_table_lookup_valuemasktable) = S ((S (dst_index_table_lookup_valuemasktable)) * dst_positive_scale_table_lookup_valuemasktable)) /\ exists ff_q_pvs_table_lookup_valuemasktableentrypositive. dst_positive_code_table_lookup_valuemasktable = ff_q_pvs_table_lookup_valuemasktableentrypositive * S ((S (dst_index_table_lookup_valuemasktable)) * dst_positive_scale_table_lookup_valuemasktable) + (dst_positive_table_lookup_valuemasktable))) /\ (((((exists ff_h_pvs_table_lookup_valuemasktableentrynegative. ff_h_pvs_table_lookup_valuemasktableentrynegative + S (dst_negative_table_lookup_valuemasktable) = S ((S (dst_index_table_lookup_valuemasktable)) * dst_negative_scale_table_lookup_valuemasktable)) /\ exists ff_q_pvs_table_lookup_valuemasktableentrynegative. dst_negative_code_table_lookup_valuemasktable = ff_q_pvs_table_lookup_valuemasktableentrynegative * S ((S (dst_index_table_lookup_valuemasktable)) * dst_negative_scale_table_lookup_valuemasktable) + (dst_negative_table_lookup_valuemasktable))) /\ (exists ge_balance_positive_table_lookup_valuemasktableentryvalue ge_balance_negative_table_lookup_valuemasktableentryvalue. (((((dst_value_table_lookup_valuemasktable) = 2 * (ge_balance_positive_table_lookup_valuemasktableentryvalue) /\ (ge_balance_negative_table_lookup_valuemasktableentryvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemasktableentryvaluedecode. (((dst_value_table_lookup_valuemasktable) = 2 * ge_signed_half_table_lookup_valuemasktableentryvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemasktableentryvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemasktableentryvalue) = S ge_signed_half_table_lookup_valuemasktableentryvaluedecode))) /\ ((dst_positive_table_lookup_valuemasktable) + ge_balance_negative_table_lookup_valuemasktableentryvalue = (dst_negative_table_lookup_valuemasktable) + ge_balance_positive_table_lookup_valuemasktableentryvalue))))))))) /\ (forall dc_index_table_lookup_valuemask dc_value_table_lookup_valuemask. (exists pvs_le_gap_table_lookup_valuemaskdomain. pvs_le_gap_table_lookup_valuemaskdomain + (dc_index_table_lookup_valuemask) = (n)) -> (exists dst_positive_code_table_lookup_valuemasklookup dst_positive_scale_table_lookup_valuemasklookup dst_negative_code_table_lookup_valuemasklookup dst_negative_scale_table_lookup_valuemasklookup dst_positive_table_lookup_valuemasklookup dst_negative_table_lookup_valuemasklookup. (((dc_mask_table_lookup_value) = (((((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) * S ((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) + ((dst_positive_scale_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup))) + (((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)))) * S ((((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) * S ((dst_positive_code_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup)) + ((dst_positive_scale_table_lookup_valuemasklookup) + (dst_positive_scale_table_lookup_valuemasklookup))) + (((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)))) + ((((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup))) + (((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) * S ((dst_negative_code_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)) + ((dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_scale_table_lookup_valuemasklookup)))))) /\ (((((exists ff_h_pvs_table_lookup_valuemasklookuppositive. ff_h_pvs_table_lookup_valuemasklookuppositive + S (dst_positive_table_lookup_valuemasklookup) = S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemasklookup)) /\ exists ff_q_pvs_table_lookup_valuemasklookuppositive. dst_positive_code_table_lookup_valuemasklookup = ff_q_pvs_table_lookup_valuemasklookuppositive * S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemasklookup) + (dst_positive_table_lookup_valuemasklookup))) /\ (((((exists ff_h_pvs_table_lookup_valuemasklookupnegative. ff_h_pvs_table_lookup_valuemasklookupnegative + S (dst_negative_table_lookup_valuemasklookup) = S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemasklookup)) /\ exists ff_q_pvs_table_lookup_valuemasklookupnegative. dst_negative_code_table_lookup_valuemasklookup = ff_q_pvs_table_lookup_valuemasklookupnegative * S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemasklookup) + (dst_negative_table_lookup_valuemasklookup))) /\ (exists ge_balance_positive_table_lookup_valuemasklookupvalue ge_balance_negative_table_lookup_valuemasklookupvalue. (((((dc_value_table_lookup_valuemask) = 2 * (ge_balance_positive_table_lookup_valuemasklookupvalue) /\ (ge_balance_negative_table_lookup_valuemasklookupvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemasklookupvaluedecode. (((dc_value_table_lookup_valuemask) = 2 * ge_signed_half_table_lookup_valuemasklookupvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemasklookupvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemasklookupvalue) = S ge_signed_half_table_lookup_valuemasklookupvaluedecode))) /\ ((dst_positive_table_lookup_valuemasklookup) + ge_balance_negative_table_lookup_valuemasklookupvalue = (dst_negative_table_lookup_valuemasklookup) + ge_balance_positive_table_lookup_valuemasklookupvalue))))))))) -> ((((~((dc_index_table_lookup_valuemask)=0)) /\ (exists dc_quotient_table_lookup_valuemaskentry dc_left_table_lookup_valuemaskentry dc_right_table_lookup_valuemaskentry. (((n)=(dc_index_table_lookup_valuemask)*dc_quotient_table_lookup_valuemaskentry) /\ (((exists dst_positive_code_table_lookup_valuemaskentryleft dst_positive_scale_table_lookup_valuemaskentryleft dst_negative_code_table_lookup_valuemaskentryleft dst_negative_scale_table_lookup_valuemaskentryleft dst_positive_table_lookup_valuemaskentryleft dst_negative_table_lookup_valuemaskentryleft. (((F) = (((((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) * S ((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) + ((dst_positive_scale_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft))) + (((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)))) * S ((((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) * S ((dst_positive_code_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft)) + ((dst_positive_scale_table_lookup_valuemaskentryleft) + (dst_positive_scale_table_lookup_valuemaskentryleft))) + (((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)))) + ((((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft))) + (((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) * S ((dst_negative_code_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)) + ((dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_scale_table_lookup_valuemaskentryleft)))))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryleftpositive. ff_h_pvs_table_lookup_valuemaskentryleftpositive + S (dst_positive_table_lookup_valuemaskentryleft) = S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemaskentryleft)) /\ exists ff_q_pvs_table_lookup_valuemaskentryleftpositive. dst_positive_code_table_lookup_valuemaskentryleft = ff_q_pvs_table_lookup_valuemaskentryleftpositive * S ((S (dc_index_table_lookup_valuemask)) * dst_positive_scale_table_lookup_valuemaskentryleft) + (dst_positive_table_lookup_valuemaskentryleft))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryleftnegative. ff_h_pvs_table_lookup_valuemaskentryleftnegative + S (dst_negative_table_lookup_valuemaskentryleft) = S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemaskentryleft)) /\ exists ff_q_pvs_table_lookup_valuemaskentryleftnegative. dst_negative_code_table_lookup_valuemaskentryleft = ff_q_pvs_table_lookup_valuemaskentryleftnegative * S ((S (dc_index_table_lookup_valuemask)) * dst_negative_scale_table_lookup_valuemaskentryleft) + (dst_negative_table_lookup_valuemaskentryleft))) /\ (exists ge_balance_positive_table_lookup_valuemaskentryleftvalue ge_balance_negative_table_lookup_valuemaskentryleftvalue. (((((dc_left_table_lookup_valuemaskentry) = 2 * (ge_balance_positive_table_lookup_valuemaskentryleftvalue) /\ (ge_balance_negative_table_lookup_valuemaskentryleftvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryleftvaluedecode. (((dc_left_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemaskentryleftvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemaskentryleftvalue) = S ge_signed_half_table_lookup_valuemaskentryleftvaluedecode))) /\ ((dst_positive_table_lookup_valuemaskentryleft) + ge_balance_negative_table_lookup_valuemaskentryleftvalue = (dst_negative_table_lookup_valuemaskentryleft) + ge_balance_positive_table_lookup_valuemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_table_lookup_valuemaskentryright dst_positive_scale_table_lookup_valuemaskentryright dst_negative_code_table_lookup_valuemaskentryright dst_negative_scale_table_lookup_valuemaskentryright dst_positive_table_lookup_valuemaskentryright dst_negative_table_lookup_valuemaskentryright. (((G) = (((((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) * S ((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) + ((dst_positive_scale_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright))) + (((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)))) * S ((((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) * S ((dst_positive_code_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright)) + ((dst_positive_scale_table_lookup_valuemaskentryright) + (dst_positive_scale_table_lookup_valuemaskentryright))) + (((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)))) + ((((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright))) + (((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) * S ((dst_negative_code_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)) + ((dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_scale_table_lookup_valuemaskentryright)))))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryrightpositive. ff_h_pvs_table_lookup_valuemaskentryrightpositive + S (dst_positive_table_lookup_valuemaskentryright) = S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_positive_scale_table_lookup_valuemaskentryright)) /\ exists ff_q_pvs_table_lookup_valuemaskentryrightpositive. dst_positive_code_table_lookup_valuemaskentryright = ff_q_pvs_table_lookup_valuemaskentryrightpositive * S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_positive_scale_table_lookup_valuemaskentryright) + (dst_positive_table_lookup_valuemaskentryright))) /\ (((((exists ff_h_pvs_table_lookup_valuemaskentryrightnegative. ff_h_pvs_table_lookup_valuemaskentryrightnegative + S (dst_negative_table_lookup_valuemaskentryright) = S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_negative_scale_table_lookup_valuemaskentryright)) /\ exists ff_q_pvs_table_lookup_valuemaskentryrightnegative. dst_negative_code_table_lookup_valuemaskentryright = ff_q_pvs_table_lookup_valuemaskentryrightnegative * S ((S (dc_quotient_table_lookup_valuemaskentry)) * dst_negative_scale_table_lookup_valuemaskentryright) + (dst_negative_table_lookup_valuemaskentryright))) /\ (exists ge_balance_positive_table_lookup_valuemaskentryrightvalue ge_balance_negative_table_lookup_valuemaskentryrightvalue. (((((dc_right_table_lookup_valuemaskentry) = 2 * (ge_balance_positive_table_lookup_valuemaskentryrightvalue) /\ (ge_balance_negative_table_lookup_valuemaskentryrightvalue) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryrightvaluedecode. (((dc_right_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_table_lookup_valuemaskentryrightvalue) = 0) /\ (ge_balance_negative_table_lookup_valuemaskentryrightvalue) = S ge_signed_half_table_lookup_valuemaskentryrightvaluedecode))) /\ ((dst_positive_table_lookup_valuemaskentryright) + ge_balance_negative_table_lookup_valuemaskentryrightvalue = (dst_negative_table_lookup_valuemaskentryright) + ge_balance_positive_table_lookup_valuemaskentryrightvalue))))))))) /\ (exists sto_ap_table_lookup_valuemaskentryproduct sto_an_table_lookup_valuemaskentryproduct sto_bp_table_lookup_valuemaskentryproduct sto_bn_table_lookup_valuemaskentryproduct sto_cp_table_lookup_valuemaskentryproduct sto_cn_table_lookup_valuemaskentryproduct. (((((dc_left_table_lookup_valuemaskentry) = 2 * (sto_ap_table_lookup_valuemaskentryproduct) /\ (sto_an_table_lookup_valuemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryproductleft. (((dc_left_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryproductleft + 1 /\ (sto_ap_table_lookup_valuemaskentryproduct) = 0) /\ (sto_an_table_lookup_valuemaskentryproduct) = S ge_signed_half_table_lookup_valuemaskentryproductleft))) /\ ((((((dc_right_table_lookup_valuemaskentry) = 2 * (sto_bp_table_lookup_valuemaskentryproduct) /\ (sto_bn_table_lookup_valuemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryproductright. (((dc_right_table_lookup_valuemaskentry) = 2 * ge_signed_half_table_lookup_valuemaskentryproductright + 1 /\ (sto_bp_table_lookup_valuemaskentryproduct) = 0) /\ (sto_bn_table_lookup_valuemaskentryproduct) = S ge_signed_half_table_lookup_valuemaskentryproductright))) /\ ((((((dc_value_table_lookup_valuemask) = 2 * (sto_cp_table_lookup_valuemaskentryproduct) /\ (sto_cn_table_lookup_valuemaskentryproduct) = 0) \/ exists ge_signed_half_table_lookup_valuemaskentryproductoutput. (((dc_value_table_lookup_valuemask) = 2 * ge_signed_half_table_lookup_valuemaskentryproductoutput + 1 /\ (sto_cp_table_lookup_valuemaskentryproduct) = 0) /\ (sto_cn_table_lookup_valuemaskentryproduct) = S ge_signed_half_table_lookup_valuemaskentryproductoutput))) /\ ((sto_ap_table_lookup_valuemaskentryproduct * sto_bp_table_lookup_valuemaskentryproduct + sto_an_table_lookup_valuemaskentryproduct * sto_bn_table_lookup_valuemaskentryproduct) + sto_cn_table_lookup_valuemaskentryproduct = (sto_ap_table_lookup_valuemaskentryproduct * sto_bn_table_lookup_valuemaskentryproduct + sto_an_table_lookup_valuemaskentryproduct * sto_bp_table_lookup_valuemaskentryproduct) + sto_cp_table_lookup_valuemaskentryproduct))))))))))))))) \/ ((((dc_index_table_lookup_valuemask)=0 \/ ~(exists pvs_factor_table_lookup_valuemaskentrynondivisor. (n) = (dc_index_table_lookup_valuemask) * pvs_factor_table_lookup_valuemaskentrynondivisor)) /\ ((dc_value_table_lookup_valuemask)=0))))))) /\ (exists dst_positive_code_table_lookup_valuefold dst_positive_scale_table_lookup_valuefold dst_negative_code_table_lookup_valuefold dst_negative_scale_table_lookup_valuefold dst_positive_sum_table_lookup_valuefold dst_negative_sum_table_lookup_valuefold. (((dc_mask_table_lookup_value) = (((((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) * S ((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) + ((dst_positive_scale_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold))) + (((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)))) * S ((((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) * S ((dst_positive_code_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold)) + ((dst_positive_scale_table_lookup_valuefold) + (dst_positive_scale_table_lookup_valuefold))) + (((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)))) + ((((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold))) + (((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) * S ((dst_negative_code_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)) + ((dst_negative_scale_table_lookup_valuefold) + (dst_negative_scale_table_lookup_valuefold)))))) /\ (((exists fs_u_dst_table_lookup_valuefoldpositive fs_v_dst_table_lookup_valuefoldpositive. ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_start. fs_h_dst_table_lookup_valuefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_start. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_start * S ((S (0)) * fs_v_dst_table_lookup_valuefoldpositive) + (0))) /\ ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_terminal. fs_h_dst_table_lookup_valuefoldpositive_body_terminal + S (dst_positive_sum_table_lookup_valuefold) = S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_terminal. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldpositive) + (dst_positive_sum_table_lookup_valuefold))) /\ forall fs_i_dst_table_lookup_valuefoldpositive_body_steps. (exists fs_lt_dst_table_lookup_valuefoldpositive_body_steps_bound. fs_lt_dst_table_lookup_valuefoldpositive_body_steps_bound + S fs_i_dst_table_lookup_valuefoldpositive_body_steps = S (n)) -> exists fs_a_dst_table_lookup_valuefoldpositive_body_steps fs_r_dst_table_lookup_valuefoldpositive_body_steps fs_s_dst_table_lookup_valuefoldpositive_body_steps. ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_steps_summand. fs_h_dst_table_lookup_valuefoldpositive_body_steps_summand + S (fs_a_dst_table_lookup_valuefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * dst_positive_scale_table_lookup_valuefold)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_steps_summand. dst_positive_code_table_lookup_valuefold = fs_q_dst_table_lookup_valuefoldpositive_body_steps_summand * S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * dst_positive_scale_table_lookup_valuefold) + (fs_a_dst_table_lookup_valuefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_steps_partial. fs_h_dst_table_lookup_valuefoldpositive_body_steps_partial + S (fs_r_dst_table_lookup_valuefoldpositive_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_steps_partial. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_steps_partial * S ((S (fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive) + (fs_r_dst_table_lookup_valuefoldpositive_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldpositive_body_steps_successor. fs_h_dst_table_lookup_valuefoldpositive_body_steps_successor + S (fs_s_dst_table_lookup_valuefoldpositive_body_steps) = S ((S (S fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive)) /\ exists fs_q_dst_table_lookup_valuefoldpositive_body_steps_successor. fs_u_dst_table_lookup_valuefoldpositive = fs_q_dst_table_lookup_valuefoldpositive_body_steps_successor * S ((S (S fs_i_dst_table_lookup_valuefoldpositive_body_steps)) * fs_v_dst_table_lookup_valuefoldpositive) + (fs_s_dst_table_lookup_valuefoldpositive_body_steps))) /\ fs_s_dst_table_lookup_valuefoldpositive_body_steps = fs_r_dst_table_lookup_valuefoldpositive_body_steps + fs_a_dst_table_lookup_valuefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_table_lookup_valuefoldnegative fs_v_dst_table_lookup_valuefoldnegative. ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_start. fs_h_dst_table_lookup_valuefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_start. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_start * S ((S (0)) * fs_v_dst_table_lookup_valuefoldnegative) + (0))) /\ ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_terminal. fs_h_dst_table_lookup_valuefoldnegative_body_terminal + S (dst_negative_sum_table_lookup_valuefold) = S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_terminal. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_table_lookup_valuefoldnegative) + (dst_negative_sum_table_lookup_valuefold))) /\ forall fs_i_dst_table_lookup_valuefoldnegative_body_steps. (exists fs_lt_dst_table_lookup_valuefoldnegative_body_steps_bound. fs_lt_dst_table_lookup_valuefoldnegative_body_steps_bound + S fs_i_dst_table_lookup_valuefoldnegative_body_steps = S (n)) -> exists fs_a_dst_table_lookup_valuefoldnegative_body_steps fs_r_dst_table_lookup_valuefoldnegative_body_steps fs_s_dst_table_lookup_valuefoldnegative_body_steps. ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_steps_summand. fs_h_dst_table_lookup_valuefoldnegative_body_steps_summand + S (fs_a_dst_table_lookup_valuefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * dst_negative_scale_table_lookup_valuefold)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_steps_summand. dst_negative_code_table_lookup_valuefold = fs_q_dst_table_lookup_valuefoldnegative_body_steps_summand * S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * dst_negative_scale_table_lookup_valuefold) + (fs_a_dst_table_lookup_valuefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_steps_partial. fs_h_dst_table_lookup_valuefoldnegative_body_steps_partial + S (fs_r_dst_table_lookup_valuefoldnegative_body_steps) = S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_steps_partial. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_steps_partial * S ((S (fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative) + (fs_r_dst_table_lookup_valuefoldnegative_body_steps))) /\ ((((exists fs_h_dst_table_lookup_valuefoldnegative_body_steps_successor. fs_h_dst_table_lookup_valuefoldnegative_body_steps_successor + S (fs_s_dst_table_lookup_valuefoldnegative_body_steps) = S ((S (S fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative)) /\ exists fs_q_dst_table_lookup_valuefoldnegative_body_steps_successor. fs_u_dst_table_lookup_valuefoldnegative = fs_q_dst_table_lookup_valuefoldnegative_body_steps_successor * S ((S (S fs_i_dst_table_lookup_valuefoldnegative_body_steps)) * fs_v_dst_table_lookup_valuefoldnegative) + (fs_s_dst_table_lookup_valuefoldnegative_body_steps))) /\ fs_s_dst_table_lookup_valuefoldnegative_body_steps = fs_r_dst_table_lookup_valuefoldnegative_body_steps + fs_a_dst_table_lookup_valuefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_table_lookup_valuefoldresult ge_balance_negative_table_lookup_valuefoldresult. (((((z) = 2 * (ge_balance_positive_table_lookup_valuefoldresult) /\ (ge_balance_negative_table_lookup_valuefoldresult) = 0) \/ exists ge_signed_half_table_lookup_valuefoldresultdecode. (((z) = 2 * ge_signed_half_table_lookup_valuefoldresultdecode + 1 /\ (ge_balance_positive_table_lookup_valuefoldresult) = 0) /\ (ge_balance_negative_table_lookup_valuefoldresult) = S ge_signed_half_table_lookup_valuefoldresultdecode))) /\ ((dst_positive_sum_table_lookup_valuefold) + ge_balance_negative_table_lookup_valuefoldresult = (dst_negative_sum_table_lookup_valuefold) + ge_balance_positive_table_lookup_valuefoldresult)))))))))))))

division_remainder_exists · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall m n. ~(m = 0) -> exists q r. n = m * q + r /\ S r <= m
```

division_remainder_unique · checked inherited prerequisite

Exact statement in the checked dependency cone

forall m n q r q2 r2. n = m * q + r -> (exists k. k + S r = m) -> n = m * q2 + r2 -> (exists k. k + S r2 = m) -> q = q2 /\ r = r2

divisor_le_nonzero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall d n. ~(n = 0) -> (exists q. n = d * q) -> exists k. k + d = n
```

divisor_signed_table_at_functional · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F i a b. (exists dst_positive_code_functional_first dst_positive_scale_functional_first dst_negative_code_functional_first dst_negative_scale_functional_first dst_positive_functional_first dst_negative_functional_first. (((F) = (((((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) * S ((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) + ((dst_positive_scale_functional_first) + (dst_positive_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))) * S ((((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) * S ((dst_positive_code_functional_first) + (dst_positive_scale_functional_first)) + ((dst_positive_scale_functional_first) + (dst_positive_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))) + ((((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first))) + (((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) * S ((dst_negative_code_functional_first) + (dst_negative_scale_functional_first)) + ((dst_negative_scale_functional_first) + (dst_negative_scale_functional_first)))))) /\ (((((exists ff_h_pvs_functional_firstpositive. ff_h_pvs_functional_firstpositive + S (dst_positive_functional_first) = S ((S (i)) * dst_positive_scale_functional_first)) /\ exists ff_q_pvs_functional_firstpositive. dst_positive_code_functional_first = ff_q_pvs_functional_firstpositive * S ((S (i)) * dst_positive_scale_functional_first) + (dst_positive_functional_first))) /\ (((((exists ff_h_pvs_functional_firstnegative. ff_h_pvs_functional_firstnegative + S (dst_negative_functional_first) = S ((S (i)) * dst_negative_scale_functional_first)) /\ exists ff_q_pvs_functional_firstnegative. dst_negative_code_functional_first = ff_q_pvs_functional_firstnegative * S ((S (i)) * dst_negative_scale_functional_first) + (dst_negative_functional_first))) /\ (exists ge_balance_positive_functional_firstvalue ge_balance_negative_functional_firstvalue. (((((a) = 2 * (ge_balance_positive_functional_firstvalue) /\ (ge_balance_negative_functional_firstvalue) = 0) \/ exists ge_signed_half_functional_firstvaluedecode. (((a) = 2 * ge_signed_half_functional_firstvaluedecode + 1 /\ (ge_balance_positive_functional_firstvalue) = 0) /\ (ge_balance_negative_functional_firstvalue) = S ge_signed_half_functional_firstvaluedecode))) /\ ((dst_positive_functional_first) + ge_balance_negative_functional_firstvalue = (dst_negative_functional_first) + ge_balance_positive_functional_firstvalue))))))))) -> (exists dst_positive_code_functional_second dst_positive_scale_functional_second dst_negative_code_functional_second dst_negative_scale_functional_second dst_positive_functional_second dst_negative_functional_second. (((F) = (((((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) * S ((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) + ((dst_positive_scale_functional_second) + (dst_positive_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))) * S ((((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) * S ((dst_positive_code_functional_second) + (dst_positive_scale_functional_second)) + ((dst_positive_scale_functional_second) + (dst_positive_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))) + ((((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second))) + (((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) * S ((dst_negative_code_functional_second) + (dst_negative_scale_functional_second)) + ((dst_negative_scale_functional_second) + (dst_negative_scale_functional_second)))))) /\ (((((exists ff_h_pvs_functional_secondpositive. ff_h_pvs_functional_secondpositive + S (dst_positive_functional_second) = S ((S (i)) * dst_positive_scale_functional_second)) /\ exists ff_q_pvs_functional_secondpositive. dst_positive_code_functional_second = ff_q_pvs_functional_secondpositive * S ((S (i)) * dst_positive_scale_functional_second) + (dst_positive_functional_second))) /\ (((((exists ff_h_pvs_functional_secondnegative. ff_h_pvs_functional_secondnegative + S (dst_negative_functional_second) = S ((S (i)) * dst_negative_scale_functional_second)) /\ exists ff_q_pvs_functional_secondnegative. dst_negative_code_functional_second = ff_q_pvs_functional_secondnegative * S ((S (i)) * dst_negative_scale_functional_second) + (dst_negative_functional_second))) /\ (exists ge_balance_positive_functional_secondvalue ge_balance_negative_functional_secondvalue. (((((b) = 2 * (ge_balance_positive_functional_secondvalue) /\ (ge_balance_negative_functional_secondvalue) = 0) \/ exists ge_signed_half_functional_secondvaluedecode. (((b) = 2 * ge_signed_half_functional_secondvaluedecode + 1 /\ (ge_balance_positive_functional_secondvalue) = 0) /\ (ge_balance_negative_functional_secondvalue) = S ge_signed_half_functional_secondvaluedecode))) /\ ((dst_positive_functional_second) + ge_balance_negative_functional_secondvalue = (dst_negative_functional_second) + ge_balance_positive_functional_secondvalue))))))))) -> a = b

divisor_signed_table_lookup · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F i. (exists dst_positive_code_lookup_table dst_positive_scale_lookup_table dst_negative_code_lookup_table dst_negative_scale_lookup_table. (((F) = (((((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) * S ((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) + ((dst_positive_scale_lookup_table) + (dst_positive_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))) * S ((((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) * S ((dst_positive_code_lookup_table) + (dst_positive_scale_lookup_table)) + ((dst_positive_scale_lookup_table) + (dst_positive_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))) + ((((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table))) + (((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) * S ((dst_negative_code_lookup_table) + (dst_negative_scale_lookup_table)) + ((dst_negative_scale_lookup_table) + (dst_negative_scale_lookup_table)))))) /\ (forall dst_index_lookup_table. (exists pvs_le_gap_lookup_tabledomain. pvs_le_gap_lookup_tabledomain + (dst_index_lookup_table) = (N)) -> exists dst_positive_lookup_table dst_negative_lookup_table dst_value_lookup_table. ((((exists ff_h_pvs_lookup_tableentrypositive. ff_h_pvs_lookup_tableentrypositive + S (dst_positive_lookup_table) = S ((S (dst_index_lookup_table)) * dst_positive_scale_lookup_table)) /\ exists ff_q_pvs_lookup_tableentrypositive. dst_positive_code_lookup_table = ff_q_pvs_lookup_tableentrypositive * S ((S (dst_index_lookup_table)) * dst_positive_scale_lookup_table) + (dst_positive_lookup_table))) /\ (((((exists ff_h_pvs_lookup_tableentrynegative. ff_h_pvs_lookup_tableentrynegative + S (dst_negative_lookup_table) = S ((S (dst_index_lookup_table)) * dst_negative_scale_lookup_table)) /\ exists ff_q_pvs_lookup_tableentrynegative. dst_negative_code_lookup_table = ff_q_pvs_lookup_tableentrynegative * S ((S (dst_index_lookup_table)) * dst_negative_scale_lookup_table) + (dst_negative_lookup_table))) /\ (exists ge_balance_positive_lookup_tableentryvalue ge_balance_negative_lookup_tableentryvalue. (((((dst_value_lookup_table) = 2 * (ge_balance_positive_lookup_tableentryvalue) /\ (ge_balance_negative_lookup_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_tableentryvaluedecode. (((dst_value_lookup_table) = 2 * ge_signed_half_lookup_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_tableentryvalue) = S ge_signed_half_lookup_tableentryvaluedecode))) /\ ((dst_positive_lookup_table) + ge_balance_negative_lookup_tableentryvalue = (dst_negative_lookup_table) + ge_balance_positive_lookup_tableentryvalue))))))))) -> (exists pvs_le_gap_lookup_domain. pvs_le_gap_lookup_domain + (i) = (N)) -> exists z. (exists dst_positive_code_lookup_result dst_positive_scale_lookup_result dst_negative_code_lookup_result dst_negative_scale_lookup_result dst_positive_lookup_result dst_negative_lookup_result. (((F) = (((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) * S ((((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) * S ((dst_positive_code_lookup_result) + (dst_positive_scale_lookup_result)) + ((dst_positive_scale_lookup_result) + (dst_positive_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))) + ((((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result))) + (((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) * S ((dst_negative_code_lookup_result) + (dst_negative_scale_lookup_result)) + ((dst_negative_scale_lookup_result) + (dst_negative_scale_lookup_result)))))) /\ (((((exists ff_h_pvs_lookup_resultpositive. ff_h_pvs_lookup_resultpositive + S (dst_positive_lookup_result) = S ((S (i)) * dst_positive_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultpositive. dst_positive_code_lookup_result = ff_q_pvs_lookup_resultpositive * S ((S (i)) * dst_positive_scale_lookup_result) + (dst_positive_lookup_result))) /\ (((((exists ff_h_pvs_lookup_resultnegative. ff_h_pvs_lookup_resultnegative + S (dst_negative_lookup_result) = S ((S (i)) * dst_negative_scale_lookup_result)) /\ exists ff_q_pvs_lookup_resultnegative. dst_negative_code_lookup_result = ff_q_pvs_lookup_resultnegative * S ((S (i)) * dst_negative_scale_lookup_result) + (dst_negative_lookup_result))) /\ (exists ge_balance_positive_lookup_resultvalue ge_balance_negative_lookup_resultvalue. (((((z) = 2 * (ge_balance_positive_lookup_resultvalue) /\ (ge_balance_negative_lookup_resultvalue) = 0) \/ exists ge_signed_half_lookup_resultvaluedecode. (((z) = 2 * ge_signed_half_lookup_resultvaluedecode + 1 /\ (ge_balance_positive_lookup_resultvalue) = 0) /\ (ge_balance_negative_lookup_resultvalue) = S ge_signed_half_lookup_resultvaluedecode))) /\ ((dst_positive_lookup_result) + ge_balance_negative_lookup_resultvalue = (dst_negative_lookup_result) + ge_balance_positive_lookup_resultvalue)))))))))

eq_decidable · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. a = b \/ ~(a = b)
```
factor_nonzero_right · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n c d. ~(n = 0) -> n = c * d -> ~(d = 0)
```
le_eq_or_lt · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + a = b) -> a = b \/ exists k. k + S a = b
```
le_of_succ_le_succ · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + S a = S b) -> exists r. r + a = b
```
le_trans · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n m k. n <= m -> m <= k -> n <= k
```
le_zero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. n <= 0 -> n = 0
```
lt_to_le · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + S a = b) -> exists r. r + a = b
```

matrix_recursive_flattened_index_bound · checked inherited prerequisite

Exact statement in the checked dependency cone

forall w r s. (exists mdr_gap_flat_row. mdr_gap_flat_row + S (r) = (w)) -> (exists mdr_gap_flat_column. mdr_gap_flat_column + S (s) = (w)) -> (exists mdr_gap_flat_result. mdr_gap_flat_result + S (r * w + s) = (w * w))

mul_assoc · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n m k. (n * m) * k = n * (m * k)
```
mul_comm · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n m. n * m = m * n
```
mul_left_cancel_nonzero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b c. ~(a = 0) -> a * b = a * c -> b = c
```
mul_ne_zero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. ~(a = 0) -> ~(b = 0) -> ~(a * b = 0)
```
multiple_decidable_nonzero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall d n. ~(d = 0) -> (exists q. n = d * q) \/ ~(exists q. n = d * q)
```
one_mul · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. 1 * n = n
```

signed_mul_functional · checked inherited prerequisite

Exact statement in the checked dependency cone

forall left right output1 output2. (exists sm_lp_functional_left sm_ln_functional_left sm_rp_functional_left sm_rn_functional_left sm_op_functional_left sm_on_functional_left. (((left = 2 * sm_lp_functional_left /\ sm_ln_functional_left = 0) \/ exists sd_half_functional_left_left. ((left = 2 * sd_half_functional_left_left + 1 /\ sm_lp_functional_left = 0) /\ sm_ln_functional_left = S sd_half_functional_left_left)) /\ (((right = 2 * sm_rp_functional_left /\ sm_rn_functional_left = 0) \/ exists sd_half_functional_left_right. ((right = 2 * sd_half_functional_left_right + 1 /\ sm_rp_functional_left = 0) /\ sm_rn_functional_left = S sd_half_functional_left_right)) /\ (((output1 = 2 * sm_op_functional_left /\ sm_on_functional_left = 0) \/ exists sd_half_functional_left_output. ((output1 = 2 * sd_half_functional_left_output + 1 /\ sm_op_functional_left = 0) /\ sm_on_functional_left = S sd_half_functional_left_output)) /\ (sm_lp_functional_left * sm_rp_functional_left + sm_ln_functional_left * sm_rn_functional_left) + sm_on_functional_left = (sm_lp_functional_left * sm_rn_functional_left + sm_ln_functional_left * sm_rp_functional_left) + sm_op_functional_left)))) -> (exists sm_lp_functional_right sm_ln_functional_right sm_rp_functional_right sm_rn_functional_right sm_op_functional_right sm_on_functional_right. (((left = 2 * sm_lp_functional_right /\ sm_ln_functional_right = 0) \/ exists sd_half_functional_right_left. ((left = 2 * sd_half_functional_right_left + 1 /\ sm_lp_functional_right = 0) /\ sm_ln_functional_right = S sd_half_functional_right_left)) /\ (((right = 2 * sm_rp_functional_right /\ sm_rn_functional_right = 0) \/ exists sd_half_functional_right_right. ((right = 2 * sd_half_functional_right_right + 1 /\ sm_rp_functional_right = 0) /\ sm_rn_functional_right = S sd_half_functional_right_right)) /\ (((output2 = 2 * sm_op_functional_right /\ sm_on_functional_right = 0) \/ exists sd_half_functional_right_output. ((output2 = 2 * sd_half_functional_right_output + 1 /\ sm_op_functional_right = 0) /\ sm_on_functional_right = S sd_half_functional_right_output)) /\ (sm_lp_functional_right * sm_rp_functional_right + sm_ln_functional_right * sm_rn_functional_right) + sm_on_functional_right = (sm_lp_functional_right * sm_rn_functional_right + sm_ln_functional_right * sm_rp_functional_right) + sm_op_functional_right)))) -> output1 = output2

signed_mul_total · checked inherited prerequisite

Exact statement in the checked dependency cone

forall left right. exists output. (exists sm_lp_total sm_ln_total sm_rp_total sm_rn_total sm_op_total sm_on_total. (((left = 2 * sm_lp_total /\ sm_ln_total = 0) \/ exists sd_half_total_left. ((left = 2 * sd_half_total_left + 1 /\ sm_lp_total = 0) /\ sm_ln_total = S sd_half_total_left)) /\ (((right = 2 * sm_rp_total /\ sm_rn_total = 0) \/ exists sd_half_total_right. ((right = 2 * sd_half_total_right + 1 /\ sm_rp_total = 0) /\ sm_rn_total = S sd_half_total_right)) /\ (((output = 2 * sm_op_total /\ sm_on_total = 0) \/ exists sd_half_total_output. ((output = 2 * sd_half_total_output + 1 /\ sm_op_total = 0) /\ sm_on_total = S sd_half_total_output)) /\ (sm_lp_total * sm_rp_total + sm_ln_total * sm_rn_total) + sm_on_total = (sm_lp_total * sm_rn_total + sm_ln_total * sm_rp_total) + sm_op_total))))

signed_mul_zero_right · checked inherited prerequisite

Exact statement in the checked dependency cone

forall input. (exists sm_lp_zero_right sm_ln_zero_right sm_rp_zero_right sm_rn_zero_right sm_op_zero_right sm_on_zero_right. (((input = 2 * sm_lp_zero_right /\ sm_ln_zero_right = 0) \/ exists sd_half_zero_right_left. ((input = 2 * sd_half_zero_right_left + 1 /\ sm_lp_zero_right = 0) /\ sm_ln_zero_right = S sd_half_zero_right_left)) /\ (((0 = 2 * sm_rp_zero_right /\ sm_rn_zero_right = 0) \/ exists sd_half_zero_right_right. ((0 = 2 * sd_half_zero_right_right + 1 /\ sm_rp_zero_right = 0) /\ sm_rn_zero_right = S sd_half_zero_right_right)) /\ (((0 = 2 * sm_op_zero_right /\ sm_on_zero_right = 0) \/ exists sd_half_zero_right_output. ((0 = 2 * sd_half_zero_right_output + 1 /\ sm_op_zero_right = 0) /\ sm_on_zero_right = S sd_half_zero_right_output)) /\ (sm_lp_zero_right * sm_rp_zero_right + sm_ln_zero_right * sm_rn_zero_right) + sm_on_zero_right = (sm_lp_zero_right * sm_rn_zero_right + sm_ln_zero_right * sm_rp_zero_right) + sm_op_zero_right))))

signed_prefix_sum_scalar_multiply · checked inherited prerequisite

Exact statement in the checked dependency cone

forall l a F G b c. (((exists dst_positive_code_scalar_pointwiseinput_table dst_positive_scale_scalar_pointwiseinput_table dst_negative_code_scalar_pointwiseinput_table dst_negative_scale_scalar_pointwiseinput_table. (((F) = (((((dst_positive_code_scalar_pointwiseinput_table) + (dst_positive_scale_scalar_pointwiseinput_table)) * S ((dst_positive_code_scalar_pointwiseinput_table) + (dst_positive_scale_scalar_pointwiseinput_table)) + ((dst_positive_scale_scalar_pointwiseinput_table) + (dst_positive_scale_scalar_pointwiseinput_table))) + (((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) * S ((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) + ((dst_negative_scale_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)))) * S ((((dst_positive_code_scalar_pointwiseinput_table) + (dst_positive_scale_scalar_pointwiseinput_table)) * S ((dst_positive_code_scalar_pointwiseinput_table) + (dst_positive_scale_scalar_pointwiseinput_table)) + ((dst_positive_scale_scalar_pointwiseinput_table) + (dst_positive_scale_scalar_pointwiseinput_table))) + (((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) * S ((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) + ((dst_negative_scale_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)))) + ((((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) * S ((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) + ((dst_negative_scale_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table))) + (((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) * S ((dst_negative_code_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)) + ((dst_negative_scale_scalar_pointwiseinput_table) + (dst_negative_scale_scalar_pointwiseinput_table)))))) /\ (forall dst_index_scalar_pointwiseinput_table. (exists pvs_le_gap_scalar_pointwiseinput_tabledomain. pvs_le_gap_scalar_pointwiseinput_tabledomain + (dst_index_scalar_pointwiseinput_table) = (l)) -> exists dst_positive_scalar_pointwiseinput_table dst_negative_scalar_pointwiseinput_table dst_value_scalar_pointwiseinput_table. ((((exists ff_h_pvs_scalar_pointwiseinput_tableentrypositive. ff_h_pvs_scalar_pointwiseinput_tableentrypositive + S (dst_positive_scalar_pointwiseinput_table) = S ((S (dst_index_scalar_pointwiseinput_table)) * dst_positive_scale_scalar_pointwiseinput_table)) /\ exists ff_q_pvs_scalar_pointwiseinput_tableentrypositive. dst_positive_code_scalar_pointwiseinput_table = ff_q_pvs_scalar_pointwiseinput_tableentrypositive * S ((S (dst_index_scalar_pointwiseinput_table)) * dst_positive_scale_scalar_pointwiseinput_table) + (dst_positive_scalar_pointwiseinput_table))) /\ (((((exists ff_h_pvs_scalar_pointwiseinput_tableentrynegative. ff_h_pvs_scalar_pointwiseinput_tableentrynegative + S (dst_negative_scalar_pointwiseinput_table) = S ((S (dst_index_scalar_pointwiseinput_table)) * dst_negative_scale_scalar_pointwiseinput_table)) /\ exists ff_q_pvs_scalar_pointwiseinput_tableentrynegative. dst_negative_code_scalar_pointwiseinput_table = ff_q_pvs_scalar_pointwiseinput_tableentrynegative * S ((S (dst_index_scalar_pointwiseinput_table)) * dst_negative_scale_scalar_pointwiseinput_table) + (dst_negative_scalar_pointwiseinput_table))) /\ (exists ge_balance_positive_scalar_pointwiseinput_tableentryvalue ge_balance_negative_scalar_pointwiseinput_tableentryvalue. (((((dst_value_scalar_pointwiseinput_table) = 2 * (ge_balance_positive_scalar_pointwiseinput_tableentryvalue) /\ (ge_balance_negative_scalar_pointwiseinput_tableentryvalue) = 0) \/ exists ge_signed_half_scalar_pointwiseinput_tableentryvaluedecode. (((dst_value_scalar_pointwiseinput_table) = 2 * ge_signed_half_scalar_pointwiseinput_tableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_pointwiseinput_tableentryvalue) = 0) /\ (ge_balance_negative_scalar_pointwiseinput_tableentryvalue) = S ge_signed_half_scalar_pointwiseinput_tableentryvaluedecode))) /\ ((dst_positive_scalar_pointwiseinput_table) + ge_balance_negative_scalar_pointwiseinput_tableentryvalue = (dst_negative_scalar_pointwiseinput_table) + ge_balance_positive_scalar_pointwiseinput_tableentryvalue))))))))) /\ (((exists dst_positive_code_scalar_pointwiseoutput_table dst_positive_scale_scalar_pointwiseoutput_table dst_negative_code_scalar_pointwiseoutput_table dst_negative_scale_scalar_pointwiseoutput_table. (((G) = (((((dst_positive_code_scalar_pointwiseoutput_table) + (dst_positive_scale_scalar_pointwiseoutput_table)) * S ((dst_positive_code_scalar_pointwiseoutput_table) + (dst_positive_scale_scalar_pointwiseoutput_table)) + ((dst_positive_scale_scalar_pointwiseoutput_table) + (dst_positive_scale_scalar_pointwiseoutput_table))) + (((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) * S ((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) + ((dst_negative_scale_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)))) * S ((((dst_positive_code_scalar_pointwiseoutput_table) + (dst_positive_scale_scalar_pointwiseoutput_table)) * S ((dst_positive_code_scalar_pointwiseoutput_table) + (dst_positive_scale_scalar_pointwiseoutput_table)) + ((dst_positive_scale_scalar_pointwiseoutput_table) + (dst_positive_scale_scalar_pointwiseoutput_table))) + (((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) * S ((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) + ((dst_negative_scale_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)))) + ((((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) * S ((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) + ((dst_negative_scale_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table))) + (((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) * S ((dst_negative_code_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)) + ((dst_negative_scale_scalar_pointwiseoutput_table) + (dst_negative_scale_scalar_pointwiseoutput_table)))))) /\ (forall dst_index_scalar_pointwiseoutput_table. (exists pvs_le_gap_scalar_pointwiseoutput_tabledomain. pvs_le_gap_scalar_pointwiseoutput_tabledomain + (dst_index_scalar_pointwiseoutput_table) = (l)) -> exists dst_positive_scalar_pointwiseoutput_table dst_negative_scalar_pointwiseoutput_table dst_value_scalar_pointwiseoutput_table. ((((exists ff_h_pvs_scalar_pointwiseoutput_tableentrypositive. ff_h_pvs_scalar_pointwiseoutput_tableentrypositive + S (dst_positive_scalar_pointwiseoutput_table) = S ((S (dst_index_scalar_pointwiseoutput_table)) * dst_positive_scale_scalar_pointwiseoutput_table)) /\ exists ff_q_pvs_scalar_pointwiseoutput_tableentrypositive. dst_positive_code_scalar_pointwiseoutput_table = ff_q_pvs_scalar_pointwiseoutput_tableentrypositive * S ((S (dst_index_scalar_pointwiseoutput_table)) * dst_positive_scale_scalar_pointwiseoutput_table) + (dst_positive_scalar_pointwiseoutput_table))) /\ (((((exists ff_h_pvs_scalar_pointwiseoutput_tableentrynegative. ff_h_pvs_scalar_pointwiseoutput_tableentrynegative + S (dst_negative_scalar_pointwiseoutput_table) = S ((S (dst_index_scalar_pointwiseoutput_table)) * dst_negative_scale_scalar_pointwiseoutput_table)) /\ exists ff_q_pvs_scalar_pointwiseoutput_tableentrynegative. dst_negative_code_scalar_pointwiseoutput_table = ff_q_pvs_scalar_pointwiseoutput_tableentrynegative * S ((S (dst_index_scalar_pointwiseoutput_table)) * dst_negative_scale_scalar_pointwiseoutput_table) + (dst_negative_scalar_pointwiseoutput_table))) /\ (exists ge_balance_positive_scalar_pointwiseoutput_tableentryvalue ge_balance_negative_scalar_pointwiseoutput_tableentryvalue. (((((dst_value_scalar_pointwiseoutput_table) = 2 * (ge_balance_positive_scalar_pointwiseoutput_tableentryvalue) /\ (ge_balance_negative_scalar_pointwiseoutput_tableentryvalue) = 0) \/ exists ge_signed_half_scalar_pointwiseoutput_tableentryvaluedecode. (((dst_value_scalar_pointwiseoutput_table) = 2 * ge_signed_half_scalar_pointwiseoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_scalar_pointwiseoutput_tableentryvalue) = 0) /\ (ge_balance_negative_scalar_pointwiseoutput_tableentryvalue) = S ge_signed_half_scalar_pointwiseoutput_tableentryvaluedecode))) /\ ((dst_positive_scalar_pointwiseoutput_table) + ge_balance_negative_scalar_pointwiseoutput_tableentryvalue = (dst_negative_scalar_pointwiseoutput_table) + ge_balance_positive_scalar_pointwiseoutput_tableentryvalue))))))))) /\ (forall sto_index_scalar_pointwiseentries. (exists pvs_gap_scalar_pointwiseentriesbound. pvs_gap_scalar_pointwiseentriesbound + S (sto_index_scalar_pointwiseentries) = (l)) -> exists sto_input_scalar_pointwiseentries sto_output_scalar_pointwiseentries. ((exists dst_positive_code_scalar_pointwiseentriesentryinput dst_positive_scale_scalar_pointwiseentriesentryinput dst_negative_code_scalar_pointwiseentriesentryinput dst_negative_scale_scalar_pointwiseentriesentryinput dst_positive_scalar_pointwiseentriesentryinput dst_negative_scalar_pointwiseentriesentryinput. (((F) = (((((dst_positive_code_scalar_pointwiseentriesentryinput) + (dst_positive_scale_scalar_pointwiseentriesentryinput)) * S ((dst_positive_code_scalar_pointwiseentriesentryinput) + (dst_positive_scale_scalar_pointwiseentriesentryinput)) + ((dst_positive_scale_scalar_pointwiseentriesentryinput) + (dst_positive_scale_scalar_pointwiseentriesentryinput))) + (((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) * S ((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) + ((dst_negative_scale_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)))) * S ((((dst_positive_code_scalar_pointwiseentriesentryinput) + (dst_positive_scale_scalar_pointwiseentriesentryinput)) * S ((dst_positive_code_scalar_pointwiseentriesentryinput) + (dst_positive_scale_scalar_pointwiseentriesentryinput)) + ((dst_positive_scale_scalar_pointwiseentriesentryinput) + (dst_positive_scale_scalar_pointwiseentriesentryinput))) + (((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) * S ((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) + ((dst_negative_scale_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)))) + ((((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) * S ((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) + ((dst_negative_scale_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput))) + (((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) * S ((dst_negative_code_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)) + ((dst_negative_scale_scalar_pointwiseentriesentryinput) + (dst_negative_scale_scalar_pointwiseentriesentryinput)))))) /\ (((((exists ff_h_pvs_scalar_pointwiseentriesentryinputpositive. ff_h_pvs_scalar_pointwiseentriesentryinputpositive + S (dst_positive_scalar_pointwiseentriesentryinput) = S ((S (sto_index_scalar_pointwiseentries)) * dst_positive_scale_scalar_pointwiseentriesentryinput)) /\ exists ff_q_pvs_scalar_pointwiseentriesentryinputpositive. dst_positive_code_scalar_pointwiseentriesentryinput = ff_q_pvs_scalar_pointwiseentriesentryinputpositive * S ((S (sto_index_scalar_pointwiseentries)) * dst_positive_scale_scalar_pointwiseentriesentryinput) + (dst_positive_scalar_pointwiseentriesentryinput))) /\ (((((exists ff_h_pvs_scalar_pointwiseentriesentryinputnegative. ff_h_pvs_scalar_pointwiseentriesentryinputnegative + S (dst_negative_scalar_pointwiseentriesentryinput) = S ((S (sto_index_scalar_pointwiseentries)) * dst_negative_scale_scalar_pointwiseentriesentryinput)) /\ exists ff_q_pvs_scalar_pointwiseentriesentryinputnegative. dst_negative_code_scalar_pointwiseentriesentryinput = ff_q_pvs_scalar_pointwiseentriesentryinputnegative * S ((S (sto_index_scalar_pointwiseentries)) * dst_negative_scale_scalar_pointwiseentriesentryinput) + (dst_negative_scalar_pointwiseentriesentryinput))) /\ (exists ge_balance_positive_scalar_pointwiseentriesentryinputvalue ge_balance_negative_scalar_pointwiseentriesentryinputvalue. (((((sto_input_scalar_pointwiseentries) = 2 * (ge_balance_positive_scalar_pointwiseentriesentryinputvalue) /\ (ge_balance_negative_scalar_pointwiseentriesentryinputvalue) = 0) \/ exists ge_signed_half_scalar_pointwiseentriesentryinputvaluedecode. (((sto_input_scalar_pointwiseentries) = 2 * ge_signed_half_scalar_pointwiseentriesentryinputvaluedecode + 1 /\ (ge_balance_positive_scalar_pointwiseentriesentryinputvalue) = 0) /\ (ge_balance_negative_scalar_pointwiseentriesentryinputvalue) = S ge_signed_half_scalar_pointwiseentriesentryinputvaluedecode))) /\ ((dst_positive_scalar_pointwiseentriesentryinput) + ge_balance_negative_scalar_pointwiseentriesentryinputvalue = (dst_negative_scalar_pointwiseentriesentryinput) + ge_balance_positive_scalar_pointwiseentriesentryinputvalue))))))))) /\ (((exists dst_positive_code_scalar_pointwiseentriesentryoutput dst_positive_scale_scalar_pointwiseentriesentryoutput dst_negative_code_scalar_pointwiseentriesentryoutput dst_negative_scale_scalar_pointwiseentriesentryoutput dst_positive_scalar_pointwiseentriesentryoutput dst_negative_scalar_pointwiseentriesentryoutput. (((G) = (((((dst_positive_code_scalar_pointwiseentriesentryoutput) + (dst_positive_scale_scalar_pointwiseentriesentryoutput)) * S ((dst_positive_code_scalar_pointwiseentriesentryoutput) + (dst_positive_scale_scalar_pointwiseentriesentryoutput)) + ((dst_positive_scale_scalar_pointwiseentriesentryoutput) + (dst_positive_scale_scalar_pointwiseentriesentryoutput))) + (((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) * S ((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) + ((dst_negative_scale_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)))) * S ((((dst_positive_code_scalar_pointwiseentriesentryoutput) + (dst_positive_scale_scalar_pointwiseentriesentryoutput)) * S ((dst_positive_code_scalar_pointwiseentriesentryoutput) + (dst_positive_scale_scalar_pointwiseentriesentryoutput)) + ((dst_positive_scale_scalar_pointwiseentriesentryoutput) + (dst_positive_scale_scalar_pointwiseentriesentryoutput))) + (((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) * S ((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) + ((dst_negative_scale_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)))) + ((((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) * S ((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) + ((dst_negative_scale_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput))) + (((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) * S ((dst_negative_code_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)) + ((dst_negative_scale_scalar_pointwiseentriesentryoutput) + (dst_negative_scale_scalar_pointwiseentriesentryoutput)))))) /\ (((((exists ff_h_pvs_scalar_pointwiseentriesentryoutputpositive. ff_h_pvs_scalar_pointwiseentriesentryoutputpositive + S (dst_positive_scalar_pointwiseentriesentryoutput) = S ((S (sto_index_scalar_pointwiseentries)) * dst_positive_scale_scalar_pointwiseentriesentryoutput)) /\ exists ff_q_pvs_scalar_pointwiseentriesentryoutputpositive. dst_positive_code_scalar_pointwiseentriesentryoutput = ff_q_pvs_scalar_pointwiseentriesentryoutputpositive * S ((S (sto_index_scalar_pointwiseentries)) * dst_positive_scale_scalar_pointwiseentriesentryoutput) + (dst_positive_scalar_pointwiseentriesentryoutput))) /\ (((((exists ff_h_pvs_scalar_pointwiseentriesentryoutputnegative. ff_h_pvs_scalar_pointwiseentriesentryoutputnegative + S (dst_negative_scalar_pointwiseentriesentryoutput) = S ((S (sto_index_scalar_pointwiseentries)) * dst_negative_scale_scalar_pointwiseentriesentryoutput)) /\ exists ff_q_pvs_scalar_pointwiseentriesentryoutputnegative. dst_negative_code_scalar_pointwiseentriesentryoutput = ff_q_pvs_scalar_pointwiseentriesentryoutputnegative * S ((S (sto_index_scalar_pointwiseentries)) * dst_negative_scale_scalar_pointwiseentriesentryoutput) + (dst_negative_scalar_pointwiseentriesentryoutput))) /\ (exists ge_balance_positive_scalar_pointwiseentriesentryoutputvalue ge_balance_negative_scalar_pointwiseentriesentryoutputvalue. (((((sto_output_scalar_pointwiseentries) = 2 * (ge_balance_positive_scalar_pointwiseentriesentryoutputvalue) /\ (ge_balance_negative_scalar_pointwiseentriesentryoutputvalue) = 0) \/ exists ge_signed_half_scalar_pointwiseentriesentryoutputvaluedecode. (((sto_output_scalar_pointwiseentries) = 2 * ge_signed_half_scalar_pointwiseentriesentryoutputvaluedecode + 1 /\ (ge_balance_positive_scalar_pointwiseentriesentryoutputvalue) = 0) /\ (ge_balance_negative_scalar_pointwiseentriesentryoutputvalue) = S ge_signed_half_scalar_pointwiseentriesentryoutputvaluedecode))) /\ ((dst_positive_scalar_pointwiseentriesentryoutput) + ge_balance_negative_scalar_pointwiseentriesentryoutputvalue = (dst_negative_scalar_pointwiseentriesentryoutput) + ge_balance_positive_scalar_pointwiseentriesentryoutputvalue))))))))) /\ (exists sto_ap_scalar_pointwiseentriesentryoperation sto_an_scalar_pointwiseentriesentryoperation sto_bp_scalar_pointwiseentriesentryoperation sto_bn_scalar_pointwiseentriesentryoperation sto_cp_scalar_pointwiseentriesentryoperation sto_cn_scalar_pointwiseentriesentryoperation. (((((a) = 2 * (sto_ap_scalar_pointwiseentriesentryoperation) /\ (sto_an_scalar_pointwiseentriesentryoperation) = 0) \/ exists ge_signed_half_scalar_pointwiseentriesentryoperationleft. (((a) = 2 * ge_signed_half_scalar_pointwiseentriesentryoperationleft + 1 /\ (sto_ap_scalar_pointwiseentriesentryoperation) = 0) /\ (sto_an_scalar_pointwiseentriesentryoperation) = S ge_signed_half_scalar_pointwiseentriesentryoperationleft))) /\ ((((((sto_input_scalar_pointwiseentries) = 2 * (sto_bp_scalar_pointwiseentriesentryoperation) /\ (sto_bn_scalar_pointwiseentriesentryoperation) = 0) \/ exists ge_signed_half_scalar_pointwiseentriesentryoperationright. (((sto_input_scalar_pointwiseentries) = 2 * ge_signed_half_scalar_pointwiseentriesentryoperationright + 1 /\ (sto_bp_scalar_pointwiseentriesentryoperation) = 0) /\ (sto_bn_scalar_pointwiseentriesentryoperation) = S ge_signed_half_scalar_pointwiseentriesentryoperationright))) /\ ((((((sto_output_scalar_pointwiseentries) = 2 * (sto_cp_scalar_pointwiseentriesentryoperation) /\ (sto_cn_scalar_pointwiseentriesentryoperation) = 0) \/ exists ge_signed_half_scalar_pointwiseentriesentryoperationoutput. (((sto_output_scalar_pointwiseentries) = 2 * ge_signed_half_scalar_pointwiseentriesentryoperationoutput + 1 /\ (sto_cp_scalar_pointwiseentriesentryoperation) = 0) /\ (sto_cn_scalar_pointwiseentriesentryoperation) = S ge_signed_half_scalar_pointwiseentriesentryoperationoutput))) /\ ((sto_ap_scalar_pointwiseentriesentryoperation * sto_bp_scalar_pointwiseentriesentryoperation + sto_an_scalar_pointwiseentriesentryoperation * sto_bn_scalar_pointwiseentriesentryoperation) + sto_cn_scalar_pointwiseentriesentryoperation = (sto_ap_scalar_pointwiseentriesentryoperation * sto_bn_scalar_pointwiseentriesentryoperation + sto_an_scalar_pointwiseentriesentryoperation * sto_bp_scalar_pointwiseentriesentryoperation) + sto_cp_scalar_pointwiseentriesentryoperation))))))))))))))) -> (exists dst_positive_code_scalar_source_sum dst_positive_scale_scalar_source_sum dst_negative_code_scalar_source_sum dst_negative_scale_scalar_source_sum dst_positive_sum_scalar_source_sum dst_negative_sum_scalar_source_sum. (((F) = (((((dst_positive_code_scalar_source_sum) + (dst_positive_scale_scalar_source_sum)) * S ((dst_positive_code_scalar_source_sum) + (dst_positive_scale_scalar_source_sum)) + ((dst_positive_scale_scalar_source_sum) + (dst_positive_scale_scalar_source_sum))) + (((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) * S ((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) + ((dst_negative_scale_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)))) * S ((((dst_positive_code_scalar_source_sum) + (dst_positive_scale_scalar_source_sum)) * S ((dst_positive_code_scalar_source_sum) + (dst_positive_scale_scalar_source_sum)) + ((dst_positive_scale_scalar_source_sum) + (dst_positive_scale_scalar_source_sum))) + (((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) * S ((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) + ((dst_negative_scale_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)))) + ((((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) * S ((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) + ((dst_negative_scale_scalar_source_sum) + (dst_negative_scale_scalar_source_sum))) + (((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) * S ((dst_negative_code_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)) + ((dst_negative_scale_scalar_source_sum) + (dst_negative_scale_scalar_source_sum)))))) /\ (((exists fs_u_dst_scalar_source_sumpositive fs_v_dst_scalar_source_sumpositive. ((((exists fs_h_dst_scalar_source_sumpositive_body_start. fs_h_dst_scalar_source_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_source_sumpositive)) /\ exists fs_q_dst_scalar_source_sumpositive_body_start. fs_u_dst_scalar_source_sumpositive = fs_q_dst_scalar_source_sumpositive_body_start * S ((S (0)) * fs_v_dst_scalar_source_sumpositive) + (0))) /\ ((((exists fs_h_dst_scalar_source_sumpositive_body_terminal. fs_h_dst_scalar_source_sumpositive_body_terminal + S (dst_positive_sum_scalar_source_sum) = S ((S (l)) * fs_v_dst_scalar_source_sumpositive)) /\ exists fs_q_dst_scalar_source_sumpositive_body_terminal. fs_u_dst_scalar_source_sumpositive = fs_q_dst_scalar_source_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_scalar_source_sumpositive) + (dst_positive_sum_scalar_source_sum))) /\ forall fs_i_dst_scalar_source_sumpositive_body_steps. (exists fs_lt_dst_scalar_source_sumpositive_body_steps_bound. fs_lt_dst_scalar_source_sumpositive_body_steps_bound + S fs_i_dst_scalar_source_sumpositive_body_steps = l) -> exists fs_a_dst_scalar_source_sumpositive_body_steps fs_r_dst_scalar_source_sumpositive_body_steps fs_s_dst_scalar_source_sumpositive_body_steps. ((((exists fs_h_dst_scalar_source_sumpositive_body_steps_summand. fs_h_dst_scalar_source_sumpositive_body_steps_summand + S (fs_a_dst_scalar_source_sumpositive_body_steps) = S ((S (fs_i_dst_scalar_source_sumpositive_body_steps)) * dst_positive_scale_scalar_source_sum)) /\ exists fs_q_dst_scalar_source_sumpositive_body_steps_summand. dst_positive_code_scalar_source_sum = fs_q_dst_scalar_source_sumpositive_body_steps_summand * S ((S (fs_i_dst_scalar_source_sumpositive_body_steps)) * dst_positive_scale_scalar_source_sum) + (fs_a_dst_scalar_source_sumpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_source_sumpositive_body_steps_partial. fs_h_dst_scalar_source_sumpositive_body_steps_partial + S (fs_r_dst_scalar_source_sumpositive_body_steps) = S ((S (fs_i_dst_scalar_source_sumpositive_body_steps)) * fs_v_dst_scalar_source_sumpositive)) /\ exists fs_q_dst_scalar_source_sumpositive_body_steps_partial. fs_u_dst_scalar_source_sumpositive = fs_q_dst_scalar_source_sumpositive_body_steps_partial * S ((S (fs_i_dst_scalar_source_sumpositive_body_steps)) * fs_v_dst_scalar_source_sumpositive) + (fs_r_dst_scalar_source_sumpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_source_sumpositive_body_steps_successor. fs_h_dst_scalar_source_sumpositive_body_steps_successor + S (fs_s_dst_scalar_source_sumpositive_body_steps) = S ((S (S fs_i_dst_scalar_source_sumpositive_body_steps)) * fs_v_dst_scalar_source_sumpositive)) /\ exists fs_q_dst_scalar_source_sumpositive_body_steps_successor. fs_u_dst_scalar_source_sumpositive = fs_q_dst_scalar_source_sumpositive_body_steps_successor * S ((S (S fs_i_dst_scalar_source_sumpositive_body_steps)) * fs_v_dst_scalar_source_sumpositive) + (fs_s_dst_scalar_source_sumpositive_body_steps))) /\ fs_s_dst_scalar_source_sumpositive_body_steps = fs_r_dst_scalar_source_sumpositive_body_steps + fs_a_dst_scalar_source_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_scalar_source_sumnegative fs_v_dst_scalar_source_sumnegative. ((((exists fs_h_dst_scalar_source_sumnegative_body_start. fs_h_dst_scalar_source_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_source_sumnegative)) /\ exists fs_q_dst_scalar_source_sumnegative_body_start. fs_u_dst_scalar_source_sumnegative = fs_q_dst_scalar_source_sumnegative_body_start * S ((S (0)) * fs_v_dst_scalar_source_sumnegative) + (0))) /\ ((((exists fs_h_dst_scalar_source_sumnegative_body_terminal. fs_h_dst_scalar_source_sumnegative_body_terminal + S (dst_negative_sum_scalar_source_sum) = S ((S (l)) * fs_v_dst_scalar_source_sumnegative)) /\ exists fs_q_dst_scalar_source_sumnegative_body_terminal. fs_u_dst_scalar_source_sumnegative = fs_q_dst_scalar_source_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_scalar_source_sumnegative) + (dst_negative_sum_scalar_source_sum))) /\ forall fs_i_dst_scalar_source_sumnegative_body_steps. (exists fs_lt_dst_scalar_source_sumnegative_body_steps_bound. fs_lt_dst_scalar_source_sumnegative_body_steps_bound + S fs_i_dst_scalar_source_sumnegative_body_steps = l) -> exists fs_a_dst_scalar_source_sumnegative_body_steps fs_r_dst_scalar_source_sumnegative_body_steps fs_s_dst_scalar_source_sumnegative_body_steps. ((((exists fs_h_dst_scalar_source_sumnegative_body_steps_summand. fs_h_dst_scalar_source_sumnegative_body_steps_summand + S (fs_a_dst_scalar_source_sumnegative_body_steps) = S ((S (fs_i_dst_scalar_source_sumnegative_body_steps)) * dst_negative_scale_scalar_source_sum)) /\ exists fs_q_dst_scalar_source_sumnegative_body_steps_summand. dst_negative_code_scalar_source_sum = fs_q_dst_scalar_source_sumnegative_body_steps_summand * S ((S (fs_i_dst_scalar_source_sumnegative_body_steps)) * dst_negative_scale_scalar_source_sum) + (fs_a_dst_scalar_source_sumnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_source_sumnegative_body_steps_partial. fs_h_dst_scalar_source_sumnegative_body_steps_partial + S (fs_r_dst_scalar_source_sumnegative_body_steps) = S ((S (fs_i_dst_scalar_source_sumnegative_body_steps)) * fs_v_dst_scalar_source_sumnegative)) /\ exists fs_q_dst_scalar_source_sumnegative_body_steps_partial. fs_u_dst_scalar_source_sumnegative = fs_q_dst_scalar_source_sumnegative_body_steps_partial * S ((S (fs_i_dst_scalar_source_sumnegative_body_steps)) * fs_v_dst_scalar_source_sumnegative) + (fs_r_dst_scalar_source_sumnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_source_sumnegative_body_steps_successor. fs_h_dst_scalar_source_sumnegative_body_steps_successor + S (fs_s_dst_scalar_source_sumnegative_body_steps) = S ((S (S fs_i_dst_scalar_source_sumnegative_body_steps)) * fs_v_dst_scalar_source_sumnegative)) /\ exists fs_q_dst_scalar_source_sumnegative_body_steps_successor. fs_u_dst_scalar_source_sumnegative = fs_q_dst_scalar_source_sumnegative_body_steps_successor * S ((S (S fs_i_dst_scalar_source_sumnegative_body_steps)) * fs_v_dst_scalar_source_sumnegative) + (fs_s_dst_scalar_source_sumnegative_body_steps))) /\ fs_s_dst_scalar_source_sumnegative_body_steps = fs_r_dst_scalar_source_sumnegative_body_steps + fs_a_dst_scalar_source_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_scalar_source_sumresult ge_balance_negative_scalar_source_sumresult. (((((b) = 2 * (ge_balance_positive_scalar_source_sumresult) /\ (ge_balance_negative_scalar_source_sumresult) = 0) \/ exists ge_signed_half_scalar_source_sumresultdecode. (((b) = 2 * ge_signed_half_scalar_source_sumresultdecode + 1 /\ (ge_balance_positive_scalar_source_sumresult) = 0) /\ (ge_balance_negative_scalar_source_sumresult) = S ge_signed_half_scalar_source_sumresultdecode))) /\ ((dst_positive_sum_scalar_source_sum) + ge_balance_negative_scalar_source_sumresult = (dst_negative_sum_scalar_source_sum) + ge_balance_positive_scalar_source_sumresult))))))))) -> (exists dst_positive_code_scalar_output_sum dst_positive_scale_scalar_output_sum dst_negative_code_scalar_output_sum dst_negative_scale_scalar_output_sum dst_positive_sum_scalar_output_sum dst_negative_sum_scalar_output_sum. (((G) = (((((dst_positive_code_scalar_output_sum) + (dst_positive_scale_scalar_output_sum)) * S ((dst_positive_code_scalar_output_sum) + (dst_positive_scale_scalar_output_sum)) + ((dst_positive_scale_scalar_output_sum) + (dst_positive_scale_scalar_output_sum))) + (((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) * S ((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) + ((dst_negative_scale_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)))) * S ((((dst_positive_code_scalar_output_sum) + (dst_positive_scale_scalar_output_sum)) * S ((dst_positive_code_scalar_output_sum) + (dst_positive_scale_scalar_output_sum)) + ((dst_positive_scale_scalar_output_sum) + (dst_positive_scale_scalar_output_sum))) + (((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) * S ((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) + ((dst_negative_scale_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)))) + ((((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) * S ((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) + ((dst_negative_scale_scalar_output_sum) + (dst_negative_scale_scalar_output_sum))) + (((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) * S ((dst_negative_code_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)) + ((dst_negative_scale_scalar_output_sum) + (dst_negative_scale_scalar_output_sum)))))) /\ (((exists fs_u_dst_scalar_output_sumpositive fs_v_dst_scalar_output_sumpositive. ((((exists fs_h_dst_scalar_output_sumpositive_body_start. fs_h_dst_scalar_output_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_output_sumpositive)) /\ exists fs_q_dst_scalar_output_sumpositive_body_start. fs_u_dst_scalar_output_sumpositive = fs_q_dst_scalar_output_sumpositive_body_start * S ((S (0)) * fs_v_dst_scalar_output_sumpositive) + (0))) /\ ((((exists fs_h_dst_scalar_output_sumpositive_body_terminal. fs_h_dst_scalar_output_sumpositive_body_terminal + S (dst_positive_sum_scalar_output_sum) = S ((S (l)) * fs_v_dst_scalar_output_sumpositive)) /\ exists fs_q_dst_scalar_output_sumpositive_body_terminal. fs_u_dst_scalar_output_sumpositive = fs_q_dst_scalar_output_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_scalar_output_sumpositive) + (dst_positive_sum_scalar_output_sum))) /\ forall fs_i_dst_scalar_output_sumpositive_body_steps. (exists fs_lt_dst_scalar_output_sumpositive_body_steps_bound. fs_lt_dst_scalar_output_sumpositive_body_steps_bound + S fs_i_dst_scalar_output_sumpositive_body_steps = l) -> exists fs_a_dst_scalar_output_sumpositive_body_steps fs_r_dst_scalar_output_sumpositive_body_steps fs_s_dst_scalar_output_sumpositive_body_steps. ((((exists fs_h_dst_scalar_output_sumpositive_body_steps_summand. fs_h_dst_scalar_output_sumpositive_body_steps_summand + S (fs_a_dst_scalar_output_sumpositive_body_steps) = S ((S (fs_i_dst_scalar_output_sumpositive_body_steps)) * dst_positive_scale_scalar_output_sum)) /\ exists fs_q_dst_scalar_output_sumpositive_body_steps_summand. dst_positive_code_scalar_output_sum = fs_q_dst_scalar_output_sumpositive_body_steps_summand * S ((S (fs_i_dst_scalar_output_sumpositive_body_steps)) * dst_positive_scale_scalar_output_sum) + (fs_a_dst_scalar_output_sumpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_output_sumpositive_body_steps_partial. fs_h_dst_scalar_output_sumpositive_body_steps_partial + S (fs_r_dst_scalar_output_sumpositive_body_steps) = S ((S (fs_i_dst_scalar_output_sumpositive_body_steps)) * fs_v_dst_scalar_output_sumpositive)) /\ exists fs_q_dst_scalar_output_sumpositive_body_steps_partial. fs_u_dst_scalar_output_sumpositive = fs_q_dst_scalar_output_sumpositive_body_steps_partial * S ((S (fs_i_dst_scalar_output_sumpositive_body_steps)) * fs_v_dst_scalar_output_sumpositive) + (fs_r_dst_scalar_output_sumpositive_body_steps))) /\ ((((exists fs_h_dst_scalar_output_sumpositive_body_steps_successor. fs_h_dst_scalar_output_sumpositive_body_steps_successor + S (fs_s_dst_scalar_output_sumpositive_body_steps) = S ((S (S fs_i_dst_scalar_output_sumpositive_body_steps)) * fs_v_dst_scalar_output_sumpositive)) /\ exists fs_q_dst_scalar_output_sumpositive_body_steps_successor. fs_u_dst_scalar_output_sumpositive = fs_q_dst_scalar_output_sumpositive_body_steps_successor * S ((S (S fs_i_dst_scalar_output_sumpositive_body_steps)) * fs_v_dst_scalar_output_sumpositive) + (fs_s_dst_scalar_output_sumpositive_body_steps))) /\ fs_s_dst_scalar_output_sumpositive_body_steps = fs_r_dst_scalar_output_sumpositive_body_steps + fs_a_dst_scalar_output_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_scalar_output_sumnegative fs_v_dst_scalar_output_sumnegative. ((((exists fs_h_dst_scalar_output_sumnegative_body_start. fs_h_dst_scalar_output_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_scalar_output_sumnegative)) /\ exists fs_q_dst_scalar_output_sumnegative_body_start. fs_u_dst_scalar_output_sumnegative = fs_q_dst_scalar_output_sumnegative_body_start * S ((S (0)) * fs_v_dst_scalar_output_sumnegative) + (0))) /\ ((((exists fs_h_dst_scalar_output_sumnegative_body_terminal. fs_h_dst_scalar_output_sumnegative_body_terminal + S (dst_negative_sum_scalar_output_sum) = S ((S (l)) * fs_v_dst_scalar_output_sumnegative)) /\ exists fs_q_dst_scalar_output_sumnegative_body_terminal. fs_u_dst_scalar_output_sumnegative = fs_q_dst_scalar_output_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_scalar_output_sumnegative) + (dst_negative_sum_scalar_output_sum))) /\ forall fs_i_dst_scalar_output_sumnegative_body_steps. (exists fs_lt_dst_scalar_output_sumnegative_body_steps_bound. fs_lt_dst_scalar_output_sumnegative_body_steps_bound + S fs_i_dst_scalar_output_sumnegative_body_steps = l) -> exists fs_a_dst_scalar_output_sumnegative_body_steps fs_r_dst_scalar_output_sumnegative_body_steps fs_s_dst_scalar_output_sumnegative_body_steps. ((((exists fs_h_dst_scalar_output_sumnegative_body_steps_summand. fs_h_dst_scalar_output_sumnegative_body_steps_summand + S (fs_a_dst_scalar_output_sumnegative_body_steps) = S ((S (fs_i_dst_scalar_output_sumnegative_body_steps)) * dst_negative_scale_scalar_output_sum)) /\ exists fs_q_dst_scalar_output_sumnegative_body_steps_summand. dst_negative_code_scalar_output_sum = fs_q_dst_scalar_output_sumnegative_body_steps_summand * S ((S (fs_i_dst_scalar_output_sumnegative_body_steps)) * dst_negative_scale_scalar_output_sum) + (fs_a_dst_scalar_output_sumnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_output_sumnegative_body_steps_partial. fs_h_dst_scalar_output_sumnegative_body_steps_partial + S (fs_r_dst_scalar_output_sumnegative_body_steps) = S ((S (fs_i_dst_scalar_output_sumnegative_body_steps)) * fs_v_dst_scalar_output_sumnegative)) /\ exists fs_q_dst_scalar_output_sumnegative_body_steps_partial. fs_u_dst_scalar_output_sumnegative = fs_q_dst_scalar_output_sumnegative_body_steps_partial * S ((S (fs_i_dst_scalar_output_sumnegative_body_steps)) * fs_v_dst_scalar_output_sumnegative) + (fs_r_dst_scalar_output_sumnegative_body_steps))) /\ ((((exists fs_h_dst_scalar_output_sumnegative_body_steps_successor. fs_h_dst_scalar_output_sumnegative_body_steps_successor + S (fs_s_dst_scalar_output_sumnegative_body_steps) = S ((S (S fs_i_dst_scalar_output_sumnegative_body_steps)) * fs_v_dst_scalar_output_sumnegative)) /\ exists fs_q_dst_scalar_output_sumnegative_body_steps_successor. fs_u_dst_scalar_output_sumnegative = fs_q_dst_scalar_output_sumnegative_body_steps_successor * S ((S (S fs_i_dst_scalar_output_sumnegative_body_steps)) * fs_v_dst_scalar_output_sumnegative) + (fs_s_dst_scalar_output_sumnegative_body_steps))) /\ fs_s_dst_scalar_output_sumnegative_body_steps = fs_r_dst_scalar_output_sumnegative_body_steps + fs_a_dst_scalar_output_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_scalar_output_sumresult ge_balance_negative_scalar_output_sumresult. (((((c) = 2 * (ge_balance_positive_scalar_output_sumresult) /\ (ge_balance_negative_scalar_output_sumresult) = 0) \/ exists ge_signed_half_scalar_output_sumresultdecode. (((c) = 2 * ge_signed_half_scalar_output_sumresultdecode + 1 /\ (ge_balance_positive_scalar_output_sumresult) = 0) /\ (ge_balance_negative_scalar_output_sumresult) = S ge_signed_half_scalar_output_sumresultdecode))) /\ ((dst_positive_sum_scalar_output_sum) + ge_balance_negative_scalar_output_sumresult = (dst_negative_sum_scalar_output_sum) + ge_balance_positive_scalar_output_sumresult))))))))) -> (exists sto_ap_scalar_sum_result sto_an_scalar_sum_result sto_bp_scalar_sum_result sto_bn_scalar_sum_result sto_cp_scalar_sum_result sto_cn_scalar_sum_result. (((((a) = 2 * (sto_ap_scalar_sum_result) /\ (sto_an_scalar_sum_result) = 0) \/ exists ge_signed_half_scalar_sum_resultleft. (((a) = 2 * ge_signed_half_scalar_sum_resultleft + 1 /\ (sto_ap_scalar_sum_result) = 0) /\ (sto_an_scalar_sum_result) = S ge_signed_half_scalar_sum_resultleft))) /\ ((((((b) = 2 * (sto_bp_scalar_sum_result) /\ (sto_bn_scalar_sum_result) = 0) \/ exists ge_signed_half_scalar_sum_resultright. (((b) = 2 * ge_signed_half_scalar_sum_resultright + 1 /\ (sto_bp_scalar_sum_result) = 0) /\ (sto_bn_scalar_sum_result) = S ge_signed_half_scalar_sum_resultright))) /\ ((((((c) = 2 * (sto_cp_scalar_sum_result) /\ (sto_cn_scalar_sum_result) = 0) \/ exists ge_signed_half_scalar_sum_resultoutput. (((c) = 2 * ge_signed_half_scalar_sum_resultoutput + 1 /\ (sto_cp_scalar_sum_result) = 0) /\ (sto_cn_scalar_sum_result) = S ge_signed_half_scalar_sum_resultoutput))) /\ ((sto_ap_scalar_sum_result * sto_bp_scalar_sum_result + sto_an_scalar_sum_result * sto_bn_scalar_sum_result) + sto_cn_scalar_sum_result = (sto_ap_scalar_sum_result * sto_bn_scalar_sum_result + sto_an_scalar_sum_result * sto_bp_scalar_sum_result) + sto_cp_scalar_sum_result)))))))

signed_prefix_sum_zero_value · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F l z. (forall sfs_index_zero_values sfs_value_zero_values. (exists pvs_le_gap_zero_valueslower. pvs_le_gap_zero_valueslower + (0) = (sfs_index_zero_values)) -> (exists pvs_gap_zero_valuesupper. pvs_gap_zero_valuesupper + S (sfs_index_zero_values) = (l)) -> (exists dst_positive_code_zero_valuesentry dst_positive_scale_zero_valuesentry dst_negative_code_zero_valuesentry dst_negative_scale_zero_valuesentry dst_positive_zero_valuesentry dst_negative_zero_valuesentry. (((F) = (((((dst_positive_code_zero_valuesentry) + (dst_positive_scale_zero_valuesentry)) * S ((dst_positive_code_zero_valuesentry) + (dst_positive_scale_zero_valuesentry)) + ((dst_positive_scale_zero_valuesentry) + (dst_positive_scale_zero_valuesentry))) + (((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) * S ((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) + ((dst_negative_scale_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)))) * S ((((dst_positive_code_zero_valuesentry) + (dst_positive_scale_zero_valuesentry)) * S ((dst_positive_code_zero_valuesentry) + (dst_positive_scale_zero_valuesentry)) + ((dst_positive_scale_zero_valuesentry) + (dst_positive_scale_zero_valuesentry))) + (((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) * S ((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) + ((dst_negative_scale_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)))) + ((((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) * S ((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) + ((dst_negative_scale_zero_valuesentry) + (dst_negative_scale_zero_valuesentry))) + (((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) * S ((dst_negative_code_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)) + ((dst_negative_scale_zero_valuesentry) + (dst_negative_scale_zero_valuesentry)))))) /\ (((((exists ff_h_pvs_zero_valuesentrypositive. ff_h_pvs_zero_valuesentrypositive + S (dst_positive_zero_valuesentry) = S ((S (sfs_index_zero_values)) * dst_positive_scale_zero_valuesentry)) /\ exists ff_q_pvs_zero_valuesentrypositive. dst_positive_code_zero_valuesentry = ff_q_pvs_zero_valuesentrypositive * S ((S (sfs_index_zero_values)) * dst_positive_scale_zero_valuesentry) + (dst_positive_zero_valuesentry))) /\ (((((exists ff_h_pvs_zero_valuesentrynegative. ff_h_pvs_zero_valuesentrynegative + S (dst_negative_zero_valuesentry) = S ((S (sfs_index_zero_values)) * dst_negative_scale_zero_valuesentry)) /\ exists ff_q_pvs_zero_valuesentrynegative. dst_negative_code_zero_valuesentry = ff_q_pvs_zero_valuesentrynegative * S ((S (sfs_index_zero_values)) * dst_negative_scale_zero_valuesentry) + (dst_negative_zero_valuesentry))) /\ (exists ge_balance_positive_zero_valuesentryvalue ge_balance_negative_zero_valuesentryvalue. (((((sfs_value_zero_values) = 2 * (ge_balance_positive_zero_valuesentryvalue) /\ (ge_balance_negative_zero_valuesentryvalue) = 0) \/ exists ge_signed_half_zero_valuesentryvaluedecode. (((sfs_value_zero_values) = 2 * ge_signed_half_zero_valuesentryvaluedecode + 1 /\ (ge_balance_positive_zero_valuesentryvalue) = 0) /\ (ge_balance_negative_zero_valuesentryvalue) = S ge_signed_half_zero_valuesentryvaluedecode))) /\ ((dst_positive_zero_valuesentry) + ge_balance_negative_zero_valuesentryvalue = (dst_negative_zero_valuesentry) + ge_balance_positive_zero_valuesentryvalue))))))))) -> sfs_value_zero_values=0) -> (exists dst_positive_code_zero_sum dst_positive_scale_zero_sum dst_negative_code_zero_sum dst_negative_scale_zero_sum dst_positive_sum_zero_sum dst_negative_sum_zero_sum. (((F) = (((((dst_positive_code_zero_sum) + (dst_positive_scale_zero_sum)) * S ((dst_positive_code_zero_sum) + (dst_positive_scale_zero_sum)) + ((dst_positive_scale_zero_sum) + (dst_positive_scale_zero_sum))) + (((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) * S ((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) + ((dst_negative_scale_zero_sum) + (dst_negative_scale_zero_sum)))) * S ((((dst_positive_code_zero_sum) + (dst_positive_scale_zero_sum)) * S ((dst_positive_code_zero_sum) + (dst_positive_scale_zero_sum)) + ((dst_positive_scale_zero_sum) + (dst_positive_scale_zero_sum))) + (((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) * S ((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) + ((dst_negative_scale_zero_sum) + (dst_negative_scale_zero_sum)))) + ((((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) * S ((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) + ((dst_negative_scale_zero_sum) + (dst_negative_scale_zero_sum))) + (((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) * S ((dst_negative_code_zero_sum) + (dst_negative_scale_zero_sum)) + ((dst_negative_scale_zero_sum) + (dst_negative_scale_zero_sum)))))) /\ (((exists fs_u_dst_zero_sumpositive fs_v_dst_zero_sumpositive. ((((exists fs_h_dst_zero_sumpositive_body_start. fs_h_dst_zero_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_sumpositive)) /\ exists fs_q_dst_zero_sumpositive_body_start. fs_u_dst_zero_sumpositive = fs_q_dst_zero_sumpositive_body_start * S ((S (0)) * fs_v_dst_zero_sumpositive) + (0))) /\ ((((exists fs_h_dst_zero_sumpositive_body_terminal. fs_h_dst_zero_sumpositive_body_terminal + S (dst_positive_sum_zero_sum) = S ((S (l)) * fs_v_dst_zero_sumpositive)) /\ exists fs_q_dst_zero_sumpositive_body_terminal. fs_u_dst_zero_sumpositive = fs_q_dst_zero_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_zero_sumpositive) + (dst_positive_sum_zero_sum))) /\ forall fs_i_dst_zero_sumpositive_body_steps. (exists fs_lt_dst_zero_sumpositive_body_steps_bound. fs_lt_dst_zero_sumpositive_body_steps_bound + S fs_i_dst_zero_sumpositive_body_steps = l) -> exists fs_a_dst_zero_sumpositive_body_steps fs_r_dst_zero_sumpositive_body_steps fs_s_dst_zero_sumpositive_body_steps. ((((exists fs_h_dst_zero_sumpositive_body_steps_summand. fs_h_dst_zero_sumpositive_body_steps_summand + S (fs_a_dst_zero_sumpositive_body_steps) = S ((S (fs_i_dst_zero_sumpositive_body_steps)) * dst_positive_scale_zero_sum)) /\ exists fs_q_dst_zero_sumpositive_body_steps_summand. dst_positive_code_zero_sum = fs_q_dst_zero_sumpositive_body_steps_summand * S ((S (fs_i_dst_zero_sumpositive_body_steps)) * dst_positive_scale_zero_sum) + (fs_a_dst_zero_sumpositive_body_steps))) /\ ((((exists fs_h_dst_zero_sumpositive_body_steps_partial. fs_h_dst_zero_sumpositive_body_steps_partial + S (fs_r_dst_zero_sumpositive_body_steps) = S ((S (fs_i_dst_zero_sumpositive_body_steps)) * fs_v_dst_zero_sumpositive)) /\ exists fs_q_dst_zero_sumpositive_body_steps_partial. fs_u_dst_zero_sumpositive = fs_q_dst_zero_sumpositive_body_steps_partial * S ((S (fs_i_dst_zero_sumpositive_body_steps)) * fs_v_dst_zero_sumpositive) + (fs_r_dst_zero_sumpositive_body_steps))) /\ ((((exists fs_h_dst_zero_sumpositive_body_steps_successor. fs_h_dst_zero_sumpositive_body_steps_successor + S (fs_s_dst_zero_sumpositive_body_steps) = S ((S (S fs_i_dst_zero_sumpositive_body_steps)) * fs_v_dst_zero_sumpositive)) /\ exists fs_q_dst_zero_sumpositive_body_steps_successor. fs_u_dst_zero_sumpositive = fs_q_dst_zero_sumpositive_body_steps_successor * S ((S (S fs_i_dst_zero_sumpositive_body_steps)) * fs_v_dst_zero_sumpositive) + (fs_s_dst_zero_sumpositive_body_steps))) /\ fs_s_dst_zero_sumpositive_body_steps = fs_r_dst_zero_sumpositive_body_steps + fs_a_dst_zero_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_zero_sumnegative fs_v_dst_zero_sumnegative. ((((exists fs_h_dst_zero_sumnegative_body_start. fs_h_dst_zero_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_zero_sumnegative)) /\ exists fs_q_dst_zero_sumnegative_body_start. fs_u_dst_zero_sumnegative = fs_q_dst_zero_sumnegative_body_start * S ((S (0)) * fs_v_dst_zero_sumnegative) + (0))) /\ ((((exists fs_h_dst_zero_sumnegative_body_terminal. fs_h_dst_zero_sumnegative_body_terminal + S (dst_negative_sum_zero_sum) = S ((S (l)) * fs_v_dst_zero_sumnegative)) /\ exists fs_q_dst_zero_sumnegative_body_terminal. fs_u_dst_zero_sumnegative = fs_q_dst_zero_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_zero_sumnegative) + (dst_negative_sum_zero_sum))) /\ forall fs_i_dst_zero_sumnegative_body_steps. (exists fs_lt_dst_zero_sumnegative_body_steps_bound. fs_lt_dst_zero_sumnegative_body_steps_bound + S fs_i_dst_zero_sumnegative_body_steps = l) -> exists fs_a_dst_zero_sumnegative_body_steps fs_r_dst_zero_sumnegative_body_steps fs_s_dst_zero_sumnegative_body_steps. ((((exists fs_h_dst_zero_sumnegative_body_steps_summand. fs_h_dst_zero_sumnegative_body_steps_summand + S (fs_a_dst_zero_sumnegative_body_steps) = S ((S (fs_i_dst_zero_sumnegative_body_steps)) * dst_negative_scale_zero_sum)) /\ exists fs_q_dst_zero_sumnegative_body_steps_summand. dst_negative_code_zero_sum = fs_q_dst_zero_sumnegative_body_steps_summand * S ((S (fs_i_dst_zero_sumnegative_body_steps)) * dst_negative_scale_zero_sum) + (fs_a_dst_zero_sumnegative_body_steps))) /\ ((((exists fs_h_dst_zero_sumnegative_body_steps_partial. fs_h_dst_zero_sumnegative_body_steps_partial + S (fs_r_dst_zero_sumnegative_body_steps) = S ((S (fs_i_dst_zero_sumnegative_body_steps)) * fs_v_dst_zero_sumnegative)) /\ exists fs_q_dst_zero_sumnegative_body_steps_partial. fs_u_dst_zero_sumnegative = fs_q_dst_zero_sumnegative_body_steps_partial * S ((S (fs_i_dst_zero_sumnegative_body_steps)) * fs_v_dst_zero_sumnegative) + (fs_r_dst_zero_sumnegative_body_steps))) /\ ((((exists fs_h_dst_zero_sumnegative_body_steps_successor. fs_h_dst_zero_sumnegative_body_steps_successor + S (fs_s_dst_zero_sumnegative_body_steps) = S ((S (S fs_i_dst_zero_sumnegative_body_steps)) * fs_v_dst_zero_sumnegative)) /\ exists fs_q_dst_zero_sumnegative_body_steps_successor. fs_u_dst_zero_sumnegative = fs_q_dst_zero_sumnegative_body_steps_successor * S ((S (S fs_i_dst_zero_sumnegative_body_steps)) * fs_v_dst_zero_sumnegative) + (fs_s_dst_zero_sumnegative_body_steps))) /\ fs_s_dst_zero_sumnegative_body_steps = fs_r_dst_zero_sumnegative_body_steps + fs_a_dst_zero_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_zero_sumresult ge_balance_negative_zero_sumresult. (((((z) = 2 * (ge_balance_positive_zero_sumresult) /\ (ge_balance_negative_zero_sumresult) = 0) \/ exists ge_signed_half_zero_sumresultdecode. (((z) = 2 * ge_signed_half_zero_sumresultdecode + 1 /\ (ge_balance_positive_zero_sumresult) = 0) /\ (ge_balance_negative_zero_sumresult) = S ge_signed_half_zero_sumresultdecode))) /\ ((dst_positive_sum_zero_sum) + ge_balance_negative_zero_sumresult = (dst_negative_sum_zero_sum) + ge_balance_positive_zero_sumresult))))))))) -> z=0

signed_rectangular_row_major_fubini · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F m n. (exists dst_positive_code_row_major_source dst_positive_scale_row_major_source dst_negative_code_row_major_source dst_negative_scale_row_major_source. (((F) = (((((dst_positive_code_row_major_source) + (dst_positive_scale_row_major_source)) * S ((dst_positive_code_row_major_source) + (dst_positive_scale_row_major_source)) + ((dst_positive_scale_row_major_source) + (dst_positive_scale_row_major_source))) + (((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) * S ((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) + ((dst_negative_scale_row_major_source) + (dst_negative_scale_row_major_source)))) * S ((((dst_positive_code_row_major_source) + (dst_positive_scale_row_major_source)) * S ((dst_positive_code_row_major_source) + (dst_positive_scale_row_major_source)) + ((dst_positive_scale_row_major_source) + (dst_positive_scale_row_major_source))) + (((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) * S ((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) + ((dst_negative_scale_row_major_source) + (dst_negative_scale_row_major_source)))) + ((((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) * S ((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) + ((dst_negative_scale_row_major_source) + (dst_negative_scale_row_major_source))) + (((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) * S ((dst_negative_code_row_major_source) + (dst_negative_scale_row_major_source)) + ((dst_negative_scale_row_major_source) + (dst_negative_scale_row_major_source)))))) /\ (forall dst_index_row_major_source. (exists pvs_le_gap_row_major_sourcedomain. pvs_le_gap_row_major_sourcedomain + (dst_index_row_major_source) = (m*n)) -> exists dst_positive_row_major_source dst_negative_row_major_source dst_value_row_major_source. ((((exists ff_h_pvs_row_major_sourceentrypositive. ff_h_pvs_row_major_sourceentrypositive + S (dst_positive_row_major_source) = S ((S (dst_index_row_major_source)) * dst_positive_scale_row_major_source)) /\ exists ff_q_pvs_row_major_sourceentrypositive. dst_positive_code_row_major_source = ff_q_pvs_row_major_sourceentrypositive * S ((S (dst_index_row_major_source)) * dst_positive_scale_row_major_source) + (dst_positive_row_major_source))) /\ (((((exists ff_h_pvs_row_major_sourceentrynegative. ff_h_pvs_row_major_sourceentrynegative + S (dst_negative_row_major_source) = S ((S (dst_index_row_major_source)) * dst_negative_scale_row_major_source)) /\ exists ff_q_pvs_row_major_sourceentrynegative. dst_negative_code_row_major_source = ff_q_pvs_row_major_sourceentrynegative * S ((S (dst_index_row_major_source)) * dst_negative_scale_row_major_source) + (dst_negative_row_major_source))) /\ (exists ge_balance_positive_row_major_sourceentryvalue ge_balance_negative_row_major_sourceentryvalue. (((((dst_value_row_major_source) = 2 * (ge_balance_positive_row_major_sourceentryvalue) /\ (ge_balance_negative_row_major_sourceentryvalue) = 0) \/ exists ge_signed_half_row_major_sourceentryvaluedecode. (((dst_value_row_major_source) = 2 * ge_signed_half_row_major_sourceentryvaluedecode + 1 /\ (ge_balance_positive_row_major_sourceentryvalue) = 0) /\ (ge_balance_negative_row_major_sourceentryvalue) = S ge_signed_half_row_major_sourceentryvaluedecode))) /\ ((dst_positive_row_major_source) + ge_balance_negative_row_major_sourceentryvalue = (dst_negative_row_major_source) + ge_balance_positive_row_major_sourceentryvalue))))))))) -> exists R C z. (((((exists dst_positive_code_row_major_resultrowssource_table dst_positive_scale_row_major_resultrowssource_table dst_negative_code_row_major_resultrowssource_table dst_negative_scale_row_major_resultrowssource_table. (((F) = (((((dst_positive_code_row_major_resultrowssource_table) + (dst_positive_scale_row_major_resultrowssource_table)) * S ((dst_positive_code_row_major_resultrowssource_table) + (dst_positive_scale_row_major_resultrowssource_table)) + ((dst_positive_scale_row_major_resultrowssource_table) + (dst_positive_scale_row_major_resultrowssource_table))) + (((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) * S ((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) + ((dst_negative_scale_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)))) * S ((((dst_positive_code_row_major_resultrowssource_table) + (dst_positive_scale_row_major_resultrowssource_table)) * S ((dst_positive_code_row_major_resultrowssource_table) + (dst_positive_scale_row_major_resultrowssource_table)) + ((dst_positive_scale_row_major_resultrowssource_table) + (dst_positive_scale_row_major_resultrowssource_table))) + (((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) * S ((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) + ((dst_negative_scale_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)))) + ((((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) * S ((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) + ((dst_negative_scale_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table))) + (((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) * S ((dst_negative_code_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)) + ((dst_negative_scale_row_major_resultrowssource_table) + (dst_negative_scale_row_major_resultrowssource_table)))))) /\ (forall dst_index_row_major_resultrowssource_table. (exists pvs_le_gap_row_major_resultrowssource_tabledomain. pvs_le_gap_row_major_resultrowssource_tabledomain + (dst_index_row_major_resultrowssource_table) = (0)) -> exists dst_positive_row_major_resultrowssource_table dst_negative_row_major_resultrowssource_table dst_value_row_major_resultrowssource_table. ((((exists ff_h_pvs_row_major_resultrowssource_tableentrypositive. ff_h_pvs_row_major_resultrowssource_tableentrypositive + S (dst_positive_row_major_resultrowssource_table) = S ((S (dst_index_row_major_resultrowssource_table)) * dst_positive_scale_row_major_resultrowssource_table)) /\ exists ff_q_pvs_row_major_resultrowssource_tableentrypositive. dst_positive_code_row_major_resultrowssource_table = ff_q_pvs_row_major_resultrowssource_tableentrypositive * S ((S (dst_index_row_major_resultrowssource_table)) * dst_positive_scale_row_major_resultrowssource_table) + (dst_positive_row_major_resultrowssource_table))) /\ (((((exists ff_h_pvs_row_major_resultrowssource_tableentrynegative. ff_h_pvs_row_major_resultrowssource_tableentrynegative + S (dst_negative_row_major_resultrowssource_table) = S ((S (dst_index_row_major_resultrowssource_table)) * dst_negative_scale_row_major_resultrowssource_table)) /\ exists ff_q_pvs_row_major_resultrowssource_tableentrynegative. dst_negative_code_row_major_resultrowssource_table = ff_q_pvs_row_major_resultrowssource_tableentrynegative * S ((S (dst_index_row_major_resultrowssource_table)) * dst_negative_scale_row_major_resultrowssource_table) + (dst_negative_row_major_resultrowssource_table))) /\ (exists ge_balance_positive_row_major_resultrowssource_tableentryvalue ge_balance_negative_row_major_resultrowssource_tableentryvalue. (((((dst_value_row_major_resultrowssource_table) = 2 * (ge_balance_positive_row_major_resultrowssource_tableentryvalue) /\ (ge_balance_negative_row_major_resultrowssource_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultrowssource_tableentryvaluedecode. (((dst_value_row_major_resultrowssource_table) = 2 * ge_signed_half_row_major_resultrowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultrowssource_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultrowssource_tableentryvalue) = S ge_signed_half_row_major_resultrowssource_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultrowssource_table) + ge_balance_negative_row_major_resultrowssource_tableentryvalue = (dst_negative_row_major_resultrowssource_table) + ge_balance_positive_row_major_resultrowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_row_major_resultrowsrow_table dst_positive_scale_row_major_resultrowsrow_table dst_negative_code_row_major_resultrowsrow_table dst_negative_scale_row_major_resultrowsrow_table. (((R) = (((((dst_positive_code_row_major_resultrowsrow_table) + (dst_positive_scale_row_major_resultrowsrow_table)) * S ((dst_positive_code_row_major_resultrowsrow_table) + (dst_positive_scale_row_major_resultrowsrow_table)) + ((dst_positive_scale_row_major_resultrowsrow_table) + (dst_positive_scale_row_major_resultrowsrow_table))) + (((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) * S ((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) + ((dst_negative_scale_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)))) * S ((((dst_positive_code_row_major_resultrowsrow_table) + (dst_positive_scale_row_major_resultrowsrow_table)) * S ((dst_positive_code_row_major_resultrowsrow_table) + (dst_positive_scale_row_major_resultrowsrow_table)) + ((dst_positive_scale_row_major_resultrowsrow_table) + (dst_positive_scale_row_major_resultrowsrow_table))) + (((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) * S ((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) + ((dst_negative_scale_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)))) + ((((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) * S ((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) + ((dst_negative_scale_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table))) + (((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) * S ((dst_negative_code_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)) + ((dst_negative_scale_row_major_resultrowsrow_table) + (dst_negative_scale_row_major_resultrowsrow_table)))))) /\ (forall dst_index_row_major_resultrowsrow_table. (exists pvs_le_gap_row_major_resultrowsrow_tabledomain. pvs_le_gap_row_major_resultrowsrow_tabledomain + (dst_index_row_major_resultrowsrow_table) = (m)) -> exists dst_positive_row_major_resultrowsrow_table dst_negative_row_major_resultrowsrow_table dst_value_row_major_resultrowsrow_table. ((((exists ff_h_pvs_row_major_resultrowsrow_tableentrypositive. ff_h_pvs_row_major_resultrowsrow_tableentrypositive + S (dst_positive_row_major_resultrowsrow_table) = S ((S (dst_index_row_major_resultrowsrow_table)) * dst_positive_scale_row_major_resultrowsrow_table)) /\ exists ff_q_pvs_row_major_resultrowsrow_tableentrypositive. dst_positive_code_row_major_resultrowsrow_table = ff_q_pvs_row_major_resultrowsrow_tableentrypositive * S ((S (dst_index_row_major_resultrowsrow_table)) * dst_positive_scale_row_major_resultrowsrow_table) + (dst_positive_row_major_resultrowsrow_table))) /\ (((((exists ff_h_pvs_row_major_resultrowsrow_tableentrynegative. ff_h_pvs_row_major_resultrowsrow_tableentrynegative + S (dst_negative_row_major_resultrowsrow_table) = S ((S (dst_index_row_major_resultrowsrow_table)) * dst_negative_scale_row_major_resultrowsrow_table)) /\ exists ff_q_pvs_row_major_resultrowsrow_tableentrynegative. dst_negative_code_row_major_resultrowsrow_table = ff_q_pvs_row_major_resultrowsrow_tableentrynegative * S ((S (dst_index_row_major_resultrowsrow_table)) * dst_negative_scale_row_major_resultrowsrow_table) + (dst_negative_row_major_resultrowsrow_table))) /\ (exists ge_balance_positive_row_major_resultrowsrow_tableentryvalue ge_balance_negative_row_major_resultrowsrow_tableentryvalue. (((((dst_value_row_major_resultrowsrow_table) = 2 * (ge_balance_positive_row_major_resultrowsrow_tableentryvalue) /\ (ge_balance_negative_row_major_resultrowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultrowsrow_tableentryvaluedecode. (((dst_value_row_major_resultrowsrow_table) = 2 * ge_signed_half_row_major_resultrowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultrowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultrowsrow_tableentryvalue) = S ge_signed_half_row_major_resultrowsrow_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultrowsrow_table) + ge_balance_negative_row_major_resultrowsrow_tableentryvalue = (dst_negative_row_major_resultrowsrow_table) + ge_balance_positive_row_major_resultrowsrow_tableentryvalue))))))))) /\ (forall srt_index_row_major_resultrows. (exists pvs_gap_row_major_resultrowsbound. pvs_gap_row_major_resultrowsbound + S (srt_index_row_major_resultrows) = (m)) -> exists srt_value_row_major_resultrows. (((exists dst_positive_code_row_major_resultrowsrowentry dst_positive_scale_row_major_resultrowsrowentry dst_negative_code_row_major_resultrowsrowentry dst_negative_scale_row_major_resultrowsrowentry dst_positive_row_major_resultrowsrowentry dst_negative_row_major_resultrowsrowentry. (((R) = (((((dst_positive_code_row_major_resultrowsrowentry) + (dst_positive_scale_row_major_resultrowsrowentry)) * S ((dst_positive_code_row_major_resultrowsrowentry) + (dst_positive_scale_row_major_resultrowsrowentry)) + ((dst_positive_scale_row_major_resultrowsrowentry) + (dst_positive_scale_row_major_resultrowsrowentry))) + (((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) * S ((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) + ((dst_negative_scale_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)))) * S ((((dst_positive_code_row_major_resultrowsrowentry) + (dst_positive_scale_row_major_resultrowsrowentry)) * S ((dst_positive_code_row_major_resultrowsrowentry) + (dst_positive_scale_row_major_resultrowsrowentry)) + ((dst_positive_scale_row_major_resultrowsrowentry) + (dst_positive_scale_row_major_resultrowsrowentry))) + (((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) * S ((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) + ((dst_negative_scale_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)))) + ((((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) * S ((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) + ((dst_negative_scale_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry))) + (((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) * S ((dst_negative_code_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)) + ((dst_negative_scale_row_major_resultrowsrowentry) + (dst_negative_scale_row_major_resultrowsrowentry)))))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowentrypositive. ff_h_pvs_row_major_resultrowsrowentrypositive + S (dst_positive_row_major_resultrowsrowentry) = S ((S (srt_index_row_major_resultrows)) * dst_positive_scale_row_major_resultrowsrowentry)) /\ exists ff_q_pvs_row_major_resultrowsrowentrypositive. dst_positive_code_row_major_resultrowsrowentry = ff_q_pvs_row_major_resultrowsrowentrypositive * S ((S (srt_index_row_major_resultrows)) * dst_positive_scale_row_major_resultrowsrowentry) + (dst_positive_row_major_resultrowsrowentry))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowentrynegative. ff_h_pvs_row_major_resultrowsrowentrynegative + S (dst_negative_row_major_resultrowsrowentry) = S ((S (srt_index_row_major_resultrows)) * dst_negative_scale_row_major_resultrowsrowentry)) /\ exists ff_q_pvs_row_major_resultrowsrowentrynegative. dst_negative_code_row_major_resultrowsrowentry = ff_q_pvs_row_major_resultrowsrowentrynegative * S ((S (srt_index_row_major_resultrows)) * dst_negative_scale_row_major_resultrowsrowentry) + (dst_negative_row_major_resultrowsrowentry))) /\ (exists ge_balance_positive_row_major_resultrowsrowentryvalue ge_balance_negative_row_major_resultrowsrowentryvalue. (((((srt_value_row_major_resultrows) = 2 * (ge_balance_positive_row_major_resultrowsrowentryvalue) /\ (ge_balance_negative_row_major_resultrowsrowentryvalue) = 0) \/ exists ge_signed_half_row_major_resultrowsrowentryvaluedecode. (((srt_value_row_major_resultrows) = 2 * ge_signed_half_row_major_resultrowsrowentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultrowsrowentryvalue) = 0) /\ (ge_balance_negative_row_major_resultrowsrowentryvalue) = S ge_signed_half_row_major_resultrowsrowentryvaluedecode))) /\ ((dst_positive_row_major_resultrowsrowentry) + ge_balance_negative_row_major_resultrowsrowentryvalue = (dst_negative_row_major_resultrowsrowentry) + ge_balance_positive_row_major_resultrowsrowentryvalue))))))))) /\ (exists srs_slice_row_major_resultrowsrowrow_sum. ((((exists dst_positive_code_row_major_resultrowsrowrow_sumslicesource_table dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table))) + (((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table))) + (((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table))) + (((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_row_major_resultrowsrowrow_sumslicesource_table. (exists pvs_le_gap_row_major_resultrowsrowrow_sumslicesource_tabledomain. pvs_le_gap_row_major_resultrowsrowrow_sumslicesource_tabledomain + (dst_index_row_major_resultrowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_row_major_resultrowsrowrow_sumslicesource_table dst_negative_row_major_resultrowsrowrow_sumslicesource_table dst_value_row_major_resultrowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_row_major_resultrowsrowrow_sumslicesource_table) = S ((S (dst_index_row_major_resultrowsrowrow_sumslicesource_table)) * dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_row_major_resultrowsrowrow_sumslicesource_table = ff_q_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_row_major_resultrowsrowrow_sumslicesource_table)) * dst_positive_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_positive_row_major_resultrowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_row_major_resultrowsrowrow_sumslicesource_table) = S ((S (dst_index_row_major_resultrowsrowrow_sumslicesource_table)) * dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_row_major_resultrowsrowrow_sumslicesource_table = ff_q_pvs_row_major_resultrowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_row_major_resultrowsrowrow_sumslicesource_table)) * dst_negative_scale_row_major_resultrowsrowrow_sumslicesource_table) + (dst_negative_row_major_resultrowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_row_major_resultrowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_row_major_resultrowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_row_major_resultrowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_row_major_resultrowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultrowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_row_major_resultrowsrowrow_sumslicesource_table) = 2 * ge_signed_half_row_major_resultrowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultrowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_row_major_resultrowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultrowsrowrow_sumslicesource_table) + ge_balance_negative_row_major_resultrowsrowrow_sumslicesource_tableentryvalue = (dst_negative_row_major_resultrowsrowrow_sumslicesource_table) + ge_balance_positive_row_major_resultrowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_row_major_resultrowsrowrow_sumsliceoutput_table dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table. (((srs_slice_row_major_resultrowsrowrow_sum) = (((((dst_positive_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_row_major_resultrowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_row_major_resultrowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_row_major_resultrowsrowrow_sumsliceoutput_tabledomain + (dst_index_row_major_resultrowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_row_major_resultrowsrowrow_sumsliceoutput_table dst_negative_row_major_resultrowsrowrow_sumsliceoutput_table dst_value_row_major_resultrowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_row_major_resultrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_row_major_resultrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_row_major_resultrowsrowrow_sumsliceoutput_table = ff_q_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_row_major_resultrowsrowrow_sumsliceoutput_table)) * dst_positive_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_positive_row_major_resultrowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_row_major_resultrowsrowrow_sumsliceoutput_table) = S ((S (dst_index_row_major_resultrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_row_major_resultrowsrowrow_sumsliceoutput_table = ff_q_pvs_row_major_resultrowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_row_major_resultrowsrowrow_sumsliceoutput_table)) * dst_negative_scale_row_major_resultrowsrowrow_sumsliceoutput_table) + (dst_negative_row_major_resultrowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_row_major_resultrowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultrowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_row_major_resultrowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_row_major_resultrowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_row_major_resultrowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultrowsrowrow_sumsliceoutput_table) + ge_balance_negative_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_row_major_resultrowsrowrow_sumsliceoutput_table) + ge_balance_positive_row_major_resultrowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_row_major_resultrowsrowrow_sumslice. (exists pvs_gap_row_major_resultrowsrowrow_sumslicebound. pvs_gap_row_major_resultrowsrowrow_sumslicebound + S (srs_index_row_major_resultrowsrowrow_sumslice) = (n)) -> exists srs_value_row_major_resultrowsrowrow_sumslice. (((exists dst_positive_code_row_major_resultrowsrowrow_sumsliceentrysource dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource dst_positive_row_major_resultrowsrowrow_sumsliceentrysource dst_negative_row_major_resultrowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_row_major_resultrowsrowrow_sumsliceentrysourcepositive + S (dst_positive_row_major_resultrowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_row_major_resultrows)))) + ((1) * (srs_index_row_major_resultrowsrowrow_sumslice))))) * dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumsliceentrysourcepositive. dst_positive_code_row_major_resultrowsrowrow_sumsliceentrysource = ff_q_pvs_row_major_resultrowsrowrow_sumsliceentrysourcepositive * S ((S (((((0) + ((n) * (srt_index_row_major_resultrows)))) + ((1) * (srs_index_row_major_resultrowsrowrow_sumslice))))) * dst_positive_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_positive_row_major_resultrowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_row_major_resultrowsrowrow_sumsliceentrysourcenegative + S (dst_negative_row_major_resultrowsrowrow_sumsliceentrysource) = S ((S (((((0) + ((n) * (srt_index_row_major_resultrows)))) + ((1) * (srs_index_row_major_resultrowsrowrow_sumslice))))) * dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumsliceentrysourcenegative. dst_negative_code_row_major_resultrowsrowrow_sumsliceentrysource = ff_q_pvs_row_major_resultrowsrowrow_sumsliceentrysourcenegative * S ((S (((((0) + ((n) * (srt_index_row_major_resultrows)))) + ((1) * (srs_index_row_major_resultrowsrowrow_sumslice))))) * dst_negative_scale_row_major_resultrowsrowrow_sumsliceentrysource) + (dst_negative_row_major_resultrowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_row_major_resultrowsrowrow_sumsliceentrysourcevalue ge_balance_negative_row_major_resultrowsrowrow_sumsliceentrysourcevalue. (((((srs_value_row_major_resultrowsrowrow_sumslice) = 2 * (ge_balance_positive_row_major_resultrowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_row_major_resultrowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_row_major_resultrowsrowrow_sumslice) = 2 * ge_signed_half_row_major_resultrowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_row_major_resultrowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_row_major_resultrowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_row_major_resultrowsrowrow_sumsliceentrysource) + ge_balance_negative_row_major_resultrowsrowrow_sumsliceentrysourcevalue = (dst_negative_row_major_resultrowsrowrow_sumsliceentrysource) + ge_balance_positive_row_major_resultrowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_row_major_resultrowsrowrow_sumsliceentryoutput dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput dst_positive_row_major_resultrowsrowrow_sumsliceentryoutput dst_negative_row_major_resultrowsrowrow_sumsliceentryoutput. (((srs_slice_row_major_resultrowsrowrow_sum) = (((((dst_positive_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_row_major_resultrowsrowrow_sumsliceentryoutputpositive + S (dst_positive_row_major_resultrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_row_major_resultrowsrowrow_sumslice)) * dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumsliceentryoutputpositive. dst_positive_code_row_major_resultrowsrowrow_sumsliceentryoutput = ff_q_pvs_row_major_resultrowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_row_major_resultrowsrowrow_sumslice)) * dst_positive_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_positive_row_major_resultrowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_row_major_resultrowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_row_major_resultrowsrowrow_sumsliceentryoutputnegative + S (dst_negative_row_major_resultrowsrowrow_sumsliceentryoutput) = S ((S (srs_index_row_major_resultrowsrowrow_sumslice)) * dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_row_major_resultrowsrowrow_sumsliceentryoutputnegative. dst_negative_code_row_major_resultrowsrowrow_sumsliceentryoutput = ff_q_pvs_row_major_resultrowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_row_major_resultrowsrowrow_sumslice)) * dst_negative_scale_row_major_resultrowsrowrow_sumsliceentryoutput) + (dst_negative_row_major_resultrowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_row_major_resultrowsrowrow_sumsliceentryoutputvalue ge_balance_negative_row_major_resultrowsrowrow_sumsliceentryoutputvalue. (((((srs_value_row_major_resultrowsrowrow_sumslice) = 2 * (ge_balance_positive_row_major_resultrowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_row_major_resultrowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_row_major_resultrowsrowrow_sumslice) = 2 * ge_signed_half_row_major_resultrowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_row_major_resultrowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_row_major_resultrowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_row_major_resultrowsrowrow_sumsliceentryoutput) + ge_balance_negative_row_major_resultrowsrowrow_sumsliceentryoutputvalue = (dst_negative_row_major_resultrowsrowrow_sumsliceentryoutput) + ge_balance_positive_row_major_resultrowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_row_major_resultrowsrowrow_sumsum dst_positive_scale_row_major_resultrowsrowrow_sumsum dst_negative_code_row_major_resultrowsrowrow_sumsum dst_negative_scale_row_major_resultrowsrowrow_sumsum dst_positive_sum_row_major_resultrowsrowrow_sumsum dst_negative_sum_row_major_resultrowsrowrow_sumsum. (((srs_slice_row_major_resultrowsrowrow_sum) = (((((dst_positive_code_row_major_resultrowsrowrow_sumsum) + (dst_positive_scale_row_major_resultrowsrowrow_sumsum)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsum) + (dst_positive_scale_row_major_resultrowsrowrow_sumsum)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsum) + (dst_positive_scale_row_major_resultrowsrowrow_sumsum))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)))) * S ((((dst_positive_code_row_major_resultrowsrowrow_sumsum) + (dst_positive_scale_row_major_resultrowsrowrow_sumsum)) * S ((dst_positive_code_row_major_resultrowsrowrow_sumsum) + (dst_positive_scale_row_major_resultrowsrowrow_sumsum)) + ((dst_positive_scale_row_major_resultrowsrowrow_sumsum) + (dst_positive_scale_row_major_resultrowsrowrow_sumsum))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)))) + ((((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum))) + (((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultrowsrowrow_sumsum) + (dst_negative_scale_row_major_resultrowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_row_major_resultrowsrowrow_sumsumpositive fs_v_dst_row_major_resultrowsrowrow_sumsumpositive. ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_start. fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_start. fs_u_dst_row_major_resultrowsrowrow_sumsumpositive = fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_terminal. fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_row_major_resultrowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_terminal. fs_u_dst_row_major_resultrowsrowrow_sumsumpositive = fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive) + (dst_positive_sum_row_major_resultrowsrowrow_sumsum))) /\ forall fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps fs_r_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps fs_s_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_row_major_resultrowsrowrow_sumsum)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_row_major_resultrowsrowrow_sumsum = fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_row_major_resultrowsrowrow_sumsum) + (fs_a_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_row_major_resultrowsrowrow_sumsumpositive = fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive) + (fs_r_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_row_major_resultrowsrowrow_sumsumpositive = fs_q_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumpositive) + (fs_s_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps = fs_r_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps + fs_a_dst_row_major_resultrowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_row_major_resultrowsrowrow_sumsumnegative fs_v_dst_row_major_resultrowsrowrow_sumsumnegative. ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_start. fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_start. fs_u_dst_row_major_resultrowsrowrow_sumsumnegative = fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_terminal. fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_row_major_resultrowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_terminal. fs_u_dst_row_major_resultrowsrowrow_sumsumnegative = fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative) + (dst_negative_sum_row_major_resultrowsrowrow_sumsum))) /\ forall fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps fs_r_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps fs_s_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_row_major_resultrowsrowrow_sumsum)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_row_major_resultrowsrowrow_sumsum = fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_row_major_resultrowsrowrow_sumsum) + (fs_a_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_row_major_resultrowsrowrow_sumsumnegative = fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative) + (fs_r_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_row_major_resultrowsrowrow_sumsumnegative = fs_q_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultrowsrowrow_sumsumnegative) + (fs_s_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps = fs_r_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps + fs_a_dst_row_major_resultrowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_row_major_resultrowsrowrow_sumsumresult ge_balance_negative_row_major_resultrowsrowrow_sumsumresult. (((((srt_value_row_major_resultrows) = 2 * (ge_balance_positive_row_major_resultrowsrowrow_sumsumresult) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_row_major_resultrowsrowrow_sumsumresultdecode. (((srt_value_row_major_resultrows) = 2 * ge_signed_half_row_major_resultrowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_row_major_resultrowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_row_major_resultrowsrowrow_sumsumresult) = S ge_signed_half_row_major_resultrowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_row_major_resultrowsrowrow_sumsum) + ge_balance_negative_row_major_resultrowsrowrow_sumsumresult = (dst_negative_sum_row_major_resultrowsrowrow_sumsum) + ge_balance_positive_row_major_resultrowsrowrow_sumsumresult)))))))))))))))))) /\ (((((exists dst_positive_code_row_major_resultcolumnssource_table dst_positive_scale_row_major_resultcolumnssource_table dst_negative_code_row_major_resultcolumnssource_table dst_negative_scale_row_major_resultcolumnssource_table. (((F) = (((((dst_positive_code_row_major_resultcolumnssource_table) + (dst_positive_scale_row_major_resultcolumnssource_table)) * S ((dst_positive_code_row_major_resultcolumnssource_table) + (dst_positive_scale_row_major_resultcolumnssource_table)) + ((dst_positive_scale_row_major_resultcolumnssource_table) + (dst_positive_scale_row_major_resultcolumnssource_table))) + (((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) * S ((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) + ((dst_negative_scale_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)))) * S ((((dst_positive_code_row_major_resultcolumnssource_table) + (dst_positive_scale_row_major_resultcolumnssource_table)) * S ((dst_positive_code_row_major_resultcolumnssource_table) + (dst_positive_scale_row_major_resultcolumnssource_table)) + ((dst_positive_scale_row_major_resultcolumnssource_table) + (dst_positive_scale_row_major_resultcolumnssource_table))) + (((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) * S ((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) + ((dst_negative_scale_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)))) + ((((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) * S ((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) + ((dst_negative_scale_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table))) + (((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) * S ((dst_negative_code_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)) + ((dst_negative_scale_row_major_resultcolumnssource_table) + (dst_negative_scale_row_major_resultcolumnssource_table)))))) /\ (forall dst_index_row_major_resultcolumnssource_table. (exists pvs_le_gap_row_major_resultcolumnssource_tabledomain. pvs_le_gap_row_major_resultcolumnssource_tabledomain + (dst_index_row_major_resultcolumnssource_table) = (0)) -> exists dst_positive_row_major_resultcolumnssource_table dst_negative_row_major_resultcolumnssource_table dst_value_row_major_resultcolumnssource_table. ((((exists ff_h_pvs_row_major_resultcolumnssource_tableentrypositive. ff_h_pvs_row_major_resultcolumnssource_tableentrypositive + S (dst_positive_row_major_resultcolumnssource_table) = S ((S (dst_index_row_major_resultcolumnssource_table)) * dst_positive_scale_row_major_resultcolumnssource_table)) /\ exists ff_q_pvs_row_major_resultcolumnssource_tableentrypositive. dst_positive_code_row_major_resultcolumnssource_table = ff_q_pvs_row_major_resultcolumnssource_tableentrypositive * S ((S (dst_index_row_major_resultcolumnssource_table)) * dst_positive_scale_row_major_resultcolumnssource_table) + (dst_positive_row_major_resultcolumnssource_table))) /\ (((((exists ff_h_pvs_row_major_resultcolumnssource_tableentrynegative. ff_h_pvs_row_major_resultcolumnssource_tableentrynegative + S (dst_negative_row_major_resultcolumnssource_table) = S ((S (dst_index_row_major_resultcolumnssource_table)) * dst_negative_scale_row_major_resultcolumnssource_table)) /\ exists ff_q_pvs_row_major_resultcolumnssource_tableentrynegative. dst_negative_code_row_major_resultcolumnssource_table = ff_q_pvs_row_major_resultcolumnssource_tableentrynegative * S ((S (dst_index_row_major_resultcolumnssource_table)) * dst_negative_scale_row_major_resultcolumnssource_table) + (dst_negative_row_major_resultcolumnssource_table))) /\ (exists ge_balance_positive_row_major_resultcolumnssource_tableentryvalue ge_balance_negative_row_major_resultcolumnssource_tableentryvalue. (((((dst_value_row_major_resultcolumnssource_table) = 2 * (ge_balance_positive_row_major_resultcolumnssource_tableentryvalue) /\ (ge_balance_negative_row_major_resultcolumnssource_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultcolumnssource_tableentryvaluedecode. (((dst_value_row_major_resultcolumnssource_table) = 2 * ge_signed_half_row_major_resultcolumnssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultcolumnssource_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultcolumnssource_tableentryvalue) = S ge_signed_half_row_major_resultcolumnssource_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultcolumnssource_table) + ge_balance_negative_row_major_resultcolumnssource_tableentryvalue = (dst_negative_row_major_resultcolumnssource_table) + ge_balance_positive_row_major_resultcolumnssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_row_major_resultcolumnsrow_table dst_positive_scale_row_major_resultcolumnsrow_table dst_negative_code_row_major_resultcolumnsrow_table dst_negative_scale_row_major_resultcolumnsrow_table. (((C) = (((((dst_positive_code_row_major_resultcolumnsrow_table) + (dst_positive_scale_row_major_resultcolumnsrow_table)) * S ((dst_positive_code_row_major_resultcolumnsrow_table) + (dst_positive_scale_row_major_resultcolumnsrow_table)) + ((dst_positive_scale_row_major_resultcolumnsrow_table) + (dst_positive_scale_row_major_resultcolumnsrow_table))) + (((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) * S ((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) + ((dst_negative_scale_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)))) * S ((((dst_positive_code_row_major_resultcolumnsrow_table) + (dst_positive_scale_row_major_resultcolumnsrow_table)) * S ((dst_positive_code_row_major_resultcolumnsrow_table) + (dst_positive_scale_row_major_resultcolumnsrow_table)) + ((dst_positive_scale_row_major_resultcolumnsrow_table) + (dst_positive_scale_row_major_resultcolumnsrow_table))) + (((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) * S ((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) + ((dst_negative_scale_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)))) + ((((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) * S ((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) + ((dst_negative_scale_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table))) + (((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) * S ((dst_negative_code_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)) + ((dst_negative_scale_row_major_resultcolumnsrow_table) + (dst_negative_scale_row_major_resultcolumnsrow_table)))))) /\ (forall dst_index_row_major_resultcolumnsrow_table. (exists pvs_le_gap_row_major_resultcolumnsrow_tabledomain. pvs_le_gap_row_major_resultcolumnsrow_tabledomain + (dst_index_row_major_resultcolumnsrow_table) = (n)) -> exists dst_positive_row_major_resultcolumnsrow_table dst_negative_row_major_resultcolumnsrow_table dst_value_row_major_resultcolumnsrow_table. ((((exists ff_h_pvs_row_major_resultcolumnsrow_tableentrypositive. ff_h_pvs_row_major_resultcolumnsrow_tableentrypositive + S (dst_positive_row_major_resultcolumnsrow_table) = S ((S (dst_index_row_major_resultcolumnsrow_table)) * dst_positive_scale_row_major_resultcolumnsrow_table)) /\ exists ff_q_pvs_row_major_resultcolumnsrow_tableentrypositive. dst_positive_code_row_major_resultcolumnsrow_table = ff_q_pvs_row_major_resultcolumnsrow_tableentrypositive * S ((S (dst_index_row_major_resultcolumnsrow_table)) * dst_positive_scale_row_major_resultcolumnsrow_table) + (dst_positive_row_major_resultcolumnsrow_table))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrow_tableentrynegative. ff_h_pvs_row_major_resultcolumnsrow_tableentrynegative + S (dst_negative_row_major_resultcolumnsrow_table) = S ((S (dst_index_row_major_resultcolumnsrow_table)) * dst_negative_scale_row_major_resultcolumnsrow_table)) /\ exists ff_q_pvs_row_major_resultcolumnsrow_tableentrynegative. dst_negative_code_row_major_resultcolumnsrow_table = ff_q_pvs_row_major_resultcolumnsrow_tableentrynegative * S ((S (dst_index_row_major_resultcolumnsrow_table)) * dst_negative_scale_row_major_resultcolumnsrow_table) + (dst_negative_row_major_resultcolumnsrow_table))) /\ (exists ge_balance_positive_row_major_resultcolumnsrow_tableentryvalue ge_balance_negative_row_major_resultcolumnsrow_tableentryvalue. (((((dst_value_row_major_resultcolumnsrow_table) = 2 * (ge_balance_positive_row_major_resultcolumnsrow_tableentryvalue) /\ (ge_balance_negative_row_major_resultcolumnsrow_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultcolumnsrow_tableentryvaluedecode. (((dst_value_row_major_resultcolumnsrow_table) = 2 * ge_signed_half_row_major_resultcolumnsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultcolumnsrow_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultcolumnsrow_tableentryvalue) = S ge_signed_half_row_major_resultcolumnsrow_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultcolumnsrow_table) + ge_balance_negative_row_major_resultcolumnsrow_tableentryvalue = (dst_negative_row_major_resultcolumnsrow_table) + ge_balance_positive_row_major_resultcolumnsrow_tableentryvalue))))))))) /\ (forall srt_index_row_major_resultcolumns. (exists pvs_gap_row_major_resultcolumnsbound. pvs_gap_row_major_resultcolumnsbound + S (srt_index_row_major_resultcolumns) = (n)) -> exists srt_value_row_major_resultcolumns. (((exists dst_positive_code_row_major_resultcolumnsrowentry dst_positive_scale_row_major_resultcolumnsrowentry dst_negative_code_row_major_resultcolumnsrowentry dst_negative_scale_row_major_resultcolumnsrowentry dst_positive_row_major_resultcolumnsrowentry dst_negative_row_major_resultcolumnsrowentry. (((C) = (((((dst_positive_code_row_major_resultcolumnsrowentry) + (dst_positive_scale_row_major_resultcolumnsrowentry)) * S ((dst_positive_code_row_major_resultcolumnsrowentry) + (dst_positive_scale_row_major_resultcolumnsrowentry)) + ((dst_positive_scale_row_major_resultcolumnsrowentry) + (dst_positive_scale_row_major_resultcolumnsrowentry))) + (((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) * S ((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) + ((dst_negative_scale_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)))) * S ((((dst_positive_code_row_major_resultcolumnsrowentry) + (dst_positive_scale_row_major_resultcolumnsrowentry)) * S ((dst_positive_code_row_major_resultcolumnsrowentry) + (dst_positive_scale_row_major_resultcolumnsrowentry)) + ((dst_positive_scale_row_major_resultcolumnsrowentry) + (dst_positive_scale_row_major_resultcolumnsrowentry))) + (((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) * S ((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) + ((dst_negative_scale_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)))) + ((((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) * S ((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) + ((dst_negative_scale_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry))) + (((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) * S ((dst_negative_code_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)) + ((dst_negative_scale_row_major_resultcolumnsrowentry) + (dst_negative_scale_row_major_resultcolumnsrowentry)))))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowentrypositive. ff_h_pvs_row_major_resultcolumnsrowentrypositive + S (dst_positive_row_major_resultcolumnsrowentry) = S ((S (srt_index_row_major_resultcolumns)) * dst_positive_scale_row_major_resultcolumnsrowentry)) /\ exists ff_q_pvs_row_major_resultcolumnsrowentrypositive. dst_positive_code_row_major_resultcolumnsrowentry = ff_q_pvs_row_major_resultcolumnsrowentrypositive * S ((S (srt_index_row_major_resultcolumns)) * dst_positive_scale_row_major_resultcolumnsrowentry) + (dst_positive_row_major_resultcolumnsrowentry))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowentrynegative. ff_h_pvs_row_major_resultcolumnsrowentrynegative + S (dst_negative_row_major_resultcolumnsrowentry) = S ((S (srt_index_row_major_resultcolumns)) * dst_negative_scale_row_major_resultcolumnsrowentry)) /\ exists ff_q_pvs_row_major_resultcolumnsrowentrynegative. dst_negative_code_row_major_resultcolumnsrowentry = ff_q_pvs_row_major_resultcolumnsrowentrynegative * S ((S (srt_index_row_major_resultcolumns)) * dst_negative_scale_row_major_resultcolumnsrowentry) + (dst_negative_row_major_resultcolumnsrowentry))) /\ (exists ge_balance_positive_row_major_resultcolumnsrowentryvalue ge_balance_negative_row_major_resultcolumnsrowentryvalue. (((((srt_value_row_major_resultcolumns) = 2 * (ge_balance_positive_row_major_resultcolumnsrowentryvalue) /\ (ge_balance_negative_row_major_resultcolumnsrowentryvalue) = 0) \/ exists ge_signed_half_row_major_resultcolumnsrowentryvaluedecode. (((srt_value_row_major_resultcolumns) = 2 * ge_signed_half_row_major_resultcolumnsrowentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultcolumnsrowentryvalue) = 0) /\ (ge_balance_negative_row_major_resultcolumnsrowentryvalue) = S ge_signed_half_row_major_resultcolumnsrowentryvaluedecode))) /\ ((dst_positive_row_major_resultcolumnsrowentry) + ge_balance_negative_row_major_resultcolumnsrowentryvalue = (dst_negative_row_major_resultcolumnsrowentry) + ge_balance_positive_row_major_resultcolumnsrowentryvalue))))))))) /\ (exists srs_slice_row_major_resultcolumnsrowrow_sum. ((((exists dst_positive_code_row_major_resultcolumnsrowrow_sumslicesource_table dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)))) + ((((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)))))) /\ (forall dst_index_row_major_resultcolumnsrowrow_sumslicesource_table. (exists pvs_le_gap_row_major_resultcolumnsrowrow_sumslicesource_tabledomain. pvs_le_gap_row_major_resultcolumnsrowrow_sumslicesource_tabledomain + (dst_index_row_major_resultcolumnsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_row_major_resultcolumnsrowrow_sumslicesource_table dst_negative_row_major_resultcolumnsrowrow_sumslicesource_table dst_value_row_major_resultcolumnsrowrow_sumslicesource_table. ((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrypositive + S (dst_positive_row_major_resultcolumnsrowrow_sumslicesource_table) = S ((S (dst_index_row_major_resultcolumnsrowrow_sumslicesource_table)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrypositive. dst_positive_code_row_major_resultcolumnsrowrow_sumslicesource_table = ff_q_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_row_major_resultcolumnsrowrow_sumslicesource_table)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_positive_row_major_resultcolumnsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrynegative + S (dst_negative_row_major_resultcolumnsrowrow_sumslicesource_table) = S ((S (dst_index_row_major_resultcolumnsrowrow_sumslicesource_table)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrynegative. dst_negative_code_row_major_resultcolumnsrowrow_sumslicesource_table = ff_q_pvs_row_major_resultcolumnsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_row_major_resultcolumnsrowrow_sumslicesource_table)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumslicesource_table) + (dst_negative_row_major_resultcolumnsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue ge_balance_negative_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue. (((((dst_value_row_major_resultcolumnsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultcolumnsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_row_major_resultcolumnsrowrow_sumslicesource_table) = 2 * ge_signed_half_row_major_resultcolumnsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_row_major_resultcolumnsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultcolumnsrowrow_sumslicesource_table) + ge_balance_negative_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue = (dst_negative_row_major_resultcolumnsrowrow_sumslicesource_table) + ge_balance_positive_row_major_resultcolumnsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_row_major_resultcolumnsrowrow_sumsliceoutput_table dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table. (((srs_slice_row_major_resultcolumnsrowrow_sum) = (((((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_row_major_resultcolumnsrowrow_sumsliceoutput_table. (exists pvs_le_gap_row_major_resultcolumnsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_row_major_resultcolumnsrowrow_sumsliceoutput_tabledomain + (dst_index_row_major_resultcolumnsrowrow_sumsliceoutput_table) = (m)) -> exists dst_positive_row_major_resultcolumnsrowrow_sumsliceoutput_table dst_negative_row_major_resultcolumnsrowrow_sumsliceoutput_table dst_value_row_major_resultcolumnsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_row_major_resultcolumnsrowrow_sumsliceoutput_table) = S ((S (dst_index_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_row_major_resultcolumnsrowrow_sumsliceoutput_table = ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_positive_row_major_resultcolumnsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_row_major_resultcolumnsrowrow_sumsliceoutput_table) = S ((S (dst_index_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_row_major_resultcolumnsrowrow_sumsliceoutput_table = ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_row_major_resultcolumnsrowrow_sumsliceoutput_table)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceoutput_table) + (dst_negative_row_major_resultcolumnsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_row_major_resultcolumnsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_row_major_resultcolumnsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_row_major_resultcolumnsrowrow_sumsliceoutput_table) + ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_row_major_resultcolumnsrowrow_sumsliceoutput_table) + ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_row_major_resultcolumnsrowrow_sumslice. (exists pvs_gap_row_major_resultcolumnsrowrow_sumslicebound. pvs_gap_row_major_resultcolumnsrowrow_sumslicebound + S (srs_index_row_major_resultcolumnsrowrow_sumslice) = (m)) -> exists srs_value_row_major_resultcolumnsrowrow_sumslice. (((exists dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentrysource dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource dst_positive_row_major_resultcolumnsrowrow_sumsliceentrysource dst_negative_row_major_resultcolumnsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcepositive. ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcepositive + S (dst_positive_row_major_resultcolumnsrowrow_sumsliceentrysource) = S ((S (((((0) + ((1) * (srt_index_row_major_resultcolumns)))) + ((n) * (srs_index_row_major_resultcolumnsrowrow_sumslice))))) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcepositive. dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentrysource = ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcepositive * S ((S (((((0) + ((1) * (srt_index_row_major_resultcolumns)))) + ((n) * (srs_index_row_major_resultcolumnsrowrow_sumslice))))) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_positive_row_major_resultcolumnsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcenegative. ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcenegative + S (dst_negative_row_major_resultcolumnsrowrow_sumsliceentrysource) = S ((S (((((0) + ((1) * (srt_index_row_major_resultcolumns)))) + ((n) * (srs_index_row_major_resultcolumnsrowrow_sumslice))))) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcenegative. dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentrysource = ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentrysourcenegative * S ((S (((((0) + ((1) * (srt_index_row_major_resultcolumns)))) + ((n) * (srs_index_row_major_resultcolumnsrowrow_sumslice))))) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentrysource) + (dst_negative_row_major_resultcolumnsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue. (((((srs_value_row_major_resultcolumnsrowrow_sumslice) = 2 * (ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_row_major_resultcolumnsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_row_major_resultcolumnsrowrow_sumslice) = 2 * ge_signed_half_row_major_resultcolumnsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_row_major_resultcolumnsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_row_major_resultcolumnsrowrow_sumsliceentrysource) + ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue = (dst_negative_row_major_resultcolumnsrowrow_sumsliceentrysource) + ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentryoutput dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput dst_positive_row_major_resultcolumnsrowrow_sumsliceentryoutput dst_negative_row_major_resultcolumnsrowrow_sumsliceentryoutput. (((srs_slice_row_major_resultcolumnsrowrow_sum) = (((((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputpositive. ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputpositive + S (dst_positive_row_major_resultcolumnsrowrow_sumsliceentryoutput) = S ((S (srs_index_row_major_resultcolumnsrowrow_sumslice)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputpositive. dst_positive_code_row_major_resultcolumnsrowrow_sumsliceentryoutput = ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_row_major_resultcolumnsrowrow_sumslice)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_positive_row_major_resultcolumnsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputnegative. ff_h_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputnegative + S (dst_negative_row_major_resultcolumnsrowrow_sumsliceentryoutput) = S ((S (srs_index_row_major_resultcolumnsrowrow_sumslice)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputnegative. dst_negative_code_row_major_resultcolumnsrowrow_sumsliceentryoutput = ff_q_pvs_row_major_resultcolumnsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_row_major_resultcolumnsrowrow_sumslice)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsliceentryoutput) + (dst_negative_row_major_resultcolumnsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue. (((((srs_value_row_major_resultcolumnsrowrow_sumslice) = 2 * (ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_row_major_resultcolumnsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_row_major_resultcolumnsrowrow_sumslice) = 2 * ge_signed_half_row_major_resultcolumnsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_row_major_resultcolumnsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_row_major_resultcolumnsrowrow_sumsliceentryoutput) + ge_balance_negative_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue = (dst_negative_row_major_resultcolumnsrowrow_sumsliceentryoutput) + ge_balance_positive_row_major_resultcolumnsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_row_major_resultcolumnsrowrow_sumsum dst_positive_scale_row_major_resultcolumnsrowrow_sumsum dst_negative_code_row_major_resultcolumnsrowrow_sumsum dst_negative_scale_row_major_resultcolumnsrowrow_sumsum dst_positive_sum_row_major_resultcolumnsrowrow_sumsum dst_negative_sum_row_major_resultcolumnsrowrow_sumsum. (((srs_slice_row_major_resultcolumnsrowrow_sum) = (((((dst_positive_code_row_major_resultcolumnsrowrow_sumsum) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsum)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsum) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsum)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsum) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsum))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)))) * S ((((dst_positive_code_row_major_resultcolumnsrowrow_sumsum) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsum)) * S ((dst_positive_code_row_major_resultcolumnsrowrow_sumsum) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsum)) + ((dst_positive_scale_row_major_resultcolumnsrowrow_sumsum) + (dst_positive_scale_row_major_resultcolumnsrowrow_sumsum))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)))) + ((((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum))) + (((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) * S ((dst_negative_code_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) + ((dst_negative_scale_row_major_resultcolumnsrowrow_sumsum) + (dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)))))) /\ (((exists fs_u_dst_row_major_resultcolumnsrowrow_sumsumpositive fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive. ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_start. fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_start. fs_u_dst_row_major_resultcolumnsrowrow_sumsumpositive = fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_terminal. fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_row_major_resultcolumnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_terminal. fs_u_dst_row_major_resultcolumnsrowrow_sumsumpositive = fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_terminal * S ((S (m)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive) + (dst_positive_sum_row_major_resultcolumnsrowrow_sumsum))) /\ forall fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps = m) -> exists fs_a_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps fs_r_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps fs_s_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsum)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_row_major_resultcolumnsrowrow_sumsum = fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_row_major_resultcolumnsrowrow_sumsum) + (fs_a_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_row_major_resultcolumnsrowrow_sumsumpositive = fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive) + (fs_r_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_row_major_resultcolumnsrowrow_sumsumpositive = fs_q_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumpositive) + (fs_s_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps = fs_r_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps + fs_a_dst_row_major_resultcolumnsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_row_major_resultcolumnsrowrow_sumsumnegative fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative. ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_start. fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_start. fs_u_dst_row_major_resultcolumnsrowrow_sumsumnegative = fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_terminal. fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_row_major_resultcolumnsrowrow_sumsum) = S ((S (m)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_terminal. fs_u_dst_row_major_resultcolumnsrowrow_sumsumnegative = fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_terminal * S ((S (m)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative) + (dst_negative_sum_row_major_resultcolumnsrowrow_sumsum))) /\ forall fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps = m) -> exists fs_a_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps fs_r_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps fs_s_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsum)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_row_major_resultcolumnsrowrow_sumsum = fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_row_major_resultcolumnsrowrow_sumsum) + (fs_a_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_row_major_resultcolumnsrowrow_sumsumnegative = fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative) + (fs_r_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative)) /\ exists fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_row_major_resultcolumnsrowrow_sumsumnegative = fs_q_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps)) * fs_v_dst_row_major_resultcolumnsrowrow_sumsumnegative) + (fs_s_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps = fs_r_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps + fs_a_dst_row_major_resultcolumnsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_row_major_resultcolumnsrowrow_sumsumresult ge_balance_negative_row_major_resultcolumnsrowrow_sumsumresult. (((((srt_value_row_major_resultcolumns) = 2 * (ge_balance_positive_row_major_resultcolumnsrowrow_sumsumresult) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_row_major_resultcolumnsrowrow_sumsumresultdecode. (((srt_value_row_major_resultcolumns) = 2 * ge_signed_half_row_major_resultcolumnsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_row_major_resultcolumnsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_row_major_resultcolumnsrowrow_sumsumresult) = S ge_signed_half_row_major_resultcolumnsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_row_major_resultcolumnsrowrow_sumsum) + ge_balance_negative_row_major_resultcolumnsrowrow_sumsumresult = (dst_negative_sum_row_major_resultcolumnsrowrow_sumsum) + ge_balance_positive_row_major_resultcolumnsrowrow_sumsumresult)))))))))))))))))) /\ (((exists dst_positive_code_row_major_resultrow_total dst_positive_scale_row_major_resultrow_total dst_negative_code_row_major_resultrow_total dst_negative_scale_row_major_resultrow_total dst_positive_sum_row_major_resultrow_total dst_negative_sum_row_major_resultrow_total. (((R) = (((((dst_positive_code_row_major_resultrow_total) + (dst_positive_scale_row_major_resultrow_total)) * S ((dst_positive_code_row_major_resultrow_total) + (dst_positive_scale_row_major_resultrow_total)) + ((dst_positive_scale_row_major_resultrow_total) + (dst_positive_scale_row_major_resultrow_total))) + (((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) * S ((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) + ((dst_negative_scale_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)))) * S ((((dst_positive_code_row_major_resultrow_total) + (dst_positive_scale_row_major_resultrow_total)) * S ((dst_positive_code_row_major_resultrow_total) + (dst_positive_scale_row_major_resultrow_total)) + ((dst_positive_scale_row_major_resultrow_total) + (dst_positive_scale_row_major_resultrow_total))) + (((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) * S ((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) + ((dst_negative_scale_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)))) + ((((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) * S ((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) + ((dst_negative_scale_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total))) + (((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) * S ((dst_negative_code_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)) + ((dst_negative_scale_row_major_resultrow_total) + (dst_negative_scale_row_major_resultrow_total)))))) /\ (((exists fs_u_dst_row_major_resultrow_totalpositive fs_v_dst_row_major_resultrow_totalpositive. ((((exists fs_h_dst_row_major_resultrow_totalpositive_body_start. fs_h_dst_row_major_resultrow_totalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultrow_totalpositive)) /\ exists fs_q_dst_row_major_resultrow_totalpositive_body_start. fs_u_dst_row_major_resultrow_totalpositive = fs_q_dst_row_major_resultrow_totalpositive_body_start * S ((S (0)) * fs_v_dst_row_major_resultrow_totalpositive) + (0))) /\ ((((exists fs_h_dst_row_major_resultrow_totalpositive_body_terminal. fs_h_dst_row_major_resultrow_totalpositive_body_terminal + S (dst_positive_sum_row_major_resultrow_total) = S ((S (m)) * fs_v_dst_row_major_resultrow_totalpositive)) /\ exists fs_q_dst_row_major_resultrow_totalpositive_body_terminal. fs_u_dst_row_major_resultrow_totalpositive = fs_q_dst_row_major_resultrow_totalpositive_body_terminal * S ((S (m)) * fs_v_dst_row_major_resultrow_totalpositive) + (dst_positive_sum_row_major_resultrow_total))) /\ forall fs_i_dst_row_major_resultrow_totalpositive_body_steps. (exists fs_lt_dst_row_major_resultrow_totalpositive_body_steps_bound. fs_lt_dst_row_major_resultrow_totalpositive_body_steps_bound + S fs_i_dst_row_major_resultrow_totalpositive_body_steps = m) -> exists fs_a_dst_row_major_resultrow_totalpositive_body_steps fs_r_dst_row_major_resultrow_totalpositive_body_steps fs_s_dst_row_major_resultrow_totalpositive_body_steps. ((((exists fs_h_dst_row_major_resultrow_totalpositive_body_steps_summand. fs_h_dst_row_major_resultrow_totalpositive_body_steps_summand + S (fs_a_dst_row_major_resultrow_totalpositive_body_steps) = S ((S (fs_i_dst_row_major_resultrow_totalpositive_body_steps)) * dst_positive_scale_row_major_resultrow_total)) /\ exists fs_q_dst_row_major_resultrow_totalpositive_body_steps_summand. dst_positive_code_row_major_resultrow_total = fs_q_dst_row_major_resultrow_totalpositive_body_steps_summand * S ((S (fs_i_dst_row_major_resultrow_totalpositive_body_steps)) * dst_positive_scale_row_major_resultrow_total) + (fs_a_dst_row_major_resultrow_totalpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrow_totalpositive_body_steps_partial. fs_h_dst_row_major_resultrow_totalpositive_body_steps_partial + S (fs_r_dst_row_major_resultrow_totalpositive_body_steps) = S ((S (fs_i_dst_row_major_resultrow_totalpositive_body_steps)) * fs_v_dst_row_major_resultrow_totalpositive)) /\ exists fs_q_dst_row_major_resultrow_totalpositive_body_steps_partial. fs_u_dst_row_major_resultrow_totalpositive = fs_q_dst_row_major_resultrow_totalpositive_body_steps_partial * S ((S (fs_i_dst_row_major_resultrow_totalpositive_body_steps)) * fs_v_dst_row_major_resultrow_totalpositive) + (fs_r_dst_row_major_resultrow_totalpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrow_totalpositive_body_steps_successor. fs_h_dst_row_major_resultrow_totalpositive_body_steps_successor + S (fs_s_dst_row_major_resultrow_totalpositive_body_steps) = S ((S (S fs_i_dst_row_major_resultrow_totalpositive_body_steps)) * fs_v_dst_row_major_resultrow_totalpositive)) /\ exists fs_q_dst_row_major_resultrow_totalpositive_body_steps_successor. fs_u_dst_row_major_resultrow_totalpositive = fs_q_dst_row_major_resultrow_totalpositive_body_steps_successor * S ((S (S fs_i_dst_row_major_resultrow_totalpositive_body_steps)) * fs_v_dst_row_major_resultrow_totalpositive) + (fs_s_dst_row_major_resultrow_totalpositive_body_steps))) /\ fs_s_dst_row_major_resultrow_totalpositive_body_steps = fs_r_dst_row_major_resultrow_totalpositive_body_steps + fs_a_dst_row_major_resultrow_totalpositive_body_steps)))))) /\ (((exists fs_u_dst_row_major_resultrow_totalnegative fs_v_dst_row_major_resultrow_totalnegative. ((((exists fs_h_dst_row_major_resultrow_totalnegative_body_start. fs_h_dst_row_major_resultrow_totalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultrow_totalnegative)) /\ exists fs_q_dst_row_major_resultrow_totalnegative_body_start. fs_u_dst_row_major_resultrow_totalnegative = fs_q_dst_row_major_resultrow_totalnegative_body_start * S ((S (0)) * fs_v_dst_row_major_resultrow_totalnegative) + (0))) /\ ((((exists fs_h_dst_row_major_resultrow_totalnegative_body_terminal. fs_h_dst_row_major_resultrow_totalnegative_body_terminal + S (dst_negative_sum_row_major_resultrow_total) = S ((S (m)) * fs_v_dst_row_major_resultrow_totalnegative)) /\ exists fs_q_dst_row_major_resultrow_totalnegative_body_terminal. fs_u_dst_row_major_resultrow_totalnegative = fs_q_dst_row_major_resultrow_totalnegative_body_terminal * S ((S (m)) * fs_v_dst_row_major_resultrow_totalnegative) + (dst_negative_sum_row_major_resultrow_total))) /\ forall fs_i_dst_row_major_resultrow_totalnegative_body_steps. (exists fs_lt_dst_row_major_resultrow_totalnegative_body_steps_bound. fs_lt_dst_row_major_resultrow_totalnegative_body_steps_bound + S fs_i_dst_row_major_resultrow_totalnegative_body_steps = m) -> exists fs_a_dst_row_major_resultrow_totalnegative_body_steps fs_r_dst_row_major_resultrow_totalnegative_body_steps fs_s_dst_row_major_resultrow_totalnegative_body_steps. ((((exists fs_h_dst_row_major_resultrow_totalnegative_body_steps_summand. fs_h_dst_row_major_resultrow_totalnegative_body_steps_summand + S (fs_a_dst_row_major_resultrow_totalnegative_body_steps) = S ((S (fs_i_dst_row_major_resultrow_totalnegative_body_steps)) * dst_negative_scale_row_major_resultrow_total)) /\ exists fs_q_dst_row_major_resultrow_totalnegative_body_steps_summand. dst_negative_code_row_major_resultrow_total = fs_q_dst_row_major_resultrow_totalnegative_body_steps_summand * S ((S (fs_i_dst_row_major_resultrow_totalnegative_body_steps)) * dst_negative_scale_row_major_resultrow_total) + (fs_a_dst_row_major_resultrow_totalnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrow_totalnegative_body_steps_partial. fs_h_dst_row_major_resultrow_totalnegative_body_steps_partial + S (fs_r_dst_row_major_resultrow_totalnegative_body_steps) = S ((S (fs_i_dst_row_major_resultrow_totalnegative_body_steps)) * fs_v_dst_row_major_resultrow_totalnegative)) /\ exists fs_q_dst_row_major_resultrow_totalnegative_body_steps_partial. fs_u_dst_row_major_resultrow_totalnegative = fs_q_dst_row_major_resultrow_totalnegative_body_steps_partial * S ((S (fs_i_dst_row_major_resultrow_totalnegative_body_steps)) * fs_v_dst_row_major_resultrow_totalnegative) + (fs_r_dst_row_major_resultrow_totalnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultrow_totalnegative_body_steps_successor. fs_h_dst_row_major_resultrow_totalnegative_body_steps_successor + S (fs_s_dst_row_major_resultrow_totalnegative_body_steps) = S ((S (S fs_i_dst_row_major_resultrow_totalnegative_body_steps)) * fs_v_dst_row_major_resultrow_totalnegative)) /\ exists fs_q_dst_row_major_resultrow_totalnegative_body_steps_successor. fs_u_dst_row_major_resultrow_totalnegative = fs_q_dst_row_major_resultrow_totalnegative_body_steps_successor * S ((S (S fs_i_dst_row_major_resultrow_totalnegative_body_steps)) * fs_v_dst_row_major_resultrow_totalnegative) + (fs_s_dst_row_major_resultrow_totalnegative_body_steps))) /\ fs_s_dst_row_major_resultrow_totalnegative_body_steps = fs_r_dst_row_major_resultrow_totalnegative_body_steps + fs_a_dst_row_major_resultrow_totalnegative_body_steps)))))) /\ (exists ge_balance_positive_row_major_resultrow_totalresult ge_balance_negative_row_major_resultrow_totalresult. (((((z) = 2 * (ge_balance_positive_row_major_resultrow_totalresult) /\ (ge_balance_negative_row_major_resultrow_totalresult) = 0) \/ exists ge_signed_half_row_major_resultrow_totalresultdecode. (((z) = 2 * ge_signed_half_row_major_resultrow_totalresultdecode + 1 /\ (ge_balance_positive_row_major_resultrow_totalresult) = 0) /\ (ge_balance_negative_row_major_resultrow_totalresult) = S ge_signed_half_row_major_resultrow_totalresultdecode))) /\ ((dst_positive_sum_row_major_resultrow_total) + ge_balance_negative_row_major_resultrow_totalresult = (dst_negative_sum_row_major_resultrow_total) + ge_balance_positive_row_major_resultrow_totalresult))))))))) /\ (exists dst_positive_code_row_major_resultcolumn_total dst_positive_scale_row_major_resultcolumn_total dst_negative_code_row_major_resultcolumn_total dst_negative_scale_row_major_resultcolumn_total dst_positive_sum_row_major_resultcolumn_total dst_negative_sum_row_major_resultcolumn_total. (((C) = (((((dst_positive_code_row_major_resultcolumn_total) + (dst_positive_scale_row_major_resultcolumn_total)) * S ((dst_positive_code_row_major_resultcolumn_total) + (dst_positive_scale_row_major_resultcolumn_total)) + ((dst_positive_scale_row_major_resultcolumn_total) + (dst_positive_scale_row_major_resultcolumn_total))) + (((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) * S ((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) + ((dst_negative_scale_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)))) * S ((((dst_positive_code_row_major_resultcolumn_total) + (dst_positive_scale_row_major_resultcolumn_total)) * S ((dst_positive_code_row_major_resultcolumn_total) + (dst_positive_scale_row_major_resultcolumn_total)) + ((dst_positive_scale_row_major_resultcolumn_total) + (dst_positive_scale_row_major_resultcolumn_total))) + (((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) * S ((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) + ((dst_negative_scale_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)))) + ((((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) * S ((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) + ((dst_negative_scale_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total))) + (((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) * S ((dst_negative_code_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)) + ((dst_negative_scale_row_major_resultcolumn_total) + (dst_negative_scale_row_major_resultcolumn_total)))))) /\ (((exists fs_u_dst_row_major_resultcolumn_totalpositive fs_v_dst_row_major_resultcolumn_totalpositive. ((((exists fs_h_dst_row_major_resultcolumn_totalpositive_body_start. fs_h_dst_row_major_resultcolumn_totalpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultcolumn_totalpositive)) /\ exists fs_q_dst_row_major_resultcolumn_totalpositive_body_start. fs_u_dst_row_major_resultcolumn_totalpositive = fs_q_dst_row_major_resultcolumn_totalpositive_body_start * S ((S (0)) * fs_v_dst_row_major_resultcolumn_totalpositive) + (0))) /\ ((((exists fs_h_dst_row_major_resultcolumn_totalpositive_body_terminal. fs_h_dst_row_major_resultcolumn_totalpositive_body_terminal + S (dst_positive_sum_row_major_resultcolumn_total) = S ((S (n)) * fs_v_dst_row_major_resultcolumn_totalpositive)) /\ exists fs_q_dst_row_major_resultcolumn_totalpositive_body_terminal. fs_u_dst_row_major_resultcolumn_totalpositive = fs_q_dst_row_major_resultcolumn_totalpositive_body_terminal * S ((S (n)) * fs_v_dst_row_major_resultcolumn_totalpositive) + (dst_positive_sum_row_major_resultcolumn_total))) /\ forall fs_i_dst_row_major_resultcolumn_totalpositive_body_steps. (exists fs_lt_dst_row_major_resultcolumn_totalpositive_body_steps_bound. fs_lt_dst_row_major_resultcolumn_totalpositive_body_steps_bound + S fs_i_dst_row_major_resultcolumn_totalpositive_body_steps = n) -> exists fs_a_dst_row_major_resultcolumn_totalpositive_body_steps fs_r_dst_row_major_resultcolumn_totalpositive_body_steps fs_s_dst_row_major_resultcolumn_totalpositive_body_steps. ((((exists fs_h_dst_row_major_resultcolumn_totalpositive_body_steps_summand. fs_h_dst_row_major_resultcolumn_totalpositive_body_steps_summand + S (fs_a_dst_row_major_resultcolumn_totalpositive_body_steps) = S ((S (fs_i_dst_row_major_resultcolumn_totalpositive_body_steps)) * dst_positive_scale_row_major_resultcolumn_total)) /\ exists fs_q_dst_row_major_resultcolumn_totalpositive_body_steps_summand. dst_positive_code_row_major_resultcolumn_total = fs_q_dst_row_major_resultcolumn_totalpositive_body_steps_summand * S ((S (fs_i_dst_row_major_resultcolumn_totalpositive_body_steps)) * dst_positive_scale_row_major_resultcolumn_total) + (fs_a_dst_row_major_resultcolumn_totalpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumn_totalpositive_body_steps_partial. fs_h_dst_row_major_resultcolumn_totalpositive_body_steps_partial + S (fs_r_dst_row_major_resultcolumn_totalpositive_body_steps) = S ((S (fs_i_dst_row_major_resultcolumn_totalpositive_body_steps)) * fs_v_dst_row_major_resultcolumn_totalpositive)) /\ exists fs_q_dst_row_major_resultcolumn_totalpositive_body_steps_partial. fs_u_dst_row_major_resultcolumn_totalpositive = fs_q_dst_row_major_resultcolumn_totalpositive_body_steps_partial * S ((S (fs_i_dst_row_major_resultcolumn_totalpositive_body_steps)) * fs_v_dst_row_major_resultcolumn_totalpositive) + (fs_r_dst_row_major_resultcolumn_totalpositive_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumn_totalpositive_body_steps_successor. fs_h_dst_row_major_resultcolumn_totalpositive_body_steps_successor + S (fs_s_dst_row_major_resultcolumn_totalpositive_body_steps) = S ((S (S fs_i_dst_row_major_resultcolumn_totalpositive_body_steps)) * fs_v_dst_row_major_resultcolumn_totalpositive)) /\ exists fs_q_dst_row_major_resultcolumn_totalpositive_body_steps_successor. fs_u_dst_row_major_resultcolumn_totalpositive = fs_q_dst_row_major_resultcolumn_totalpositive_body_steps_successor * S ((S (S fs_i_dst_row_major_resultcolumn_totalpositive_body_steps)) * fs_v_dst_row_major_resultcolumn_totalpositive) + (fs_s_dst_row_major_resultcolumn_totalpositive_body_steps))) /\ fs_s_dst_row_major_resultcolumn_totalpositive_body_steps = fs_r_dst_row_major_resultcolumn_totalpositive_body_steps + fs_a_dst_row_major_resultcolumn_totalpositive_body_steps)))))) /\ (((exists fs_u_dst_row_major_resultcolumn_totalnegative fs_v_dst_row_major_resultcolumn_totalnegative. ((((exists fs_h_dst_row_major_resultcolumn_totalnegative_body_start. fs_h_dst_row_major_resultcolumn_totalnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_row_major_resultcolumn_totalnegative)) /\ exists fs_q_dst_row_major_resultcolumn_totalnegative_body_start. fs_u_dst_row_major_resultcolumn_totalnegative = fs_q_dst_row_major_resultcolumn_totalnegative_body_start * S ((S (0)) * fs_v_dst_row_major_resultcolumn_totalnegative) + (0))) /\ ((((exists fs_h_dst_row_major_resultcolumn_totalnegative_body_terminal. fs_h_dst_row_major_resultcolumn_totalnegative_body_terminal + S (dst_negative_sum_row_major_resultcolumn_total) = S ((S (n)) * fs_v_dst_row_major_resultcolumn_totalnegative)) /\ exists fs_q_dst_row_major_resultcolumn_totalnegative_body_terminal. fs_u_dst_row_major_resultcolumn_totalnegative = fs_q_dst_row_major_resultcolumn_totalnegative_body_terminal * S ((S (n)) * fs_v_dst_row_major_resultcolumn_totalnegative) + (dst_negative_sum_row_major_resultcolumn_total))) /\ forall fs_i_dst_row_major_resultcolumn_totalnegative_body_steps. (exists fs_lt_dst_row_major_resultcolumn_totalnegative_body_steps_bound. fs_lt_dst_row_major_resultcolumn_totalnegative_body_steps_bound + S fs_i_dst_row_major_resultcolumn_totalnegative_body_steps = n) -> exists fs_a_dst_row_major_resultcolumn_totalnegative_body_steps fs_r_dst_row_major_resultcolumn_totalnegative_body_steps fs_s_dst_row_major_resultcolumn_totalnegative_body_steps. ((((exists fs_h_dst_row_major_resultcolumn_totalnegative_body_steps_summand. fs_h_dst_row_major_resultcolumn_totalnegative_body_steps_summand + S (fs_a_dst_row_major_resultcolumn_totalnegative_body_steps) = S ((S (fs_i_dst_row_major_resultcolumn_totalnegative_body_steps)) * dst_negative_scale_row_major_resultcolumn_total)) /\ exists fs_q_dst_row_major_resultcolumn_totalnegative_body_steps_summand. dst_negative_code_row_major_resultcolumn_total = fs_q_dst_row_major_resultcolumn_totalnegative_body_steps_summand * S ((S (fs_i_dst_row_major_resultcolumn_totalnegative_body_steps)) * dst_negative_scale_row_major_resultcolumn_total) + (fs_a_dst_row_major_resultcolumn_totalnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumn_totalnegative_body_steps_partial. fs_h_dst_row_major_resultcolumn_totalnegative_body_steps_partial + S (fs_r_dst_row_major_resultcolumn_totalnegative_body_steps) = S ((S (fs_i_dst_row_major_resultcolumn_totalnegative_body_steps)) * fs_v_dst_row_major_resultcolumn_totalnegative)) /\ exists fs_q_dst_row_major_resultcolumn_totalnegative_body_steps_partial. fs_u_dst_row_major_resultcolumn_totalnegative = fs_q_dst_row_major_resultcolumn_totalnegative_body_steps_partial * S ((S (fs_i_dst_row_major_resultcolumn_totalnegative_body_steps)) * fs_v_dst_row_major_resultcolumn_totalnegative) + (fs_r_dst_row_major_resultcolumn_totalnegative_body_steps))) /\ ((((exists fs_h_dst_row_major_resultcolumn_totalnegative_body_steps_successor. fs_h_dst_row_major_resultcolumn_totalnegative_body_steps_successor + S (fs_s_dst_row_major_resultcolumn_totalnegative_body_steps) = S ((S (S fs_i_dst_row_major_resultcolumn_totalnegative_body_steps)) * fs_v_dst_row_major_resultcolumn_totalnegative)) /\ exists fs_q_dst_row_major_resultcolumn_totalnegative_body_steps_successor. fs_u_dst_row_major_resultcolumn_totalnegative = fs_q_dst_row_major_resultcolumn_totalnegative_body_steps_successor * S ((S (S fs_i_dst_row_major_resultcolumn_totalnegative_body_steps)) * fs_v_dst_row_major_resultcolumn_totalnegative) + (fs_s_dst_row_major_resultcolumn_totalnegative_body_steps))) /\ fs_s_dst_row_major_resultcolumn_totalnegative_body_steps = fs_r_dst_row_major_resultcolumn_totalnegative_body_steps + fs_a_dst_row_major_resultcolumn_totalnegative_body_steps)))))) /\ (exists ge_balance_positive_row_major_resultcolumn_totalresult ge_balance_negative_row_major_resultcolumn_totalresult. (((((z) = 2 * (ge_balance_positive_row_major_resultcolumn_totalresult) /\ (ge_balance_negative_row_major_resultcolumn_totalresult) = 0) \/ exists ge_signed_half_row_major_resultcolumn_totalresultdecode. (((z) = 2 * ge_signed_half_row_major_resultcolumn_totalresultdecode + 1 /\ (ge_balance_positive_row_major_resultcolumn_totalresult) = 0) /\ (ge_balance_negative_row_major_resultcolumn_totalresult) = S ge_signed_half_row_major_resultcolumn_totalresultdecode))) /\ ((dst_positive_sum_row_major_resultcolumn_total) + ge_balance_negative_row_major_resultcolumn_totalresult = (dst_negative_sum_row_major_resultcolumn_total) + ge_balance_positive_row_major_resultcolumn_totalresult)))))))))))))))

signed_rectangular_row_sums_lookup · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F R o s t m n i z. (((exists dst_positive_code_lookup_rowssource_table dst_positive_scale_lookup_rowssource_table dst_negative_code_lookup_rowssource_table dst_negative_scale_lookup_rowssource_table. (((F) = (((((dst_positive_code_lookup_rowssource_table) + (dst_positive_scale_lookup_rowssource_table)) * S ((dst_positive_code_lookup_rowssource_table) + (dst_positive_scale_lookup_rowssource_table)) + ((dst_positive_scale_lookup_rowssource_table) + (dst_positive_scale_lookup_rowssource_table))) + (((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) * S ((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) + ((dst_negative_scale_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)))) * S ((((dst_positive_code_lookup_rowssource_table) + (dst_positive_scale_lookup_rowssource_table)) * S ((dst_positive_code_lookup_rowssource_table) + (dst_positive_scale_lookup_rowssource_table)) + ((dst_positive_scale_lookup_rowssource_table) + (dst_positive_scale_lookup_rowssource_table))) + (((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) * S ((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) + ((dst_negative_scale_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)))) + ((((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) * S ((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) + ((dst_negative_scale_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table))) + (((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) * S ((dst_negative_code_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)) + ((dst_negative_scale_lookup_rowssource_table) + (dst_negative_scale_lookup_rowssource_table)))))) /\ (forall dst_index_lookup_rowssource_table. (exists pvs_le_gap_lookup_rowssource_tabledomain. pvs_le_gap_lookup_rowssource_tabledomain + (dst_index_lookup_rowssource_table) = (0)) -> exists dst_positive_lookup_rowssource_table dst_negative_lookup_rowssource_table dst_value_lookup_rowssource_table. ((((exists ff_h_pvs_lookup_rowssource_tableentrypositive. ff_h_pvs_lookup_rowssource_tableentrypositive + S (dst_positive_lookup_rowssource_table) = S ((S (dst_index_lookup_rowssource_table)) * dst_positive_scale_lookup_rowssource_table)) /\ exists ff_q_pvs_lookup_rowssource_tableentrypositive. dst_positive_code_lookup_rowssource_table = ff_q_pvs_lookup_rowssource_tableentrypositive * S ((S (dst_index_lookup_rowssource_table)) * dst_positive_scale_lookup_rowssource_table) + (dst_positive_lookup_rowssource_table))) /\ (((((exists ff_h_pvs_lookup_rowssource_tableentrynegative. ff_h_pvs_lookup_rowssource_tableentrynegative + S (dst_negative_lookup_rowssource_table) = S ((S (dst_index_lookup_rowssource_table)) * dst_negative_scale_lookup_rowssource_table)) /\ exists ff_q_pvs_lookup_rowssource_tableentrynegative. dst_negative_code_lookup_rowssource_table = ff_q_pvs_lookup_rowssource_tableentrynegative * S ((S (dst_index_lookup_rowssource_table)) * dst_negative_scale_lookup_rowssource_table) + (dst_negative_lookup_rowssource_table))) /\ (exists ge_balance_positive_lookup_rowssource_tableentryvalue ge_balance_negative_lookup_rowssource_tableentryvalue. (((((dst_value_lookup_rowssource_table) = 2 * (ge_balance_positive_lookup_rowssource_tableentryvalue) /\ (ge_balance_negative_lookup_rowssource_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_rowssource_tableentryvaluedecode. (((dst_value_lookup_rowssource_table) = 2 * ge_signed_half_lookup_rowssource_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_rowssource_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_rowssource_tableentryvalue) = S ge_signed_half_lookup_rowssource_tableentryvaluedecode))) /\ ((dst_positive_lookup_rowssource_table) + ge_balance_negative_lookup_rowssource_tableentryvalue = (dst_negative_lookup_rowssource_table) + ge_balance_positive_lookup_rowssource_tableentryvalue))))))))) /\ (((exists dst_positive_code_lookup_rowsrow_table dst_positive_scale_lookup_rowsrow_table dst_negative_code_lookup_rowsrow_table dst_negative_scale_lookup_rowsrow_table. (((R) = (((((dst_positive_code_lookup_rowsrow_table) + (dst_positive_scale_lookup_rowsrow_table)) * S ((dst_positive_code_lookup_rowsrow_table) + (dst_positive_scale_lookup_rowsrow_table)) + ((dst_positive_scale_lookup_rowsrow_table) + (dst_positive_scale_lookup_rowsrow_table))) + (((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) * S ((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) + ((dst_negative_scale_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)))) * S ((((dst_positive_code_lookup_rowsrow_table) + (dst_positive_scale_lookup_rowsrow_table)) * S ((dst_positive_code_lookup_rowsrow_table) + (dst_positive_scale_lookup_rowsrow_table)) + ((dst_positive_scale_lookup_rowsrow_table) + (dst_positive_scale_lookup_rowsrow_table))) + (((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) * S ((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) + ((dst_negative_scale_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)))) + ((((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) * S ((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) + ((dst_negative_scale_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table))) + (((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) * S ((dst_negative_code_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)) + ((dst_negative_scale_lookup_rowsrow_table) + (dst_negative_scale_lookup_rowsrow_table)))))) /\ (forall dst_index_lookup_rowsrow_table. (exists pvs_le_gap_lookup_rowsrow_tabledomain. pvs_le_gap_lookup_rowsrow_tabledomain + (dst_index_lookup_rowsrow_table) = (m)) -> exists dst_positive_lookup_rowsrow_table dst_negative_lookup_rowsrow_table dst_value_lookup_rowsrow_table. ((((exists ff_h_pvs_lookup_rowsrow_tableentrypositive. ff_h_pvs_lookup_rowsrow_tableentrypositive + S (dst_positive_lookup_rowsrow_table) = S ((S (dst_index_lookup_rowsrow_table)) * dst_positive_scale_lookup_rowsrow_table)) /\ exists ff_q_pvs_lookup_rowsrow_tableentrypositive. dst_positive_code_lookup_rowsrow_table = ff_q_pvs_lookup_rowsrow_tableentrypositive * S ((S (dst_index_lookup_rowsrow_table)) * dst_positive_scale_lookup_rowsrow_table) + (dst_positive_lookup_rowsrow_table))) /\ (((((exists ff_h_pvs_lookup_rowsrow_tableentrynegative. ff_h_pvs_lookup_rowsrow_tableentrynegative + S (dst_negative_lookup_rowsrow_table) = S ((S (dst_index_lookup_rowsrow_table)) * dst_negative_scale_lookup_rowsrow_table)) /\ exists ff_q_pvs_lookup_rowsrow_tableentrynegative. dst_negative_code_lookup_rowsrow_table = ff_q_pvs_lookup_rowsrow_tableentrynegative * S ((S (dst_index_lookup_rowsrow_table)) * dst_negative_scale_lookup_rowsrow_table) + (dst_negative_lookup_rowsrow_table))) /\ (exists ge_balance_positive_lookup_rowsrow_tableentryvalue ge_balance_negative_lookup_rowsrow_tableentryvalue. (((((dst_value_lookup_rowsrow_table) = 2 * (ge_balance_positive_lookup_rowsrow_tableentryvalue) /\ (ge_balance_negative_lookup_rowsrow_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_rowsrow_tableentryvaluedecode. (((dst_value_lookup_rowsrow_table) = 2 * ge_signed_half_lookup_rowsrow_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_rowsrow_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_rowsrow_tableentryvalue) = S ge_signed_half_lookup_rowsrow_tableentryvaluedecode))) /\ ((dst_positive_lookup_rowsrow_table) + ge_balance_negative_lookup_rowsrow_tableentryvalue = (dst_negative_lookup_rowsrow_table) + ge_balance_positive_lookup_rowsrow_tableentryvalue))))))))) /\ (forall srt_index_lookup_rows. (exists pvs_gap_lookup_rowsbound. pvs_gap_lookup_rowsbound + S (srt_index_lookup_rows) = (m)) -> exists srt_value_lookup_rows. (((exists dst_positive_code_lookup_rowsrowentry dst_positive_scale_lookup_rowsrowentry dst_negative_code_lookup_rowsrowentry dst_negative_scale_lookup_rowsrowentry dst_positive_lookup_rowsrowentry dst_negative_lookup_rowsrowentry. (((R) = (((((dst_positive_code_lookup_rowsrowentry) + (dst_positive_scale_lookup_rowsrowentry)) * S ((dst_positive_code_lookup_rowsrowentry) + (dst_positive_scale_lookup_rowsrowentry)) + ((dst_positive_scale_lookup_rowsrowentry) + (dst_positive_scale_lookup_rowsrowentry))) + (((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) * S ((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) + ((dst_negative_scale_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)))) * S ((((dst_positive_code_lookup_rowsrowentry) + (dst_positive_scale_lookup_rowsrowentry)) * S ((dst_positive_code_lookup_rowsrowentry) + (dst_positive_scale_lookup_rowsrowentry)) + ((dst_positive_scale_lookup_rowsrowentry) + (dst_positive_scale_lookup_rowsrowentry))) + (((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) * S ((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) + ((dst_negative_scale_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)))) + ((((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) * S ((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) + ((dst_negative_scale_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry))) + (((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) * S ((dst_negative_code_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)) + ((dst_negative_scale_lookup_rowsrowentry) + (dst_negative_scale_lookup_rowsrowentry)))))) /\ (((((exists ff_h_pvs_lookup_rowsrowentrypositive. ff_h_pvs_lookup_rowsrowentrypositive + S (dst_positive_lookup_rowsrowentry) = S ((S (srt_index_lookup_rows)) * dst_positive_scale_lookup_rowsrowentry)) /\ exists ff_q_pvs_lookup_rowsrowentrypositive. dst_positive_code_lookup_rowsrowentry = ff_q_pvs_lookup_rowsrowentrypositive * S ((S (srt_index_lookup_rows)) * dst_positive_scale_lookup_rowsrowentry) + (dst_positive_lookup_rowsrowentry))) /\ (((((exists ff_h_pvs_lookup_rowsrowentrynegative. ff_h_pvs_lookup_rowsrowentrynegative + S (dst_negative_lookup_rowsrowentry) = S ((S (srt_index_lookup_rows)) * dst_negative_scale_lookup_rowsrowentry)) /\ exists ff_q_pvs_lookup_rowsrowentrynegative. dst_negative_code_lookup_rowsrowentry = ff_q_pvs_lookup_rowsrowentrynegative * S ((S (srt_index_lookup_rows)) * dst_negative_scale_lookup_rowsrowentry) + (dst_negative_lookup_rowsrowentry))) /\ (exists ge_balance_positive_lookup_rowsrowentryvalue ge_balance_negative_lookup_rowsrowentryvalue. (((((srt_value_lookup_rows) = 2 * (ge_balance_positive_lookup_rowsrowentryvalue) /\ (ge_balance_negative_lookup_rowsrowentryvalue) = 0) \/ exists ge_signed_half_lookup_rowsrowentryvaluedecode. (((srt_value_lookup_rows) = 2 * ge_signed_half_lookup_rowsrowentryvaluedecode + 1 /\ (ge_balance_positive_lookup_rowsrowentryvalue) = 0) /\ (ge_balance_negative_lookup_rowsrowentryvalue) = S ge_signed_half_lookup_rowsrowentryvaluedecode))) /\ ((dst_positive_lookup_rowsrowentry) + ge_balance_negative_lookup_rowsrowentryvalue = (dst_negative_lookup_rowsrowentry) + ge_balance_positive_lookup_rowsrowentryvalue))))))))) /\ (exists srs_slice_lookup_rowsrowrow_sum. ((((exists dst_positive_code_lookup_rowsrowrow_sumslicesource_table dst_positive_scale_lookup_rowsrowrow_sumslicesource_table dst_negative_code_lookup_rowsrowrow_sumslicesource_table dst_negative_scale_lookup_rowsrowrow_sumslicesource_table. (((F) = (((((dst_positive_code_lookup_rowsrowrow_sumslicesource_table) + (dst_positive_scale_lookup_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_lookup_rowsrowrow_sumslicesource_table) + (dst_positive_scale_lookup_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_positive_scale_lookup_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)))) * S ((((dst_positive_code_lookup_rowsrowrow_sumslicesource_table) + (dst_positive_scale_lookup_rowsrowrow_sumslicesource_table)) * S ((dst_positive_code_lookup_rowsrowrow_sumslicesource_table) + (dst_positive_scale_lookup_rowsrowrow_sumslicesource_table)) + ((dst_positive_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_positive_scale_lookup_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)))) + ((((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table))) + (((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)))))) /\ (forall dst_index_lookup_rowsrowrow_sumslicesource_table. (exists pvs_le_gap_lookup_rowsrowrow_sumslicesource_tabledomain. pvs_le_gap_lookup_rowsrowrow_sumslicesource_tabledomain + (dst_index_lookup_rowsrowrow_sumslicesource_table) = (0)) -> exists dst_positive_lookup_rowsrowrow_sumslicesource_table dst_negative_lookup_rowsrowrow_sumslicesource_table dst_value_lookup_rowsrowrow_sumslicesource_table. ((((exists ff_h_pvs_lookup_rowsrowrow_sumslicesource_tableentrypositive. ff_h_pvs_lookup_rowsrowrow_sumslicesource_tableentrypositive + S (dst_positive_lookup_rowsrowrow_sumslicesource_table) = S ((S (dst_index_lookup_rowsrowrow_sumslicesource_table)) * dst_positive_scale_lookup_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumslicesource_tableentrypositive. dst_positive_code_lookup_rowsrowrow_sumslicesource_table = ff_q_pvs_lookup_rowsrowrow_sumslicesource_tableentrypositive * S ((S (dst_index_lookup_rowsrowrow_sumslicesource_table)) * dst_positive_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_positive_lookup_rowsrowrow_sumslicesource_table))) /\ (((((exists ff_h_pvs_lookup_rowsrowrow_sumslicesource_tableentrynegative. ff_h_pvs_lookup_rowsrowrow_sumslicesource_tableentrynegative + S (dst_negative_lookup_rowsrowrow_sumslicesource_table) = S ((S (dst_index_lookup_rowsrowrow_sumslicesource_table)) * dst_negative_scale_lookup_rowsrowrow_sumslicesource_table)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumslicesource_tableentrynegative. dst_negative_code_lookup_rowsrowrow_sumslicesource_table = ff_q_pvs_lookup_rowsrowrow_sumslicesource_tableentrynegative * S ((S (dst_index_lookup_rowsrowrow_sumslicesource_table)) * dst_negative_scale_lookup_rowsrowrow_sumslicesource_table) + (dst_negative_lookup_rowsrowrow_sumslicesource_table))) /\ (exists ge_balance_positive_lookup_rowsrowrow_sumslicesource_tableentryvalue ge_balance_negative_lookup_rowsrowrow_sumslicesource_tableentryvalue. (((((dst_value_lookup_rowsrowrow_sumslicesource_table) = 2 * (ge_balance_positive_lookup_rowsrowrow_sumslicesource_tableentryvalue) /\ (ge_balance_negative_lookup_rowsrowrow_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_rowsrowrow_sumslicesource_tableentryvaluedecode. (((dst_value_lookup_rowsrowrow_sumslicesource_table) = 2 * ge_signed_half_lookup_rowsrowrow_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_rowsrowrow_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_rowsrowrow_sumslicesource_tableentryvalue) = S ge_signed_half_lookup_rowsrowrow_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_lookup_rowsrowrow_sumslicesource_table) + ge_balance_negative_lookup_rowsrowrow_sumslicesource_tableentryvalue = (dst_negative_lookup_rowsrowrow_sumslicesource_table) + ge_balance_positive_lookup_rowsrowrow_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_lookup_rowsrowrow_sumsliceoutput_table dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table. (((srs_slice_lookup_rowsrowrow_sum) = (((((dst_positive_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)))) * S ((((dst_positive_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table)) * S ((dst_positive_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table)) + ((dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)))) + ((((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)))))) /\ (forall dst_index_lookup_rowsrowrow_sumsliceoutput_table. (exists pvs_le_gap_lookup_rowsrowrow_sumsliceoutput_tabledomain. pvs_le_gap_lookup_rowsrowrow_sumsliceoutput_tabledomain + (dst_index_lookup_rowsrowrow_sumsliceoutput_table) = (n)) -> exists dst_positive_lookup_rowsrowrow_sumsliceoutput_table dst_negative_lookup_rowsrowrow_sumsliceoutput_table dst_value_lookup_rowsrowrow_sumsliceoutput_table. ((((exists ff_h_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrypositive. ff_h_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrypositive + S (dst_positive_lookup_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_lookup_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrypositive. dst_positive_code_lookup_rowsrowrow_sumsliceoutput_table = ff_q_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrypositive * S ((S (dst_index_lookup_rowsrowrow_sumsliceoutput_table)) * dst_positive_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_positive_lookup_rowsrowrow_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrynegative. ff_h_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrynegative + S (dst_negative_lookup_rowsrowrow_sumsliceoutput_table) = S ((S (dst_index_lookup_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrynegative. dst_negative_code_lookup_rowsrowrow_sumsliceoutput_table = ff_q_pvs_lookup_rowsrowrow_sumsliceoutput_tableentrynegative * S ((S (dst_index_lookup_rowsrowrow_sumsliceoutput_table)) * dst_negative_scale_lookup_rowsrowrow_sumsliceoutput_table) + (dst_negative_lookup_rowsrowrow_sumsliceoutput_table))) /\ (exists ge_balance_positive_lookup_rowsrowrow_sumsliceoutput_tableentryvalue ge_balance_negative_lookup_rowsrowrow_sumsliceoutput_tableentryvalue. (((((dst_value_lookup_rowsrowrow_sumsliceoutput_table) = 2 * (ge_balance_positive_lookup_rowsrowrow_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_lookup_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_rowsrowrow_sumsliceoutput_tableentryvaluedecode. (((dst_value_lookup_rowsrowrow_sumsliceoutput_table) = 2 * ge_signed_half_lookup_rowsrowrow_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_rowsrowrow_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_rowsrowrow_sumsliceoutput_tableentryvalue) = S ge_signed_half_lookup_rowsrowrow_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_lookup_rowsrowrow_sumsliceoutput_table) + ge_balance_negative_lookup_rowsrowrow_sumsliceoutput_tableentryvalue = (dst_negative_lookup_rowsrowrow_sumsliceoutput_table) + ge_balance_positive_lookup_rowsrowrow_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_lookup_rowsrowrow_sumslice. (exists pvs_gap_lookup_rowsrowrow_sumslicebound. pvs_gap_lookup_rowsrowrow_sumslicebound + S (srs_index_lookup_rowsrowrow_sumslice) = (n)) -> exists srs_value_lookup_rowsrowrow_sumslice. (((exists dst_positive_code_lookup_rowsrowrow_sumsliceentrysource dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource dst_negative_code_lookup_rowsrowrow_sumsliceentrysource dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource dst_positive_lookup_rowsrowrow_sumsliceentrysource dst_negative_lookup_rowsrowrow_sumsliceentrysource. (((F) = (((((dst_positive_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)))) * S ((((dst_positive_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource)) * S ((dst_positive_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource)) + ((dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)))) + ((((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_lookup_rowsrowrow_sumsliceentrysourcepositive. ff_h_pvs_lookup_rowsrowrow_sumsliceentrysourcepositive + S (dst_positive_lookup_rowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_lookup_rows)))) + ((t) * (srs_index_lookup_rowsrowrow_sumslice))))) * dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumsliceentrysourcepositive. dst_positive_code_lookup_rowsrowrow_sumsliceentrysource = ff_q_pvs_lookup_rowsrowrow_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (srt_index_lookup_rows)))) + ((t) * (srs_index_lookup_rowsrowrow_sumslice))))) * dst_positive_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_positive_lookup_rowsrowrow_sumsliceentrysource))) /\ (((((exists ff_h_pvs_lookup_rowsrowrow_sumsliceentrysourcenegative. ff_h_pvs_lookup_rowsrowrow_sumsliceentrysourcenegative + S (dst_negative_lookup_rowsrowrow_sumsliceentrysource) = S ((S (((((o) + ((s) * (srt_index_lookup_rows)))) + ((t) * (srs_index_lookup_rowsrowrow_sumslice))))) * dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumsliceentrysourcenegative. dst_negative_code_lookup_rowsrowrow_sumsliceentrysource = ff_q_pvs_lookup_rowsrowrow_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (srt_index_lookup_rows)))) + ((t) * (srs_index_lookup_rowsrowrow_sumslice))))) * dst_negative_scale_lookup_rowsrowrow_sumsliceentrysource) + (dst_negative_lookup_rowsrowrow_sumsliceentrysource))) /\ (exists ge_balance_positive_lookup_rowsrowrow_sumsliceentrysourcevalue ge_balance_negative_lookup_rowsrowrow_sumsliceentrysourcevalue. (((((srs_value_lookup_rowsrowrow_sumslice) = 2 * (ge_balance_positive_lookup_rowsrowrow_sumsliceentrysourcevalue) /\ (ge_balance_negative_lookup_rowsrowrow_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_lookup_rowsrowrow_sumsliceentrysourcevaluedecode. (((srs_value_lookup_rowsrowrow_sumslice) = 2 * ge_signed_half_lookup_rowsrowrow_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_lookup_rowsrowrow_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_lookup_rowsrowrow_sumsliceentrysourcevalue) = S ge_signed_half_lookup_rowsrowrow_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_lookup_rowsrowrow_sumsliceentrysource) + ge_balance_negative_lookup_rowsrowrow_sumsliceentrysourcevalue = (dst_negative_lookup_rowsrowrow_sumsliceentrysource) + ge_balance_positive_lookup_rowsrowrow_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_lookup_rowsrowrow_sumsliceentryoutput dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput dst_positive_lookup_rowsrowrow_sumsliceentryoutput dst_negative_lookup_rowsrowrow_sumsliceentryoutput. (((srs_slice_lookup_rowsrowrow_sum) = (((((dst_positive_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)))) * S ((((dst_positive_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput)) * S ((dst_positive_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput)) + ((dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)))) + ((((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput))) + (((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) * S ((dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) + ((dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_lookup_rowsrowrow_sumsliceentryoutputpositive. ff_h_pvs_lookup_rowsrowrow_sumsliceentryoutputpositive + S (dst_positive_lookup_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_lookup_rowsrowrow_sumslice)) * dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumsliceentryoutputpositive. dst_positive_code_lookup_rowsrowrow_sumsliceentryoutput = ff_q_pvs_lookup_rowsrowrow_sumsliceentryoutputpositive * S ((S (srs_index_lookup_rowsrowrow_sumslice)) * dst_positive_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_positive_lookup_rowsrowrow_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_lookup_rowsrowrow_sumsliceentryoutputnegative. ff_h_pvs_lookup_rowsrowrow_sumsliceentryoutputnegative + S (dst_negative_lookup_rowsrowrow_sumsliceentryoutput) = S ((S (srs_index_lookup_rowsrowrow_sumslice)) * dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput)) /\ exists ff_q_pvs_lookup_rowsrowrow_sumsliceentryoutputnegative. dst_negative_code_lookup_rowsrowrow_sumsliceentryoutput = ff_q_pvs_lookup_rowsrowrow_sumsliceentryoutputnegative * S ((S (srs_index_lookup_rowsrowrow_sumslice)) * dst_negative_scale_lookup_rowsrowrow_sumsliceentryoutput) + (dst_negative_lookup_rowsrowrow_sumsliceentryoutput))) /\ (exists ge_balance_positive_lookup_rowsrowrow_sumsliceentryoutputvalue ge_balance_negative_lookup_rowsrowrow_sumsliceentryoutputvalue. (((((srs_value_lookup_rowsrowrow_sumslice) = 2 * (ge_balance_positive_lookup_rowsrowrow_sumsliceentryoutputvalue) /\ (ge_balance_negative_lookup_rowsrowrow_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_lookup_rowsrowrow_sumsliceentryoutputvaluedecode. (((srs_value_lookup_rowsrowrow_sumslice) = 2 * ge_signed_half_lookup_rowsrowrow_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_lookup_rowsrowrow_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_lookup_rowsrowrow_sumsliceentryoutputvalue) = S ge_signed_half_lookup_rowsrowrow_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_lookup_rowsrowrow_sumsliceentryoutput) + ge_balance_negative_lookup_rowsrowrow_sumsliceentryoutputvalue = (dst_negative_lookup_rowsrowrow_sumsliceentryoutput) + ge_balance_positive_lookup_rowsrowrow_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_lookup_rowsrowrow_sumsum dst_positive_scale_lookup_rowsrowrow_sumsum dst_negative_code_lookup_rowsrowrow_sumsum dst_negative_scale_lookup_rowsrowrow_sumsum dst_positive_sum_lookup_rowsrowrow_sumsum dst_negative_sum_lookup_rowsrowrow_sumsum. (((srs_slice_lookup_rowsrowrow_sum) = (((((dst_positive_code_lookup_rowsrowrow_sumsum) + (dst_positive_scale_lookup_rowsrowrow_sumsum)) * S ((dst_positive_code_lookup_rowsrowrow_sumsum) + (dst_positive_scale_lookup_rowsrowrow_sumsum)) + ((dst_positive_scale_lookup_rowsrowrow_sumsum) + (dst_positive_scale_lookup_rowsrowrow_sumsum))) + (((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) * S ((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) + ((dst_negative_scale_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)))) * S ((((dst_positive_code_lookup_rowsrowrow_sumsum) + (dst_positive_scale_lookup_rowsrowrow_sumsum)) * S ((dst_positive_code_lookup_rowsrowrow_sumsum) + (dst_positive_scale_lookup_rowsrowrow_sumsum)) + ((dst_positive_scale_lookup_rowsrowrow_sumsum) + (dst_positive_scale_lookup_rowsrowrow_sumsum))) + (((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) * S ((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) + ((dst_negative_scale_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)))) + ((((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) * S ((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) + ((dst_negative_scale_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum))) + (((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) * S ((dst_negative_code_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)) + ((dst_negative_scale_lookup_rowsrowrow_sumsum) + (dst_negative_scale_lookup_rowsrowrow_sumsum)))))) /\ (((exists fs_u_dst_lookup_rowsrowrow_sumsumpositive fs_v_dst_lookup_rowsrowrow_sumsumpositive. ((((exists fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_start. fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_start. fs_u_dst_lookup_rowsrowrow_sumsumpositive = fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_terminal. fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_terminal + S (dst_positive_sum_lookup_rowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_terminal. fs_u_dst_lookup_rowsrowrow_sumsumpositive = fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive) + (dst_positive_sum_lookup_rowsrowrow_sumsum))) /\ forall fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps. (exists fs_lt_dst_lookup_rowsrowrow_sumsumpositive_body_steps_bound. fs_lt_dst_lookup_rowsrowrow_sumsumpositive_body_steps_bound + S fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps = n) -> exists fs_a_dst_lookup_rowsrowrow_sumsumpositive_body_steps fs_r_dst_lookup_rowsrowrow_sumsumpositive_body_steps fs_s_dst_lookup_rowsrowrow_sumsumpositive_body_steps. ((((exists fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_steps_summand. fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_steps_summand + S (fs_a_dst_lookup_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_lookup_rowsrowrow_sumsum)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_steps_summand. dst_positive_code_lookup_rowsrowrow_sumsum = fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps)) * dst_positive_scale_lookup_rowsrowrow_sumsum) + (fs_a_dst_lookup_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_steps_partial. fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_steps_partial + S (fs_r_dst_lookup_rowsrowrow_sumsumpositive_body_steps) = S ((S (fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_steps_partial. fs_u_dst_lookup_rowsrowrow_sumsumpositive = fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive) + (fs_r_dst_lookup_rowsrowrow_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_steps_successor. fs_h_dst_lookup_rowsrowrow_sumsumpositive_body_steps_successor + S (fs_s_dst_lookup_rowsrowrow_sumsumpositive_body_steps) = S ((S (S fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_steps_successor. fs_u_dst_lookup_rowsrowrow_sumsumpositive = fs_q_dst_lookup_rowsrowrow_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_lookup_rowsrowrow_sumsumpositive_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumpositive) + (fs_s_dst_lookup_rowsrowrow_sumsumpositive_body_steps))) /\ fs_s_dst_lookup_rowsrowrow_sumsumpositive_body_steps = fs_r_dst_lookup_rowsrowrow_sumsumpositive_body_steps + fs_a_dst_lookup_rowsrowrow_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_lookup_rowsrowrow_sumsumnegative fs_v_dst_lookup_rowsrowrow_sumsumnegative. ((((exists fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_start. fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_start. fs_u_dst_lookup_rowsrowrow_sumsumnegative = fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_terminal. fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_terminal + S (dst_negative_sum_lookup_rowsrowrow_sumsum) = S ((S (n)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_terminal. fs_u_dst_lookup_rowsrowrow_sumsumnegative = fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative) + (dst_negative_sum_lookup_rowsrowrow_sumsum))) /\ forall fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps. (exists fs_lt_dst_lookup_rowsrowrow_sumsumnegative_body_steps_bound. fs_lt_dst_lookup_rowsrowrow_sumsumnegative_body_steps_bound + S fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps = n) -> exists fs_a_dst_lookup_rowsrowrow_sumsumnegative_body_steps fs_r_dst_lookup_rowsrowrow_sumsumnegative_body_steps fs_s_dst_lookup_rowsrowrow_sumsumnegative_body_steps. ((((exists fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_steps_summand. fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_steps_summand + S (fs_a_dst_lookup_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_lookup_rowsrowrow_sumsum)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_steps_summand. dst_negative_code_lookup_rowsrowrow_sumsum = fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps)) * dst_negative_scale_lookup_rowsrowrow_sumsum) + (fs_a_dst_lookup_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_steps_partial. fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_steps_partial + S (fs_r_dst_lookup_rowsrowrow_sumsumnegative_body_steps) = S ((S (fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_steps_partial. fs_u_dst_lookup_rowsrowrow_sumsumnegative = fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative) + (fs_r_dst_lookup_rowsrowrow_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_steps_successor. fs_h_dst_lookup_rowsrowrow_sumsumnegative_body_steps_successor + S (fs_s_dst_lookup_rowsrowrow_sumsumnegative_body_steps) = S ((S (S fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative)) /\ exists fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_steps_successor. fs_u_dst_lookup_rowsrowrow_sumsumnegative = fs_q_dst_lookup_rowsrowrow_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_lookup_rowsrowrow_sumsumnegative_body_steps)) * fs_v_dst_lookup_rowsrowrow_sumsumnegative) + (fs_s_dst_lookup_rowsrowrow_sumsumnegative_body_steps))) /\ fs_s_dst_lookup_rowsrowrow_sumsumnegative_body_steps = fs_r_dst_lookup_rowsrowrow_sumsumnegative_body_steps + fs_a_dst_lookup_rowsrowrow_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_lookup_rowsrowrow_sumsumresult ge_balance_negative_lookup_rowsrowrow_sumsumresult. (((((srt_value_lookup_rows) = 2 * (ge_balance_positive_lookup_rowsrowrow_sumsumresult) /\ (ge_balance_negative_lookup_rowsrowrow_sumsumresult) = 0) \/ exists ge_signed_half_lookup_rowsrowrow_sumsumresultdecode. (((srt_value_lookup_rows) = 2 * ge_signed_half_lookup_rowsrowrow_sumsumresultdecode + 1 /\ (ge_balance_positive_lookup_rowsrowrow_sumsumresult) = 0) /\ (ge_balance_negative_lookup_rowsrowrow_sumsumresult) = S ge_signed_half_lookup_rowsrowrow_sumsumresultdecode))) /\ ((dst_positive_sum_lookup_rowsrowrow_sumsum) + ge_balance_negative_lookup_rowsrowrow_sumsumresult = (dst_negative_sum_lookup_rowsrowrow_sumsum) + ge_balance_positive_lookup_rowsrowrow_sumsumresult)))))))))))))))))) -> (exists pvs_gap_lookup_bound. pvs_gap_lookup_bound + S (i) = (m)) -> (exists dst_positive_code_lookup_value dst_positive_scale_lookup_value dst_negative_code_lookup_value dst_negative_scale_lookup_value dst_positive_lookup_value dst_negative_lookup_value. (((R) = (((((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) * S ((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) + ((dst_positive_scale_lookup_value) + (dst_positive_scale_lookup_value))) + (((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value)))) * S ((((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) * S ((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) + ((dst_positive_scale_lookup_value) + (dst_positive_scale_lookup_value))) + (((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value)))) + ((((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value))) + (((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value)))))) /\ (((((exists ff_h_pvs_lookup_valuepositive. ff_h_pvs_lookup_valuepositive + S (dst_positive_lookup_value) = S ((S (i)) * dst_positive_scale_lookup_value)) /\ exists ff_q_pvs_lookup_valuepositive. dst_positive_code_lookup_value = ff_q_pvs_lookup_valuepositive * S ((S (i)) * dst_positive_scale_lookup_value) + (dst_positive_lookup_value))) /\ (((((exists ff_h_pvs_lookup_valuenegative. ff_h_pvs_lookup_valuenegative + S (dst_negative_lookup_value) = S ((S (i)) * dst_negative_scale_lookup_value)) /\ exists ff_q_pvs_lookup_valuenegative. dst_negative_code_lookup_value = ff_q_pvs_lookup_valuenegative * S ((S (i)) * dst_negative_scale_lookup_value) + (dst_negative_lookup_value))) /\ (exists ge_balance_positive_lookup_valuevalue ge_balance_negative_lookup_valuevalue. (((((z) = 2 * (ge_balance_positive_lookup_valuevalue) /\ (ge_balance_negative_lookup_valuevalue) = 0) \/ exists ge_signed_half_lookup_valuevaluedecode. (((z) = 2 * ge_signed_half_lookup_valuevaluedecode + 1 /\ (ge_balance_positive_lookup_valuevalue) = 0) /\ (ge_balance_negative_lookup_valuevalue) = S ge_signed_half_lookup_valuevaluedecode))) /\ ((dst_positive_lookup_value) + ge_balance_negative_lookup_valuevalue = (dst_negative_lookup_value) + ge_balance_positive_lookup_valuevalue))))))))) -> (exists srs_slice_lookup_sum. ((((exists dst_positive_code_lookup_sumslicesource_table dst_positive_scale_lookup_sumslicesource_table dst_negative_code_lookup_sumslicesource_table dst_negative_scale_lookup_sumslicesource_table. (((F) = (((((dst_positive_code_lookup_sumslicesource_table) + (dst_positive_scale_lookup_sumslicesource_table)) * S ((dst_positive_code_lookup_sumslicesource_table) + (dst_positive_scale_lookup_sumslicesource_table)) + ((dst_positive_scale_lookup_sumslicesource_table) + (dst_positive_scale_lookup_sumslicesource_table))) + (((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) * S ((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) + ((dst_negative_scale_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)))) * S ((((dst_positive_code_lookup_sumslicesource_table) + (dst_positive_scale_lookup_sumslicesource_table)) * S ((dst_positive_code_lookup_sumslicesource_table) + (dst_positive_scale_lookup_sumslicesource_table)) + ((dst_positive_scale_lookup_sumslicesource_table) + (dst_positive_scale_lookup_sumslicesource_table))) + (((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) * S ((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) + ((dst_negative_scale_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)))) + ((((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) * S ((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) + ((dst_negative_scale_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table))) + (((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) * S ((dst_negative_code_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)) + ((dst_negative_scale_lookup_sumslicesource_table) + (dst_negative_scale_lookup_sumslicesource_table)))))) /\ (forall dst_index_lookup_sumslicesource_table. (exists pvs_le_gap_lookup_sumslicesource_tabledomain. pvs_le_gap_lookup_sumslicesource_tabledomain + (dst_index_lookup_sumslicesource_table) = (0)) -> exists dst_positive_lookup_sumslicesource_table dst_negative_lookup_sumslicesource_table dst_value_lookup_sumslicesource_table. ((((exists ff_h_pvs_lookup_sumslicesource_tableentrypositive. ff_h_pvs_lookup_sumslicesource_tableentrypositive + S (dst_positive_lookup_sumslicesource_table) = S ((S (dst_index_lookup_sumslicesource_table)) * dst_positive_scale_lookup_sumslicesource_table)) /\ exists ff_q_pvs_lookup_sumslicesource_tableentrypositive. dst_positive_code_lookup_sumslicesource_table = ff_q_pvs_lookup_sumslicesource_tableentrypositive * S ((S (dst_index_lookup_sumslicesource_table)) * dst_positive_scale_lookup_sumslicesource_table) + (dst_positive_lookup_sumslicesource_table))) /\ (((((exists ff_h_pvs_lookup_sumslicesource_tableentrynegative. ff_h_pvs_lookup_sumslicesource_tableentrynegative + S (dst_negative_lookup_sumslicesource_table) = S ((S (dst_index_lookup_sumslicesource_table)) * dst_negative_scale_lookup_sumslicesource_table)) /\ exists ff_q_pvs_lookup_sumslicesource_tableentrynegative. dst_negative_code_lookup_sumslicesource_table = ff_q_pvs_lookup_sumslicesource_tableentrynegative * S ((S (dst_index_lookup_sumslicesource_table)) * dst_negative_scale_lookup_sumslicesource_table) + (dst_negative_lookup_sumslicesource_table))) /\ (exists ge_balance_positive_lookup_sumslicesource_tableentryvalue ge_balance_negative_lookup_sumslicesource_tableentryvalue. (((((dst_value_lookup_sumslicesource_table) = 2 * (ge_balance_positive_lookup_sumslicesource_tableentryvalue) /\ (ge_balance_negative_lookup_sumslicesource_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_sumslicesource_tableentryvaluedecode. (((dst_value_lookup_sumslicesource_table) = 2 * ge_signed_half_lookup_sumslicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_sumslicesource_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_sumslicesource_tableentryvalue) = S ge_signed_half_lookup_sumslicesource_tableentryvaluedecode))) /\ ((dst_positive_lookup_sumslicesource_table) + ge_balance_negative_lookup_sumslicesource_tableentryvalue = (dst_negative_lookup_sumslicesource_table) + ge_balance_positive_lookup_sumslicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_lookup_sumsliceoutput_table dst_positive_scale_lookup_sumsliceoutput_table dst_negative_code_lookup_sumsliceoutput_table dst_negative_scale_lookup_sumsliceoutput_table. (((srs_slice_lookup_sum) = (((((dst_positive_code_lookup_sumsliceoutput_table) + (dst_positive_scale_lookup_sumsliceoutput_table)) * S ((dst_positive_code_lookup_sumsliceoutput_table) + (dst_positive_scale_lookup_sumsliceoutput_table)) + ((dst_positive_scale_lookup_sumsliceoutput_table) + (dst_positive_scale_lookup_sumsliceoutput_table))) + (((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) * S ((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) + ((dst_negative_scale_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)))) * S ((((dst_positive_code_lookup_sumsliceoutput_table) + (dst_positive_scale_lookup_sumsliceoutput_table)) * S ((dst_positive_code_lookup_sumsliceoutput_table) + (dst_positive_scale_lookup_sumsliceoutput_table)) + ((dst_positive_scale_lookup_sumsliceoutput_table) + (dst_positive_scale_lookup_sumsliceoutput_table))) + (((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) * S ((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) + ((dst_negative_scale_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)))) + ((((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) * S ((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) + ((dst_negative_scale_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table))) + (((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) * S ((dst_negative_code_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)) + ((dst_negative_scale_lookup_sumsliceoutput_table) + (dst_negative_scale_lookup_sumsliceoutput_table)))))) /\ (forall dst_index_lookup_sumsliceoutput_table. (exists pvs_le_gap_lookup_sumsliceoutput_tabledomain. pvs_le_gap_lookup_sumsliceoutput_tabledomain + (dst_index_lookup_sumsliceoutput_table) = (n)) -> exists dst_positive_lookup_sumsliceoutput_table dst_negative_lookup_sumsliceoutput_table dst_value_lookup_sumsliceoutput_table. ((((exists ff_h_pvs_lookup_sumsliceoutput_tableentrypositive. ff_h_pvs_lookup_sumsliceoutput_tableentrypositive + S (dst_positive_lookup_sumsliceoutput_table) = S ((S (dst_index_lookup_sumsliceoutput_table)) * dst_positive_scale_lookup_sumsliceoutput_table)) /\ exists ff_q_pvs_lookup_sumsliceoutput_tableentrypositive. dst_positive_code_lookup_sumsliceoutput_table = ff_q_pvs_lookup_sumsliceoutput_tableentrypositive * S ((S (dst_index_lookup_sumsliceoutput_table)) * dst_positive_scale_lookup_sumsliceoutput_table) + (dst_positive_lookup_sumsliceoutput_table))) /\ (((((exists ff_h_pvs_lookup_sumsliceoutput_tableentrynegative. ff_h_pvs_lookup_sumsliceoutput_tableentrynegative + S (dst_negative_lookup_sumsliceoutput_table) = S ((S (dst_index_lookup_sumsliceoutput_table)) * dst_negative_scale_lookup_sumsliceoutput_table)) /\ exists ff_q_pvs_lookup_sumsliceoutput_tableentrynegative. dst_negative_code_lookup_sumsliceoutput_table = ff_q_pvs_lookup_sumsliceoutput_tableentrynegative * S ((S (dst_index_lookup_sumsliceoutput_table)) * dst_negative_scale_lookup_sumsliceoutput_table) + (dst_negative_lookup_sumsliceoutput_table))) /\ (exists ge_balance_positive_lookup_sumsliceoutput_tableentryvalue ge_balance_negative_lookup_sumsliceoutput_tableentryvalue. (((((dst_value_lookup_sumsliceoutput_table) = 2 * (ge_balance_positive_lookup_sumsliceoutput_tableentryvalue) /\ (ge_balance_negative_lookup_sumsliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_sumsliceoutput_tableentryvaluedecode. (((dst_value_lookup_sumsliceoutput_table) = 2 * ge_signed_half_lookup_sumsliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_sumsliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_sumsliceoutput_tableentryvalue) = S ge_signed_half_lookup_sumsliceoutput_tableentryvaluedecode))) /\ ((dst_positive_lookup_sumsliceoutput_table) + ge_balance_negative_lookup_sumsliceoutput_tableentryvalue = (dst_negative_lookup_sumsliceoutput_table) + ge_balance_positive_lookup_sumsliceoutput_tableentryvalue))))))))) /\ (forall srs_index_lookup_sumslice. (exists pvs_gap_lookup_sumslicebound. pvs_gap_lookup_sumslicebound + S (srs_index_lookup_sumslice) = (n)) -> exists srs_value_lookup_sumslice. (((exists dst_positive_code_lookup_sumsliceentrysource dst_positive_scale_lookup_sumsliceentrysource dst_negative_code_lookup_sumsliceentrysource dst_negative_scale_lookup_sumsliceentrysource dst_positive_lookup_sumsliceentrysource dst_negative_lookup_sumsliceentrysource. (((F) = (((((dst_positive_code_lookup_sumsliceentrysource) + (dst_positive_scale_lookup_sumsliceentrysource)) * S ((dst_positive_code_lookup_sumsliceentrysource) + (dst_positive_scale_lookup_sumsliceentrysource)) + ((dst_positive_scale_lookup_sumsliceentrysource) + (dst_positive_scale_lookup_sumsliceentrysource))) + (((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) * S ((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) + ((dst_negative_scale_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)))) * S ((((dst_positive_code_lookup_sumsliceentrysource) + (dst_positive_scale_lookup_sumsliceentrysource)) * S ((dst_positive_code_lookup_sumsliceentrysource) + (dst_positive_scale_lookup_sumsliceentrysource)) + ((dst_positive_scale_lookup_sumsliceentrysource) + (dst_positive_scale_lookup_sumsliceentrysource))) + (((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) * S ((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) + ((dst_negative_scale_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)))) + ((((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) * S ((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) + ((dst_negative_scale_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource))) + (((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) * S ((dst_negative_code_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)) + ((dst_negative_scale_lookup_sumsliceentrysource) + (dst_negative_scale_lookup_sumsliceentrysource)))))) /\ (((((exists ff_h_pvs_lookup_sumsliceentrysourcepositive. ff_h_pvs_lookup_sumsliceentrysourcepositive + S (dst_positive_lookup_sumsliceentrysource) = S ((S (((((o) + ((s) * (i)))) + ((t) * (srs_index_lookup_sumslice))))) * dst_positive_scale_lookup_sumsliceentrysource)) /\ exists ff_q_pvs_lookup_sumsliceentrysourcepositive. dst_positive_code_lookup_sumsliceentrysource = ff_q_pvs_lookup_sumsliceentrysourcepositive * S ((S (((((o) + ((s) * (i)))) + ((t) * (srs_index_lookup_sumslice))))) * dst_positive_scale_lookup_sumsliceentrysource) + (dst_positive_lookup_sumsliceentrysource))) /\ (((((exists ff_h_pvs_lookup_sumsliceentrysourcenegative. ff_h_pvs_lookup_sumsliceentrysourcenegative + S (dst_negative_lookup_sumsliceentrysource) = S ((S (((((o) + ((s) * (i)))) + ((t) * (srs_index_lookup_sumslice))))) * dst_negative_scale_lookup_sumsliceentrysource)) /\ exists ff_q_pvs_lookup_sumsliceentrysourcenegative. dst_negative_code_lookup_sumsliceentrysource = ff_q_pvs_lookup_sumsliceentrysourcenegative * S ((S (((((o) + ((s) * (i)))) + ((t) * (srs_index_lookup_sumslice))))) * dst_negative_scale_lookup_sumsliceentrysource) + (dst_negative_lookup_sumsliceentrysource))) /\ (exists ge_balance_positive_lookup_sumsliceentrysourcevalue ge_balance_negative_lookup_sumsliceentrysourcevalue. (((((srs_value_lookup_sumslice) = 2 * (ge_balance_positive_lookup_sumsliceentrysourcevalue) /\ (ge_balance_negative_lookup_sumsliceentrysourcevalue) = 0) \/ exists ge_signed_half_lookup_sumsliceentrysourcevaluedecode. (((srs_value_lookup_sumslice) = 2 * ge_signed_half_lookup_sumsliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_lookup_sumsliceentrysourcevalue) = 0) /\ (ge_balance_negative_lookup_sumsliceentrysourcevalue) = S ge_signed_half_lookup_sumsliceentrysourcevaluedecode))) /\ ((dst_positive_lookup_sumsliceentrysource) + ge_balance_negative_lookup_sumsliceentrysourcevalue = (dst_negative_lookup_sumsliceentrysource) + ge_balance_positive_lookup_sumsliceentrysourcevalue))))))))) /\ (exists dst_positive_code_lookup_sumsliceentryoutput dst_positive_scale_lookup_sumsliceentryoutput dst_negative_code_lookup_sumsliceentryoutput dst_negative_scale_lookup_sumsliceentryoutput dst_positive_lookup_sumsliceentryoutput dst_negative_lookup_sumsliceentryoutput. (((srs_slice_lookup_sum) = (((((dst_positive_code_lookup_sumsliceentryoutput) + (dst_positive_scale_lookup_sumsliceentryoutput)) * S ((dst_positive_code_lookup_sumsliceentryoutput) + (dst_positive_scale_lookup_sumsliceentryoutput)) + ((dst_positive_scale_lookup_sumsliceentryoutput) + (dst_positive_scale_lookup_sumsliceentryoutput))) + (((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) * S ((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) + ((dst_negative_scale_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)))) * S ((((dst_positive_code_lookup_sumsliceentryoutput) + (dst_positive_scale_lookup_sumsliceentryoutput)) * S ((dst_positive_code_lookup_sumsliceentryoutput) + (dst_positive_scale_lookup_sumsliceentryoutput)) + ((dst_positive_scale_lookup_sumsliceentryoutput) + (dst_positive_scale_lookup_sumsliceentryoutput))) + (((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) * S ((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) + ((dst_negative_scale_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)))) + ((((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) * S ((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) + ((dst_negative_scale_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput))) + (((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) * S ((dst_negative_code_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)) + ((dst_negative_scale_lookup_sumsliceentryoutput) + (dst_negative_scale_lookup_sumsliceentryoutput)))))) /\ (((((exists ff_h_pvs_lookup_sumsliceentryoutputpositive. ff_h_pvs_lookup_sumsliceentryoutputpositive + S (dst_positive_lookup_sumsliceentryoutput) = S ((S (srs_index_lookup_sumslice)) * dst_positive_scale_lookup_sumsliceentryoutput)) /\ exists ff_q_pvs_lookup_sumsliceentryoutputpositive. dst_positive_code_lookup_sumsliceentryoutput = ff_q_pvs_lookup_sumsliceentryoutputpositive * S ((S (srs_index_lookup_sumslice)) * dst_positive_scale_lookup_sumsliceentryoutput) + (dst_positive_lookup_sumsliceentryoutput))) /\ (((((exists ff_h_pvs_lookup_sumsliceentryoutputnegative. ff_h_pvs_lookup_sumsliceentryoutputnegative + S (dst_negative_lookup_sumsliceentryoutput) = S ((S (srs_index_lookup_sumslice)) * dst_negative_scale_lookup_sumsliceentryoutput)) /\ exists ff_q_pvs_lookup_sumsliceentryoutputnegative. dst_negative_code_lookup_sumsliceentryoutput = ff_q_pvs_lookup_sumsliceentryoutputnegative * S ((S (srs_index_lookup_sumslice)) * dst_negative_scale_lookup_sumsliceentryoutput) + (dst_negative_lookup_sumsliceentryoutput))) /\ (exists ge_balance_positive_lookup_sumsliceentryoutputvalue ge_balance_negative_lookup_sumsliceentryoutputvalue. (((((srs_value_lookup_sumslice) = 2 * (ge_balance_positive_lookup_sumsliceentryoutputvalue) /\ (ge_balance_negative_lookup_sumsliceentryoutputvalue) = 0) \/ exists ge_signed_half_lookup_sumsliceentryoutputvaluedecode. (((srs_value_lookup_sumslice) = 2 * ge_signed_half_lookup_sumsliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_lookup_sumsliceentryoutputvalue) = 0) /\ (ge_balance_negative_lookup_sumsliceentryoutputvalue) = S ge_signed_half_lookup_sumsliceentryoutputvaluedecode))) /\ ((dst_positive_lookup_sumsliceentryoutput) + ge_balance_negative_lookup_sumsliceentryoutputvalue = (dst_negative_lookup_sumsliceentryoutput) + ge_balance_positive_lookup_sumsliceentryoutputvalue)))))))))))))))) /\ (exists dst_positive_code_lookup_sumsum dst_positive_scale_lookup_sumsum dst_negative_code_lookup_sumsum dst_negative_scale_lookup_sumsum dst_positive_sum_lookup_sumsum dst_negative_sum_lookup_sumsum. (((srs_slice_lookup_sum) = (((((dst_positive_code_lookup_sumsum) + (dst_positive_scale_lookup_sumsum)) * S ((dst_positive_code_lookup_sumsum) + (dst_positive_scale_lookup_sumsum)) + ((dst_positive_scale_lookup_sumsum) + (dst_positive_scale_lookup_sumsum))) + (((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) * S ((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) + ((dst_negative_scale_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)))) * S ((((dst_positive_code_lookup_sumsum) + (dst_positive_scale_lookup_sumsum)) * S ((dst_positive_code_lookup_sumsum) + (dst_positive_scale_lookup_sumsum)) + ((dst_positive_scale_lookup_sumsum) + (dst_positive_scale_lookup_sumsum))) + (((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) * S ((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) + ((dst_negative_scale_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)))) + ((((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) * S ((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) + ((dst_negative_scale_lookup_sumsum) + (dst_negative_scale_lookup_sumsum))) + (((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) * S ((dst_negative_code_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)) + ((dst_negative_scale_lookup_sumsum) + (dst_negative_scale_lookup_sumsum)))))) /\ (((exists fs_u_dst_lookup_sumsumpositive fs_v_dst_lookup_sumsumpositive. ((((exists fs_h_dst_lookup_sumsumpositive_body_start. fs_h_dst_lookup_sumsumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_lookup_sumsumpositive)) /\ exists fs_q_dst_lookup_sumsumpositive_body_start. fs_u_dst_lookup_sumsumpositive = fs_q_dst_lookup_sumsumpositive_body_start * S ((S (0)) * fs_v_dst_lookup_sumsumpositive) + (0))) /\ ((((exists fs_h_dst_lookup_sumsumpositive_body_terminal. fs_h_dst_lookup_sumsumpositive_body_terminal + S (dst_positive_sum_lookup_sumsum) = S ((S (n)) * fs_v_dst_lookup_sumsumpositive)) /\ exists fs_q_dst_lookup_sumsumpositive_body_terminal. fs_u_dst_lookup_sumsumpositive = fs_q_dst_lookup_sumsumpositive_body_terminal * S ((S (n)) * fs_v_dst_lookup_sumsumpositive) + (dst_positive_sum_lookup_sumsum))) /\ forall fs_i_dst_lookup_sumsumpositive_body_steps. (exists fs_lt_dst_lookup_sumsumpositive_body_steps_bound. fs_lt_dst_lookup_sumsumpositive_body_steps_bound + S fs_i_dst_lookup_sumsumpositive_body_steps = n) -> exists fs_a_dst_lookup_sumsumpositive_body_steps fs_r_dst_lookup_sumsumpositive_body_steps fs_s_dst_lookup_sumsumpositive_body_steps. ((((exists fs_h_dst_lookup_sumsumpositive_body_steps_summand. fs_h_dst_lookup_sumsumpositive_body_steps_summand + S (fs_a_dst_lookup_sumsumpositive_body_steps) = S ((S (fs_i_dst_lookup_sumsumpositive_body_steps)) * dst_positive_scale_lookup_sumsum)) /\ exists fs_q_dst_lookup_sumsumpositive_body_steps_summand. dst_positive_code_lookup_sumsum = fs_q_dst_lookup_sumsumpositive_body_steps_summand * S ((S (fs_i_dst_lookup_sumsumpositive_body_steps)) * dst_positive_scale_lookup_sumsum) + (fs_a_dst_lookup_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_lookup_sumsumpositive_body_steps_partial. fs_h_dst_lookup_sumsumpositive_body_steps_partial + S (fs_r_dst_lookup_sumsumpositive_body_steps) = S ((S (fs_i_dst_lookup_sumsumpositive_body_steps)) * fs_v_dst_lookup_sumsumpositive)) /\ exists fs_q_dst_lookup_sumsumpositive_body_steps_partial. fs_u_dst_lookup_sumsumpositive = fs_q_dst_lookup_sumsumpositive_body_steps_partial * S ((S (fs_i_dst_lookup_sumsumpositive_body_steps)) * fs_v_dst_lookup_sumsumpositive) + (fs_r_dst_lookup_sumsumpositive_body_steps))) /\ ((((exists fs_h_dst_lookup_sumsumpositive_body_steps_successor. fs_h_dst_lookup_sumsumpositive_body_steps_successor + S (fs_s_dst_lookup_sumsumpositive_body_steps) = S ((S (S fs_i_dst_lookup_sumsumpositive_body_steps)) * fs_v_dst_lookup_sumsumpositive)) /\ exists fs_q_dst_lookup_sumsumpositive_body_steps_successor. fs_u_dst_lookup_sumsumpositive = fs_q_dst_lookup_sumsumpositive_body_steps_successor * S ((S (S fs_i_dst_lookup_sumsumpositive_body_steps)) * fs_v_dst_lookup_sumsumpositive) + (fs_s_dst_lookup_sumsumpositive_body_steps))) /\ fs_s_dst_lookup_sumsumpositive_body_steps = fs_r_dst_lookup_sumsumpositive_body_steps + fs_a_dst_lookup_sumsumpositive_body_steps)))))) /\ (((exists fs_u_dst_lookup_sumsumnegative fs_v_dst_lookup_sumsumnegative. ((((exists fs_h_dst_lookup_sumsumnegative_body_start. fs_h_dst_lookup_sumsumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_lookup_sumsumnegative)) /\ exists fs_q_dst_lookup_sumsumnegative_body_start. fs_u_dst_lookup_sumsumnegative = fs_q_dst_lookup_sumsumnegative_body_start * S ((S (0)) * fs_v_dst_lookup_sumsumnegative) + (0))) /\ ((((exists fs_h_dst_lookup_sumsumnegative_body_terminal. fs_h_dst_lookup_sumsumnegative_body_terminal + S (dst_negative_sum_lookup_sumsum) = S ((S (n)) * fs_v_dst_lookup_sumsumnegative)) /\ exists fs_q_dst_lookup_sumsumnegative_body_terminal. fs_u_dst_lookup_sumsumnegative = fs_q_dst_lookup_sumsumnegative_body_terminal * S ((S (n)) * fs_v_dst_lookup_sumsumnegative) + (dst_negative_sum_lookup_sumsum))) /\ forall fs_i_dst_lookup_sumsumnegative_body_steps. (exists fs_lt_dst_lookup_sumsumnegative_body_steps_bound. fs_lt_dst_lookup_sumsumnegative_body_steps_bound + S fs_i_dst_lookup_sumsumnegative_body_steps = n) -> exists fs_a_dst_lookup_sumsumnegative_body_steps fs_r_dst_lookup_sumsumnegative_body_steps fs_s_dst_lookup_sumsumnegative_body_steps. ((((exists fs_h_dst_lookup_sumsumnegative_body_steps_summand. fs_h_dst_lookup_sumsumnegative_body_steps_summand + S (fs_a_dst_lookup_sumsumnegative_body_steps) = S ((S (fs_i_dst_lookup_sumsumnegative_body_steps)) * dst_negative_scale_lookup_sumsum)) /\ exists fs_q_dst_lookup_sumsumnegative_body_steps_summand. dst_negative_code_lookup_sumsum = fs_q_dst_lookup_sumsumnegative_body_steps_summand * S ((S (fs_i_dst_lookup_sumsumnegative_body_steps)) * dst_negative_scale_lookup_sumsum) + (fs_a_dst_lookup_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_lookup_sumsumnegative_body_steps_partial. fs_h_dst_lookup_sumsumnegative_body_steps_partial + S (fs_r_dst_lookup_sumsumnegative_body_steps) = S ((S (fs_i_dst_lookup_sumsumnegative_body_steps)) * fs_v_dst_lookup_sumsumnegative)) /\ exists fs_q_dst_lookup_sumsumnegative_body_steps_partial. fs_u_dst_lookup_sumsumnegative = fs_q_dst_lookup_sumsumnegative_body_steps_partial * S ((S (fs_i_dst_lookup_sumsumnegative_body_steps)) * fs_v_dst_lookup_sumsumnegative) + (fs_r_dst_lookup_sumsumnegative_body_steps))) /\ ((((exists fs_h_dst_lookup_sumsumnegative_body_steps_successor. fs_h_dst_lookup_sumsumnegative_body_steps_successor + S (fs_s_dst_lookup_sumsumnegative_body_steps) = S ((S (S fs_i_dst_lookup_sumsumnegative_body_steps)) * fs_v_dst_lookup_sumsumnegative)) /\ exists fs_q_dst_lookup_sumsumnegative_body_steps_successor. fs_u_dst_lookup_sumsumnegative = fs_q_dst_lookup_sumsumnegative_body_steps_successor * S ((S (S fs_i_dst_lookup_sumsumnegative_body_steps)) * fs_v_dst_lookup_sumsumnegative) + (fs_s_dst_lookup_sumsumnegative_body_steps))) /\ fs_s_dst_lookup_sumsumnegative_body_steps = fs_r_dst_lookup_sumsumnegative_body_steps + fs_a_dst_lookup_sumsumnegative_body_steps)))))) /\ (exists ge_balance_positive_lookup_sumsumresult ge_balance_negative_lookup_sumsumresult. (((((z) = 2 * (ge_balance_positive_lookup_sumsumresult) /\ (ge_balance_negative_lookup_sumsumresult) = 0) \/ exists ge_signed_half_lookup_sumsumresultdecode. (((z) = 2 * ge_signed_half_lookup_sumsumresultdecode + 1 /\ (ge_balance_positive_lookup_sumsumresult) = 0) /\ (ge_balance_negative_lookup_sumsumresult) = S ge_signed_half_lookup_sumsumresultdecode))) /\ ((dst_positive_sum_lookup_sumsum) + ge_balance_negative_lookup_sumsumresult = (dst_negative_sum_lookup_sumsum) + ge_balance_positive_lookup_sumsumresult)))))))))))

signed_rectangular_slice_lookup · checked inherited prerequisite

Exact statement in the checked dependency cone

forall F G o s l i z. (((exists dst_positive_code_lookup_slicesource_table dst_positive_scale_lookup_slicesource_table dst_negative_code_lookup_slicesource_table dst_negative_scale_lookup_slicesource_table. (((F) = (((((dst_positive_code_lookup_slicesource_table) + (dst_positive_scale_lookup_slicesource_table)) * S ((dst_positive_code_lookup_slicesource_table) + (dst_positive_scale_lookup_slicesource_table)) + ((dst_positive_scale_lookup_slicesource_table) + (dst_positive_scale_lookup_slicesource_table))) + (((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) * S ((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) + ((dst_negative_scale_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)))) * S ((((dst_positive_code_lookup_slicesource_table) + (dst_positive_scale_lookup_slicesource_table)) * S ((dst_positive_code_lookup_slicesource_table) + (dst_positive_scale_lookup_slicesource_table)) + ((dst_positive_scale_lookup_slicesource_table) + (dst_positive_scale_lookup_slicesource_table))) + (((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) * S ((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) + ((dst_negative_scale_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)))) + ((((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) * S ((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) + ((dst_negative_scale_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table))) + (((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) * S ((dst_negative_code_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)) + ((dst_negative_scale_lookup_slicesource_table) + (dst_negative_scale_lookup_slicesource_table)))))) /\ (forall dst_index_lookup_slicesource_table. (exists pvs_le_gap_lookup_slicesource_tabledomain. pvs_le_gap_lookup_slicesource_tabledomain + (dst_index_lookup_slicesource_table) = (0)) -> exists dst_positive_lookup_slicesource_table dst_negative_lookup_slicesource_table dst_value_lookup_slicesource_table. ((((exists ff_h_pvs_lookup_slicesource_tableentrypositive. ff_h_pvs_lookup_slicesource_tableentrypositive + S (dst_positive_lookup_slicesource_table) = S ((S (dst_index_lookup_slicesource_table)) * dst_positive_scale_lookup_slicesource_table)) /\ exists ff_q_pvs_lookup_slicesource_tableentrypositive. dst_positive_code_lookup_slicesource_table = ff_q_pvs_lookup_slicesource_tableentrypositive * S ((S (dst_index_lookup_slicesource_table)) * dst_positive_scale_lookup_slicesource_table) + (dst_positive_lookup_slicesource_table))) /\ (((((exists ff_h_pvs_lookup_slicesource_tableentrynegative. ff_h_pvs_lookup_slicesource_tableentrynegative + S (dst_negative_lookup_slicesource_table) = S ((S (dst_index_lookup_slicesource_table)) * dst_negative_scale_lookup_slicesource_table)) /\ exists ff_q_pvs_lookup_slicesource_tableentrynegative. dst_negative_code_lookup_slicesource_table = ff_q_pvs_lookup_slicesource_tableentrynegative * S ((S (dst_index_lookup_slicesource_table)) * dst_negative_scale_lookup_slicesource_table) + (dst_negative_lookup_slicesource_table))) /\ (exists ge_balance_positive_lookup_slicesource_tableentryvalue ge_balance_negative_lookup_slicesource_tableentryvalue. (((((dst_value_lookup_slicesource_table) = 2 * (ge_balance_positive_lookup_slicesource_tableentryvalue) /\ (ge_balance_negative_lookup_slicesource_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_slicesource_tableentryvaluedecode. (((dst_value_lookup_slicesource_table) = 2 * ge_signed_half_lookup_slicesource_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_slicesource_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_slicesource_tableentryvalue) = S ge_signed_half_lookup_slicesource_tableentryvaluedecode))) /\ ((dst_positive_lookup_slicesource_table) + ge_balance_negative_lookup_slicesource_tableentryvalue = (dst_negative_lookup_slicesource_table) + ge_balance_positive_lookup_slicesource_tableentryvalue))))))))) /\ (((exists dst_positive_code_lookup_sliceoutput_table dst_positive_scale_lookup_sliceoutput_table dst_negative_code_lookup_sliceoutput_table dst_negative_scale_lookup_sliceoutput_table. (((G) = (((((dst_positive_code_lookup_sliceoutput_table) + (dst_positive_scale_lookup_sliceoutput_table)) * S ((dst_positive_code_lookup_sliceoutput_table) + (dst_positive_scale_lookup_sliceoutput_table)) + ((dst_positive_scale_lookup_sliceoutput_table) + (dst_positive_scale_lookup_sliceoutput_table))) + (((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) * S ((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) + ((dst_negative_scale_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)))) * S ((((dst_positive_code_lookup_sliceoutput_table) + (dst_positive_scale_lookup_sliceoutput_table)) * S ((dst_positive_code_lookup_sliceoutput_table) + (dst_positive_scale_lookup_sliceoutput_table)) + ((dst_positive_scale_lookup_sliceoutput_table) + (dst_positive_scale_lookup_sliceoutput_table))) + (((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) * S ((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) + ((dst_negative_scale_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)))) + ((((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) * S ((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) + ((dst_negative_scale_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table))) + (((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) * S ((dst_negative_code_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)) + ((dst_negative_scale_lookup_sliceoutput_table) + (dst_negative_scale_lookup_sliceoutput_table)))))) /\ (forall dst_index_lookup_sliceoutput_table. (exists pvs_le_gap_lookup_sliceoutput_tabledomain. pvs_le_gap_lookup_sliceoutput_tabledomain + (dst_index_lookup_sliceoutput_table) = (l)) -> exists dst_positive_lookup_sliceoutput_table dst_negative_lookup_sliceoutput_table dst_value_lookup_sliceoutput_table. ((((exists ff_h_pvs_lookup_sliceoutput_tableentrypositive. ff_h_pvs_lookup_sliceoutput_tableentrypositive + S (dst_positive_lookup_sliceoutput_table) = S ((S (dst_index_lookup_sliceoutput_table)) * dst_positive_scale_lookup_sliceoutput_table)) /\ exists ff_q_pvs_lookup_sliceoutput_tableentrypositive. dst_positive_code_lookup_sliceoutput_table = ff_q_pvs_lookup_sliceoutput_tableentrypositive * S ((S (dst_index_lookup_sliceoutput_table)) * dst_positive_scale_lookup_sliceoutput_table) + (dst_positive_lookup_sliceoutput_table))) /\ (((((exists ff_h_pvs_lookup_sliceoutput_tableentrynegative. ff_h_pvs_lookup_sliceoutput_tableentrynegative + S (dst_negative_lookup_sliceoutput_table) = S ((S (dst_index_lookup_sliceoutput_table)) * dst_negative_scale_lookup_sliceoutput_table)) /\ exists ff_q_pvs_lookup_sliceoutput_tableentrynegative. dst_negative_code_lookup_sliceoutput_table = ff_q_pvs_lookup_sliceoutput_tableentrynegative * S ((S (dst_index_lookup_sliceoutput_table)) * dst_negative_scale_lookup_sliceoutput_table) + (dst_negative_lookup_sliceoutput_table))) /\ (exists ge_balance_positive_lookup_sliceoutput_tableentryvalue ge_balance_negative_lookup_sliceoutput_tableentryvalue. (((((dst_value_lookup_sliceoutput_table) = 2 * (ge_balance_positive_lookup_sliceoutput_tableentryvalue) /\ (ge_balance_negative_lookup_sliceoutput_tableentryvalue) = 0) \/ exists ge_signed_half_lookup_sliceoutput_tableentryvaluedecode. (((dst_value_lookup_sliceoutput_table) = 2 * ge_signed_half_lookup_sliceoutput_tableentryvaluedecode + 1 /\ (ge_balance_positive_lookup_sliceoutput_tableentryvalue) = 0) /\ (ge_balance_negative_lookup_sliceoutput_tableentryvalue) = S ge_signed_half_lookup_sliceoutput_tableentryvaluedecode))) /\ ((dst_positive_lookup_sliceoutput_table) + ge_balance_negative_lookup_sliceoutput_tableentryvalue = (dst_negative_lookup_sliceoutput_table) + ge_balance_positive_lookup_sliceoutput_tableentryvalue))))))))) /\ (forall srs_index_lookup_slice. (exists pvs_gap_lookup_slicebound. pvs_gap_lookup_slicebound + S (srs_index_lookup_slice) = (l)) -> exists srs_value_lookup_slice. (((exists dst_positive_code_lookup_sliceentrysource dst_positive_scale_lookup_sliceentrysource dst_negative_code_lookup_sliceentrysource dst_negative_scale_lookup_sliceentrysource dst_positive_lookup_sliceentrysource dst_negative_lookup_sliceentrysource. (((F) = (((((dst_positive_code_lookup_sliceentrysource) + (dst_positive_scale_lookup_sliceentrysource)) * S ((dst_positive_code_lookup_sliceentrysource) + (dst_positive_scale_lookup_sliceentrysource)) + ((dst_positive_scale_lookup_sliceentrysource) + (dst_positive_scale_lookup_sliceentrysource))) + (((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) * S ((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) + ((dst_negative_scale_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)))) * S ((((dst_positive_code_lookup_sliceentrysource) + (dst_positive_scale_lookup_sliceentrysource)) * S ((dst_positive_code_lookup_sliceentrysource) + (dst_positive_scale_lookup_sliceentrysource)) + ((dst_positive_scale_lookup_sliceentrysource) + (dst_positive_scale_lookup_sliceentrysource))) + (((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) * S ((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) + ((dst_negative_scale_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)))) + ((((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) * S ((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) + ((dst_negative_scale_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource))) + (((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) * S ((dst_negative_code_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)) + ((dst_negative_scale_lookup_sliceentrysource) + (dst_negative_scale_lookup_sliceentrysource)))))) /\ (((((exists ff_h_pvs_lookup_sliceentrysourcepositive. ff_h_pvs_lookup_sliceentrysourcepositive + S (dst_positive_lookup_sliceentrysource) = S ((S (((o) + ((s) * (srs_index_lookup_slice))))) * dst_positive_scale_lookup_sliceentrysource)) /\ exists ff_q_pvs_lookup_sliceentrysourcepositive. dst_positive_code_lookup_sliceentrysource = ff_q_pvs_lookup_sliceentrysourcepositive * S ((S (((o) + ((s) * (srs_index_lookup_slice))))) * dst_positive_scale_lookup_sliceentrysource) + (dst_positive_lookup_sliceentrysource))) /\ (((((exists ff_h_pvs_lookup_sliceentrysourcenegative. ff_h_pvs_lookup_sliceentrysourcenegative + S (dst_negative_lookup_sliceentrysource) = S ((S (((o) + ((s) * (srs_index_lookup_slice))))) * dst_negative_scale_lookup_sliceentrysource)) /\ exists ff_q_pvs_lookup_sliceentrysourcenegative. dst_negative_code_lookup_sliceentrysource = ff_q_pvs_lookup_sliceentrysourcenegative * S ((S (((o) + ((s) * (srs_index_lookup_slice))))) * dst_negative_scale_lookup_sliceentrysource) + (dst_negative_lookup_sliceentrysource))) /\ (exists ge_balance_positive_lookup_sliceentrysourcevalue ge_balance_negative_lookup_sliceentrysourcevalue. (((((srs_value_lookup_slice) = 2 * (ge_balance_positive_lookup_sliceentrysourcevalue) /\ (ge_balance_negative_lookup_sliceentrysourcevalue) = 0) \/ exists ge_signed_half_lookup_sliceentrysourcevaluedecode. (((srs_value_lookup_slice) = 2 * ge_signed_half_lookup_sliceentrysourcevaluedecode + 1 /\ (ge_balance_positive_lookup_sliceentrysourcevalue) = 0) /\ (ge_balance_negative_lookup_sliceentrysourcevalue) = S ge_signed_half_lookup_sliceentrysourcevaluedecode))) /\ ((dst_positive_lookup_sliceentrysource) + ge_balance_negative_lookup_sliceentrysourcevalue = (dst_negative_lookup_sliceentrysource) + ge_balance_positive_lookup_sliceentrysourcevalue))))))))) /\ (exists dst_positive_code_lookup_sliceentryoutput dst_positive_scale_lookup_sliceentryoutput dst_negative_code_lookup_sliceentryoutput dst_negative_scale_lookup_sliceentryoutput dst_positive_lookup_sliceentryoutput dst_negative_lookup_sliceentryoutput. (((G) = (((((dst_positive_code_lookup_sliceentryoutput) + (dst_positive_scale_lookup_sliceentryoutput)) * S ((dst_positive_code_lookup_sliceentryoutput) + (dst_positive_scale_lookup_sliceentryoutput)) + ((dst_positive_scale_lookup_sliceentryoutput) + (dst_positive_scale_lookup_sliceentryoutput))) + (((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) * S ((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) + ((dst_negative_scale_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)))) * S ((((dst_positive_code_lookup_sliceentryoutput) + (dst_positive_scale_lookup_sliceentryoutput)) * S ((dst_positive_code_lookup_sliceentryoutput) + (dst_positive_scale_lookup_sliceentryoutput)) + ((dst_positive_scale_lookup_sliceentryoutput) + (dst_positive_scale_lookup_sliceentryoutput))) + (((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) * S ((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) + ((dst_negative_scale_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)))) + ((((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) * S ((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) + ((dst_negative_scale_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput))) + (((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) * S ((dst_negative_code_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)) + ((dst_negative_scale_lookup_sliceentryoutput) + (dst_negative_scale_lookup_sliceentryoutput)))))) /\ (((((exists ff_h_pvs_lookup_sliceentryoutputpositive. ff_h_pvs_lookup_sliceentryoutputpositive + S (dst_positive_lookup_sliceentryoutput) = S ((S (srs_index_lookup_slice)) * dst_positive_scale_lookup_sliceentryoutput)) /\ exists ff_q_pvs_lookup_sliceentryoutputpositive. dst_positive_code_lookup_sliceentryoutput = ff_q_pvs_lookup_sliceentryoutputpositive * S ((S (srs_index_lookup_slice)) * dst_positive_scale_lookup_sliceentryoutput) + (dst_positive_lookup_sliceentryoutput))) /\ (((((exists ff_h_pvs_lookup_sliceentryoutputnegative. ff_h_pvs_lookup_sliceentryoutputnegative + S (dst_negative_lookup_sliceentryoutput) = S ((S (srs_index_lookup_slice)) * dst_negative_scale_lookup_sliceentryoutput)) /\ exists ff_q_pvs_lookup_sliceentryoutputnegative. dst_negative_code_lookup_sliceentryoutput = ff_q_pvs_lookup_sliceentryoutputnegative * S ((S (srs_index_lookup_slice)) * dst_negative_scale_lookup_sliceentryoutput) + (dst_negative_lookup_sliceentryoutput))) /\ (exists ge_balance_positive_lookup_sliceentryoutputvalue ge_balance_negative_lookup_sliceentryoutputvalue. (((((srs_value_lookup_slice) = 2 * (ge_balance_positive_lookup_sliceentryoutputvalue) /\ (ge_balance_negative_lookup_sliceentryoutputvalue) = 0) \/ exists ge_signed_half_lookup_sliceentryoutputvaluedecode. (((srs_value_lookup_slice) = 2 * ge_signed_half_lookup_sliceentryoutputvaluedecode + 1 /\ (ge_balance_positive_lookup_sliceentryoutputvalue) = 0) /\ (ge_balance_negative_lookup_sliceentryoutputvalue) = S ge_signed_half_lookup_sliceentryoutputvaluedecode))) /\ ((dst_positive_lookup_sliceentryoutput) + ge_balance_negative_lookup_sliceentryoutputvalue = (dst_negative_lookup_sliceentryoutput) + ge_balance_positive_lookup_sliceentryoutputvalue)))))))))))))))) -> (exists pvs_gap_lookup_bound. pvs_gap_lookup_bound + S (i) = (l)) -> (exists dst_positive_code_lookup_value dst_positive_scale_lookup_value dst_negative_code_lookup_value dst_negative_scale_lookup_value dst_positive_lookup_value dst_negative_lookup_value. (((G) = (((((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) * S ((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) + ((dst_positive_scale_lookup_value) + (dst_positive_scale_lookup_value))) + (((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value)))) * S ((((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) * S ((dst_positive_code_lookup_value) + (dst_positive_scale_lookup_value)) + ((dst_positive_scale_lookup_value) + (dst_positive_scale_lookup_value))) + (((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value)))) + ((((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value))) + (((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) * S ((dst_negative_code_lookup_value) + (dst_negative_scale_lookup_value)) + ((dst_negative_scale_lookup_value) + (dst_negative_scale_lookup_value)))))) /\ (((((exists ff_h_pvs_lookup_valuepositive. ff_h_pvs_lookup_valuepositive + S (dst_positive_lookup_value) = S ((S (i)) * dst_positive_scale_lookup_value)) /\ exists ff_q_pvs_lookup_valuepositive. dst_positive_code_lookup_value = ff_q_pvs_lookup_valuepositive * S ((S (i)) * dst_positive_scale_lookup_value) + (dst_positive_lookup_value))) /\ (((((exists ff_h_pvs_lookup_valuenegative. ff_h_pvs_lookup_valuenegative + S (dst_negative_lookup_value) = S ((S (i)) * dst_negative_scale_lookup_value)) /\ exists ff_q_pvs_lookup_valuenegative. dst_negative_code_lookup_value = ff_q_pvs_lookup_valuenegative * S ((S (i)) * dst_negative_scale_lookup_value) + (dst_negative_lookup_value))) /\ (exists ge_balance_positive_lookup_valuevalue ge_balance_negative_lookup_valuevalue. (((((z) = 2 * (ge_balance_positive_lookup_valuevalue) /\ (ge_balance_negative_lookup_valuevalue) = 0) \/ exists ge_signed_half_lookup_valuevaluedecode. (((z) = 2 * ge_signed_half_lookup_valuevaluedecode + 1 /\ (ge_balance_positive_lookup_valuevalue) = 0) /\ (ge_balance_negative_lookup_valuevalue) = S ge_signed_half_lookup_valuevaluedecode))) /\ ((dst_positive_lookup_value) + ge_balance_negative_lookup_valuevalue = (dst_negative_lookup_value) + ge_balance_positive_lookup_valuevalue))))))))) -> (exists dst_positive_code_lookup_source dst_positive_scale_lookup_source dst_negative_code_lookup_source dst_negative_scale_lookup_source dst_positive_lookup_source dst_negative_lookup_source. (((F) = (((((dst_positive_code_lookup_source) + (dst_positive_scale_lookup_source)) * S ((dst_positive_code_lookup_source) + (dst_positive_scale_lookup_source)) + ((dst_positive_scale_lookup_source) + (dst_positive_scale_lookup_source))) + (((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) * S ((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) + ((dst_negative_scale_lookup_source) + (dst_negative_scale_lookup_source)))) * S ((((dst_positive_code_lookup_source) + (dst_positive_scale_lookup_source)) * S ((dst_positive_code_lookup_source) + (dst_positive_scale_lookup_source)) + ((dst_positive_scale_lookup_source) + (dst_positive_scale_lookup_source))) + (((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) * S ((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) + ((dst_negative_scale_lookup_source) + (dst_negative_scale_lookup_source)))) + ((((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) * S ((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) + ((dst_negative_scale_lookup_source) + (dst_negative_scale_lookup_source))) + (((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) * S ((dst_negative_code_lookup_source) + (dst_negative_scale_lookup_source)) + ((dst_negative_scale_lookup_source) + (dst_negative_scale_lookup_source)))))) /\ (((((exists ff_h_pvs_lookup_sourcepositive. ff_h_pvs_lookup_sourcepositive + S (dst_positive_lookup_source) = S ((S (((o) + ((s) * (i))))) * dst_positive_scale_lookup_source)) /\ exists ff_q_pvs_lookup_sourcepositive. dst_positive_code_lookup_source = ff_q_pvs_lookup_sourcepositive * S ((S (((o) + ((s) * (i))))) * dst_positive_scale_lookup_source) + (dst_positive_lookup_source))) /\ (((((exists ff_h_pvs_lookup_sourcenegative. ff_h_pvs_lookup_sourcenegative + S (dst_negative_lookup_source) = S ((S (((o) + ((s) * (i))))) * dst_negative_scale_lookup_source)) /\ exists ff_q_pvs_lookup_sourcenegative. dst_negative_code_lookup_source = ff_q_pvs_lookup_sourcenegative * S ((S (((o) + ((s) * (i))))) * dst_negative_scale_lookup_source) + (dst_negative_lookup_source))) /\ (exists ge_balance_positive_lookup_sourcevalue ge_balance_negative_lookup_sourcevalue. (((((z) = 2 * (ge_balance_positive_lookup_sourcevalue) /\ (ge_balance_negative_lookup_sourcevalue) = 0) \/ exists ge_signed_half_lookup_sourcevaluedecode. (((z) = 2 * ge_signed_half_lookup_sourcevaluedecode + 1 /\ (ge_balance_positive_lookup_sourcevalue) = 0) /\ (ge_balance_negative_lookup_sourcevalue) = S ge_signed_half_lookup_sourcevaluedecode))) /\ ((dst_positive_lookup_source) + ge_balance_negative_lookup_sourcevalue = (dst_negative_lookup_source) + ge_balance_positive_lookup_sourcevalue)))))))))

signed_table_domain_resize · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N M F. (exists dst_positive_code_resize_input dst_positive_scale_resize_input dst_negative_code_resize_input dst_negative_scale_resize_input. (((F) = (((((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) * S ((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) + ((dst_positive_scale_resize_input) + (dst_positive_scale_resize_input))) + (((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input)))) * S ((((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) * S ((dst_positive_code_resize_input) + (dst_positive_scale_resize_input)) + ((dst_positive_scale_resize_input) + (dst_positive_scale_resize_input))) + (((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input)))) + ((((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input))) + (((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) * S ((dst_negative_code_resize_input) + (dst_negative_scale_resize_input)) + ((dst_negative_scale_resize_input) + (dst_negative_scale_resize_input)))))) /\ (forall dst_index_resize_input. (exists pvs_le_gap_resize_inputdomain. pvs_le_gap_resize_inputdomain + (dst_index_resize_input) = (N)) -> exists dst_positive_resize_input dst_negative_resize_input dst_value_resize_input. ((((exists ff_h_pvs_resize_inputentrypositive. ff_h_pvs_resize_inputentrypositive + S (dst_positive_resize_input) = S ((S (dst_index_resize_input)) * dst_positive_scale_resize_input)) /\ exists ff_q_pvs_resize_inputentrypositive. dst_positive_code_resize_input = ff_q_pvs_resize_inputentrypositive * S ((S (dst_index_resize_input)) * dst_positive_scale_resize_input) + (dst_positive_resize_input))) /\ (((((exists ff_h_pvs_resize_inputentrynegative. ff_h_pvs_resize_inputentrynegative + S (dst_negative_resize_input) = S ((S (dst_index_resize_input)) * dst_negative_scale_resize_input)) /\ exists ff_q_pvs_resize_inputentrynegative. dst_negative_code_resize_input = ff_q_pvs_resize_inputentrynegative * S ((S (dst_index_resize_input)) * dst_negative_scale_resize_input) + (dst_negative_resize_input))) /\ (exists ge_balance_positive_resize_inputentryvalue ge_balance_negative_resize_inputentryvalue. (((((dst_value_resize_input) = 2 * (ge_balance_positive_resize_inputentryvalue) /\ (ge_balance_negative_resize_inputentryvalue) = 0) \/ exists ge_signed_half_resize_inputentryvaluedecode. (((dst_value_resize_input) = 2 * ge_signed_half_resize_inputentryvaluedecode + 1 /\ (ge_balance_positive_resize_inputentryvalue) = 0) /\ (ge_balance_negative_resize_inputentryvalue) = S ge_signed_half_resize_inputentryvaluedecode))) /\ ((dst_positive_resize_input) + ge_balance_negative_resize_inputentryvalue = (dst_negative_resize_input) + ge_balance_positive_resize_inputentryvalue))))))))) -> (exists dst_positive_code_resize_output dst_positive_scale_resize_output dst_negative_code_resize_output dst_negative_scale_resize_output. (((F) = (((((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) * S ((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) + ((dst_positive_scale_resize_output) + (dst_positive_scale_resize_output))) + (((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output)))) * S ((((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) * S ((dst_positive_code_resize_output) + (dst_positive_scale_resize_output)) + ((dst_positive_scale_resize_output) + (dst_positive_scale_resize_output))) + (((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output)))) + ((((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output))) + (((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) * S ((dst_negative_code_resize_output) + (dst_negative_scale_resize_output)) + ((dst_negative_scale_resize_output) + (dst_negative_scale_resize_output)))))) /\ (forall dst_index_resize_output. (exists pvs_le_gap_resize_outputdomain. pvs_le_gap_resize_outputdomain + (dst_index_resize_output) = (M)) -> exists dst_positive_resize_output dst_negative_resize_output dst_value_resize_output. ((((exists ff_h_pvs_resize_outputentrypositive. ff_h_pvs_resize_outputentrypositive + S (dst_positive_resize_output) = S ((S (dst_index_resize_output)) * dst_positive_scale_resize_output)) /\ exists ff_q_pvs_resize_outputentrypositive. dst_positive_code_resize_output = ff_q_pvs_resize_outputentrypositive * S ((S (dst_index_resize_output)) * dst_positive_scale_resize_output) + (dst_positive_resize_output))) /\ (((((exists ff_h_pvs_resize_outputentrynegative. ff_h_pvs_resize_outputentrynegative + S (dst_negative_resize_output) = S ((S (dst_index_resize_output)) * dst_negative_scale_resize_output)) /\ exists ff_q_pvs_resize_outputentrynegative. dst_negative_code_resize_output = ff_q_pvs_resize_outputentrynegative * S ((S (dst_index_resize_output)) * dst_negative_scale_resize_output) + (dst_negative_resize_output))) /\ (exists ge_balance_positive_resize_outputentryvalue ge_balance_negative_resize_outputentryvalue. (((((dst_value_resize_output) = 2 * (ge_balance_positive_resize_outputentryvalue) /\ (ge_balance_negative_resize_outputentryvalue) = 0) \/ exists ge_signed_half_resize_outputentryvaluedecode. (((dst_value_resize_output) = 2 * ge_signed_half_resize_outputentryvaluedecode + 1 /\ (ge_balance_positive_resize_outputentryvalue) = 0) /\ (ge_balance_negative_resize_outputentryvalue) = S ge_signed_half_resize_outputentryvaluedecode))) /\ ((dst_positive_resize_output) + ge_balance_negative_resize_outputentryvalue = (dst_negative_resize_output) + ge_balance_positive_resize_outputentryvalue)))))))))

signed_table_lookup_any · checked inherited prerequisite

Exact statement in the checked dependency cone

forall N F i. (exists dst_positive_code_any_lookup_table dst_positive_scale_any_lookup_table dst_negative_code_any_lookup_table dst_negative_scale_any_lookup_table. (((F) = (((((dst_positive_code_any_lookup_table) + (dst_positive_scale_any_lookup_table)) * S ((dst_positive_code_any_lookup_table) + (dst_positive_scale_any_lookup_table)) + ((dst_positive_scale_any_lookup_table) + (dst_positive_scale_any_lookup_table))) + (((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) * S ((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) + ((dst_negative_scale_any_lookup_table) + (dst_negative_scale_any_lookup_table)))) * S ((((dst_positive_code_any_lookup_table) + (dst_positive_scale_any_lookup_table)) * S ((dst_positive_code_any_lookup_table) + (dst_positive_scale_any_lookup_table)) + ((dst_positive_scale_any_lookup_table) + (dst_positive_scale_any_lookup_table))) + (((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) * S ((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) + ((dst_negative_scale_any_lookup_table) + (dst_negative_scale_any_lookup_table)))) + ((((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) * S ((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) + ((dst_negative_scale_any_lookup_table) + (dst_negative_scale_any_lookup_table))) + (((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) * S ((dst_negative_code_any_lookup_table) + (dst_negative_scale_any_lookup_table)) + ((dst_negative_scale_any_lookup_table) + (dst_negative_scale_any_lookup_table)))))) /\ (forall dst_index_any_lookup_table. (exists pvs_le_gap_any_lookup_tabledomain. pvs_le_gap_any_lookup_tabledomain + (dst_index_any_lookup_table) = (N)) -> exists dst_positive_any_lookup_table dst_negative_any_lookup_table dst_value_any_lookup_table. ((((exists ff_h_pvs_any_lookup_tableentrypositive. ff_h_pvs_any_lookup_tableentrypositive + S (dst_positive_any_lookup_table) = S ((S (dst_index_any_lookup_table)) * dst_positive_scale_any_lookup_table)) /\ exists ff_q_pvs_any_lookup_tableentrypositive. dst_positive_code_any_lookup_table = ff_q_pvs_any_lookup_tableentrypositive * S ((S (dst_index_any_lookup_table)) * dst_positive_scale_any_lookup_table) + (dst_positive_any_lookup_table))) /\ (((((exists ff_h_pvs_any_lookup_tableentrynegative. ff_h_pvs_any_lookup_tableentrynegative + S (dst_negative_any_lookup_table) = S ((S (dst_index_any_lookup_table)) * dst_negative_scale_any_lookup_table)) /\ exists ff_q_pvs_any_lookup_tableentrynegative. dst_negative_code_any_lookup_table = ff_q_pvs_any_lookup_tableentrynegative * S ((S (dst_index_any_lookup_table)) * dst_negative_scale_any_lookup_table) + (dst_negative_any_lookup_table))) /\ (exists ge_balance_positive_any_lookup_tableentryvalue ge_balance_negative_any_lookup_tableentryvalue. (((((dst_value_any_lookup_table) = 2 * (ge_balance_positive_any_lookup_tableentryvalue) /\ (ge_balance_negative_any_lookup_tableentryvalue) = 0) \/ exists ge_signed_half_any_lookup_tableentryvaluedecode. (((dst_value_any_lookup_table) = 2 * ge_signed_half_any_lookup_tableentryvaluedecode + 1 /\ (ge_balance_positive_any_lookup_tableentryvalue) = 0) /\ (ge_balance_negative_any_lookup_tableentryvalue) = S ge_signed_half_any_lookup_tableentryvaluedecode))) /\ ((dst_positive_any_lookup_table) + ge_balance_negative_any_lookup_tableentryvalue = (dst_negative_any_lookup_table) + ge_balance_positive_any_lookup_tableentryvalue))))))))) -> exists z. (exists dst_positive_code_any_lookup_result dst_positive_scale_any_lookup_result dst_negative_code_any_lookup_result dst_negative_scale_any_lookup_result dst_positive_any_lookup_result dst_negative_any_lookup_result. (((F) = (((((dst_positive_code_any_lookup_result) + (dst_positive_scale_any_lookup_result)) * S ((dst_positive_code_any_lookup_result) + (dst_positive_scale_any_lookup_result)) + ((dst_positive_scale_any_lookup_result) + (dst_positive_scale_any_lookup_result))) + (((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) * S ((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) + ((dst_negative_scale_any_lookup_result) + (dst_negative_scale_any_lookup_result)))) * S ((((dst_positive_code_any_lookup_result) + (dst_positive_scale_any_lookup_result)) * S ((dst_positive_code_any_lookup_result) + (dst_positive_scale_any_lookup_result)) + ((dst_positive_scale_any_lookup_result) + (dst_positive_scale_any_lookup_result))) + (((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) * S ((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) + ((dst_negative_scale_any_lookup_result) + (dst_negative_scale_any_lookup_result)))) + ((((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) * S ((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) + ((dst_negative_scale_any_lookup_result) + (dst_negative_scale_any_lookup_result))) + (((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) * S ((dst_negative_code_any_lookup_result) + (dst_negative_scale_any_lookup_result)) + ((dst_negative_scale_any_lookup_result) + (dst_negative_scale_any_lookup_result)))))) /\ (((((exists ff_h_pvs_any_lookup_resultpositive. ff_h_pvs_any_lookup_resultpositive + S (dst_positive_any_lookup_result) = S ((S (i)) * dst_positive_scale_any_lookup_result)) /\ exists ff_q_pvs_any_lookup_resultpositive. dst_positive_code_any_lookup_result = ff_q_pvs_any_lookup_resultpositive * S ((S (i)) * dst_positive_scale_any_lookup_result) + (dst_positive_any_lookup_result))) /\ (((((exists ff_h_pvs_any_lookup_resultnegative. ff_h_pvs_any_lookup_resultnegative + S (dst_negative_any_lookup_result) = S ((S (i)) * dst_negative_scale_any_lookup_result)) /\ exists ff_q_pvs_any_lookup_resultnegative. dst_negative_code_any_lookup_result = ff_q_pvs_any_lookup_resultnegative * S ((S (i)) * dst_negative_scale_any_lookup_result) + (dst_negative_any_lookup_result))) /\ (exists ge_balance_positive_any_lookup_resultvalue ge_balance_negative_any_lookup_resultvalue. (((((z) = 2 * (ge_balance_positive_any_lookup_resultvalue) /\ (ge_balance_negative_any_lookup_resultvalue) = 0) \/ exists ge_signed_half_any_lookup_resultvaluedecode. (((z) = 2 * ge_signed_half_any_lookup_resultvaluedecode + 1 /\ (ge_balance_positive_any_lookup_resultvalue) = 0) /\ (ge_balance_negative_any_lookup_resultvalue) = S ge_signed_half_any_lookup_resultvaluedecode))) /\ ((dst_positive_any_lookup_result) + ge_balance_negative_any_lookup_resultvalue = (dst_negative_any_lookup_result) + ge_balance_positive_any_lookup_resultvalue)))))))))

signed_weighted_scalar_commute · checked inherited prerequisite

Exact statement in the checked dependency cone

forall a b c ab cb out. (exists sto_ap_weighted_commute_first sto_an_weighted_commute_first sto_bp_weighted_commute_first sto_bn_weighted_commute_first sto_cp_weighted_commute_first sto_cn_weighted_commute_first. (((((a) = 2 * (sto_ap_weighted_commute_first) /\ (sto_an_weighted_commute_first) = 0) \/ exists ge_signed_half_weighted_commute_firstleft. (((a) = 2 * ge_signed_half_weighted_commute_firstleft + 1 /\ (sto_ap_weighted_commute_first) = 0) /\ (sto_an_weighted_commute_first) = S ge_signed_half_weighted_commute_firstleft))) /\ ((((((b) = 2 * (sto_bp_weighted_commute_first) /\ (sto_bn_weighted_commute_first) = 0) \/ exists ge_signed_half_weighted_commute_firstright. (((b) = 2 * ge_signed_half_weighted_commute_firstright + 1 /\ (sto_bp_weighted_commute_first) = 0) /\ (sto_bn_weighted_commute_first) = S ge_signed_half_weighted_commute_firstright))) /\ ((((((ab) = 2 * (sto_cp_weighted_commute_first) /\ (sto_cn_weighted_commute_first) = 0) \/ exists ge_signed_half_weighted_commute_firstoutput. (((ab) = 2 * ge_signed_half_weighted_commute_firstoutput + 1 /\ (sto_cp_weighted_commute_first) = 0) /\ (sto_cn_weighted_commute_first) = S ge_signed_half_weighted_commute_firstoutput))) /\ ((sto_ap_weighted_commute_first * sto_bp_weighted_commute_first + sto_an_weighted_commute_first * sto_bn_weighted_commute_first) + sto_cn_weighted_commute_first = (sto_ap_weighted_commute_first * sto_bn_weighted_commute_first + sto_an_weighted_commute_first * sto_bp_weighted_commute_first) + sto_cp_weighted_commute_first))))))) -> (exists sto_ap_weighted_commute_second sto_an_weighted_commute_second sto_bp_weighted_commute_second sto_bn_weighted_commute_second sto_cp_weighted_commute_second sto_cn_weighted_commute_second. (((((c) = 2 * (sto_ap_weighted_commute_second) /\ (sto_an_weighted_commute_second) = 0) \/ exists ge_signed_half_weighted_commute_secondleft. (((c) = 2 * ge_signed_half_weighted_commute_secondleft + 1 /\ (sto_ap_weighted_commute_second) = 0) /\ (sto_an_weighted_commute_second) = S ge_signed_half_weighted_commute_secondleft))) /\ ((((((b) = 2 * (sto_bp_weighted_commute_second) /\ (sto_bn_weighted_commute_second) = 0) \/ exists ge_signed_half_weighted_commute_secondright. (((b) = 2 * ge_signed_half_weighted_commute_secondright + 1 /\ (sto_bp_weighted_commute_second) = 0) /\ (sto_bn_weighted_commute_second) = S ge_signed_half_weighted_commute_secondright))) /\ ((((((cb) = 2 * (sto_cp_weighted_commute_second) /\ (sto_cn_weighted_commute_second) = 0) \/ exists ge_signed_half_weighted_commute_secondoutput. (((cb) = 2 * ge_signed_half_weighted_commute_secondoutput + 1 /\ (sto_cp_weighted_commute_second) = 0) /\ (sto_cn_weighted_commute_second) = S ge_signed_half_weighted_commute_secondoutput))) /\ ((sto_ap_weighted_commute_second * sto_bp_weighted_commute_second + sto_an_weighted_commute_second * sto_bn_weighted_commute_second) + sto_cn_weighted_commute_second = (sto_ap_weighted_commute_second * sto_bn_weighted_commute_second + sto_an_weighted_commute_second * sto_bp_weighted_commute_second) + sto_cp_weighted_commute_second))))))) -> (exists sto_ap_weighted_commute_output sto_an_weighted_commute_output sto_bp_weighted_commute_output sto_bn_weighted_commute_output sto_cp_weighted_commute_output sto_cn_weighted_commute_output. (((((c) = 2 * (sto_ap_weighted_commute_output) /\ (sto_an_weighted_commute_output) = 0) \/ exists ge_signed_half_weighted_commute_outputleft. (((c) = 2 * ge_signed_half_weighted_commute_outputleft + 1 /\ (sto_ap_weighted_commute_output) = 0) /\ (sto_an_weighted_commute_output) = S ge_signed_half_weighted_commute_outputleft))) /\ ((((((ab) = 2 * (sto_bp_weighted_commute_output) /\ (sto_bn_weighted_commute_output) = 0) \/ exists ge_signed_half_weighted_commute_outputright. (((ab) = 2 * ge_signed_half_weighted_commute_outputright + 1 /\ (sto_bp_weighted_commute_output) = 0) /\ (sto_bn_weighted_commute_output) = S ge_signed_half_weighted_commute_outputright))) /\ ((((((out) = 2 * (sto_cp_weighted_commute_output) /\ (sto_cn_weighted_commute_output) = 0) \/ exists ge_signed_half_weighted_commute_outputoutput. (((out) = 2 * ge_signed_half_weighted_commute_outputoutput + 1 /\ (sto_cp_weighted_commute_output) = 0) /\ (sto_cn_weighted_commute_output) = S ge_signed_half_weighted_commute_outputoutput))) /\ ((sto_ap_weighted_commute_output * sto_bp_weighted_commute_output + sto_an_weighted_commute_output * sto_bn_weighted_commute_output) + sto_cn_weighted_commute_output = (sto_ap_weighted_commute_output * sto_bn_weighted_commute_output + sto_an_weighted_commute_output * sto_bp_weighted_commute_output) + sto_cp_weighted_commute_output))))))) -> (exists sto_ap_weighted_commute_target sto_an_weighted_commute_target sto_bp_weighted_commute_target sto_bn_weighted_commute_target sto_cp_weighted_commute_target sto_cn_weighted_commute_target. (((((a) = 2 * (sto_ap_weighted_commute_target) /\ (sto_an_weighted_commute_target) = 0) \/ exists ge_signed_half_weighted_commute_targetleft. (((a) = 2 * ge_signed_half_weighted_commute_targetleft + 1 /\ (sto_ap_weighted_commute_target) = 0) /\ (sto_an_weighted_commute_target) = S ge_signed_half_weighted_commute_targetleft))) /\ ((((((cb) = 2 * (sto_bp_weighted_commute_target) /\ (sto_bn_weighted_commute_target) = 0) \/ exists ge_signed_half_weighted_commute_targetright. (((cb) = 2 * ge_signed_half_weighted_commute_targetright + 1 /\ (sto_bp_weighted_commute_target) = 0) /\ (sto_bn_weighted_commute_target) = S ge_signed_half_weighted_commute_targetright))) /\ ((((((out) = 2 * (sto_cp_weighted_commute_target) /\ (sto_cn_weighted_commute_target) = 0) \/ exists ge_signed_half_weighted_commute_targetoutput. (((out) = 2 * ge_signed_half_weighted_commute_targetoutput + 1 /\ (sto_cp_weighted_commute_target) = 0) /\ (sto_cn_weighted_commute_target) = S ge_signed_half_weighted_commute_targetoutput))) /\ ((sto_ap_weighted_commute_target * sto_bp_weighted_commute_target + sto_an_weighted_commute_target * sto_bn_weighted_commute_target) + sto_cn_weighted_commute_target = (sto_ap_weighted_commute_target * sto_bn_weighted_commute_target + sto_an_weighted_commute_target * sto_bp_weighted_commute_target) + sto_cp_weighted_commute_target)))))))

succ_le_succ · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall a b. (exists k. k + a = b) -> exists r. r + S a = S b
```
succ_ne_zero · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. ~(S n = 0)
```
zero_add · checked inherited prerequisite
Exact statement in the checked dependency cone
```
forall n. 0 + n = n
```