Möbius divisor cancellation — exact evidence

Exact theorem nodes and inherited prerequisites

• MC0001 prime_toggle_square_quotient_divides · actual bundle node 348
• MC0002 prime_toggle_fresh_divisor_product · actual bundle node 349
• MC0003 prime_factor_toggle_exists · actual bundle node 350
• MC0004 prime_factor_toggle_functional · actual bundle node 351
• MC0005 prime_factor_toggle_symmetric · actual bundle node 352
• MC0006 prime_factor_toggle_positive · actual bundle node 353
• MC0007 prime_factor_toggle_preserves_divisor · actual bundle node 354
• MC0008 divisor_prime_toggle_exists · actual bundle node 355
• MC0009 divisor_prime_toggle_functional · actual bundle node 356
• MC000A divisor_prime_toggle_symmetric · actual bundle node 357
• MC000B divisor_prime_toggle_bounded · actual bundle node 358
• MC000C divisor_prime_toggle_prefix_exists · actual bundle node 359
• MC000D divisor_prime_toggle_prefix_lookup · actual bundle node 360
• MC000E divisor_prime_toggle_prefix_permutation · actual bundle node 361
• MC000F divisor_prime_toggle_permutation_exists · actual bundle node 362
• MC0010 mobius_prime_factor_toggle_negates · actual bundle node 363
• MC0011 mobius_divisor_mask_actual_value · actual bundle node 364
• MC0012 mobius_divisor_mask_prime_toggle_negates · actual bundle node 365
• MC0013 signed_table_swapped_components_negation_at · actual bundle node 366
• MC0014 signed_prefix_sum_pointwise_negate · actual bundle node 367
• MC0015 anti_invariant_signed_permutation_sum_zero · actual bundle node 368
• MC0016 mobius_divisor_mask_prime_factor_sum_zero · actual bundle node 369
• MC0017 mobius_divisor_sum_nonunit_value_zero · actual bundle node 370
• MC0018 mobius_divisor_sum_nonunit_zero · actual bundle node 371
• MC0019 mobius_divisor_sum_unit_one · actual bundle node 372
• MC001A mobius_divisor_sum_cancellation · actual bundle node 373
• MC001B mobius_divisor_sum_cancellation_exists · actual bundle node 374
• MC001C mobius_divisor_sum_cancellation_on_positive_values · actual bundle node 375
• 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)))))))))

• beta_at_unique · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall b c i x y. ((exists h. h + S x = S ((S i) * c)) /\ exists q. b = q * S ((S i) * c) + x) -> ((exists h. h + S y = S ((S i) * c)) /\ exists q. b = q * S ((S i) * c) + y) -> x = y

• beta_prefix_extend · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall k b e s. exists z c. (((exists h. h + S s = S ((S k) * c)) /\ exists q. z = q * S ((S k) * c) + s) /\ forall i a. (exists h. h + S i = k) -> ((exists h. h + S a = S ((S i) * e)) /\ exists q. b = q * S ((S i) * e) + a) -> ((exists h. h + S a = S ((S i) * c)) /\ exists q. z = q * S ((S i) * c) + a))

• 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_mask_entry_omitted_value · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F n d z. (d=0 \/ ~(exists pvs_factor_zero_guard. (n) = (d) * pvs_factor_zero_guard)) -> ((((~((d)=0)) /\ (exists dm_quotient_zero_mask. (((n)=(d)*dm_quotient_zero_mask) /\ (exists dst_positive_code_zero_maskinput dst_positive_scale_zero_maskinput dst_negative_code_zero_maskinput dst_negative_scale_zero_maskinput dst_positive_zero_maskinput dst_negative_zero_maskinput. (((F) = (((((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) * S ((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) + ((dst_positive_scale_zero_maskinput) + (dst_positive_scale_zero_maskinput))) + (((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput)))) * S ((((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) * S ((dst_positive_code_zero_maskinput) + (dst_positive_scale_zero_maskinput)) + ((dst_positive_scale_zero_maskinput) + (dst_positive_scale_zero_maskinput))) + (((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput)))) + ((((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput))) + (((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) * S ((dst_negative_code_zero_maskinput) + (dst_negative_scale_zero_maskinput)) + ((dst_negative_scale_zero_maskinput) + (dst_negative_scale_zero_maskinput)))))) /\ (((((exists ff_h_pvs_zero_maskinputpositive. ff_h_pvs_zero_maskinputpositive + S (dst_positive_zero_maskinput) = S ((S (d)) * dst_positive_scale_zero_maskinput)) /\ exists ff_q_pvs_zero_maskinputpositive. dst_positive_code_zero_maskinput = ff_q_pvs_zero_maskinputpositive * S ((S (d)) * dst_positive_scale_zero_maskinput) + (dst_positive_zero_maskinput))) /\ (((((exists ff_h_pvs_zero_maskinputnegative. ff_h_pvs_zero_maskinputnegative + S (dst_negative_zero_maskinput) = S ((S (d)) * dst_negative_scale_zero_maskinput)) /\ exists ff_q_pvs_zero_maskinputnegative. dst_negative_code_zero_maskinput = ff_q_pvs_zero_maskinputnegative * S ((S (d)) * dst_negative_scale_zero_maskinput) + (dst_negative_zero_maskinput))) /\ (exists ge_balance_positive_zero_maskinputvalue ge_balance_negative_zero_maskinputvalue. (((((z) = 2 * (ge_balance_positive_zero_maskinputvalue) /\ (ge_balance_negative_zero_maskinputvalue) = 0) \/ exists ge_signed_half_zero_maskinputvaluedecode. (((z) = 2 * ge_signed_half_zero_maskinputvaluedecode + 1 /\ (ge_balance_positive_zero_maskinputvalue) = 0) /\ (ge_balance_negative_zero_maskinputvalue) = S ge_signed_half_zero_maskinputvaluedecode))) /\ ((dst_positive_zero_maskinput) + ge_balance_negative_zero_maskinputvalue = (dst_negative_zero_maskinput) + ge_balance_positive_zero_maskinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_zero_masknondivisor. (n) = (d) * pvs_factor_zero_masknondivisor)) /\ ((z)=0)))) -> z=0

• divisor_mask_entry_quotient_input · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F n d q z. ~(d=0) -> n=d*q -> ((((~((d)=0)) /\ (exists dm_quotient_read_mask. (((n)=(d)*dm_quotient_read_mask) /\ (exists dst_positive_code_read_maskinput dst_positive_scale_read_maskinput dst_negative_code_read_maskinput dst_negative_scale_read_maskinput dst_positive_read_maskinput dst_negative_read_maskinput. (((F) = (((((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) * S ((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) + ((dst_positive_scale_read_maskinput) + (dst_positive_scale_read_maskinput))) + (((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput)))) * S ((((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) * S ((dst_positive_code_read_maskinput) + (dst_positive_scale_read_maskinput)) + ((dst_positive_scale_read_maskinput) + (dst_positive_scale_read_maskinput))) + (((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput)))) + ((((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput))) + (((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) * S ((dst_negative_code_read_maskinput) + (dst_negative_scale_read_maskinput)) + ((dst_negative_scale_read_maskinput) + (dst_negative_scale_read_maskinput)))))) /\ (((((exists ff_h_pvs_read_maskinputpositive. ff_h_pvs_read_maskinputpositive + S (dst_positive_read_maskinput) = S ((S (d)) * dst_positive_scale_read_maskinput)) /\ exists ff_q_pvs_read_maskinputpositive. dst_positive_code_read_maskinput = ff_q_pvs_read_maskinputpositive * S ((S (d)) * dst_positive_scale_read_maskinput) + (dst_positive_read_maskinput))) /\ (((((exists ff_h_pvs_read_maskinputnegative. ff_h_pvs_read_maskinputnegative + S (dst_negative_read_maskinput) = S ((S (d)) * dst_negative_scale_read_maskinput)) /\ exists ff_q_pvs_read_maskinputnegative. dst_negative_code_read_maskinput = ff_q_pvs_read_maskinputnegative * S ((S (d)) * dst_negative_scale_read_maskinput) + (dst_negative_read_maskinput))) /\ (exists ge_balance_positive_read_maskinputvalue ge_balance_negative_read_maskinputvalue. (((((z) = 2 * (ge_balance_positive_read_maskinputvalue) /\ (ge_balance_negative_read_maskinputvalue) = 0) \/ exists ge_signed_half_read_maskinputvaluedecode. (((z) = 2 * ge_signed_half_read_maskinputvaluedecode + 1 /\ (ge_balance_positive_read_maskinputvalue) = 0) /\ (ge_balance_negative_read_maskinputvalue) = S ge_signed_half_read_maskinputvaluedecode))) /\ ((dst_positive_read_maskinput) + ge_balance_negative_read_maskinputvalue = (dst_negative_read_maskinput) + ge_balance_positive_read_maskinputvalue))))))))))))) \/ ((((d)=0 \/ ~(exists pvs_factor_read_masknondivisor. (n) = (d) * pvs_factor_read_masknondivisor)) /\ ((z)=0)))) -> (exists dst_positive_code_read_input dst_positive_scale_read_input dst_negative_code_read_input dst_negative_scale_read_input dst_positive_read_input dst_negative_read_input. (((F) = (((((dst_positive_code_read_input) + (dst_positive_scale_read_input)) * S ((dst_positive_code_read_input) + (dst_positive_scale_read_input)) + ((dst_positive_scale_read_input) + (dst_positive_scale_read_input))) + (((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input)))) * S ((((dst_positive_code_read_input) + (dst_positive_scale_read_input)) * S ((dst_positive_code_read_input) + (dst_positive_scale_read_input)) + ((dst_positive_scale_read_input) + (dst_positive_scale_read_input))) + (((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input)))) + ((((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input))) + (((dst_negative_code_read_input) + (dst_negative_scale_read_input)) * S ((dst_negative_code_read_input) + (dst_negative_scale_read_input)) + ((dst_negative_scale_read_input) + (dst_negative_scale_read_input)))))) /\ (((((exists ff_h_pvs_read_inputpositive. ff_h_pvs_read_inputpositive + S (dst_positive_read_input) = S ((S (d)) * dst_positive_scale_read_input)) /\ exists ff_q_pvs_read_inputpositive. dst_positive_code_read_input = ff_q_pvs_read_inputpositive * S ((S (d)) * dst_positive_scale_read_input) + (dst_positive_read_input))) /\ (((((exists ff_h_pvs_read_inputnegative. ff_h_pvs_read_inputnegative + S (dst_negative_read_input) = S ((S (d)) * dst_negative_scale_read_input)) /\ exists ff_q_pvs_read_inputnegative. dst_negative_code_read_input = ff_q_pvs_read_inputnegative * S ((S (d)) * dst_negative_scale_read_input) + (dst_negative_read_input))) /\ (exists ge_balance_positive_read_inputvalue ge_balance_negative_read_inputvalue. (((((z) = 2 * (ge_balance_positive_read_inputvalue) /\ (ge_balance_negative_read_inputvalue) = 0) \/ exists ge_signed_half_read_inputvaluedecode. (((z) = 2 * ge_signed_half_read_inputvaluedecode + 1 /\ (ge_balance_positive_read_inputvalue) = 0) /\ (ge_balance_negative_read_inputvalue) = S ge_signed_half_read_inputvaluedecode))) /\ ((dst_positive_read_input) + ge_balance_negative_read_inputvalue = (dst_negative_read_input) + ge_balance_positive_read_inputvalue)))))))))

• divisor_signed_balance_negate · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall a b p n. (exists ge_balance_positive_negate_balance ge_balance_negative_negate_balance. (((((a) = 2 * (ge_balance_positive_negate_balance) /\ (ge_balance_negative_negate_balance) = 0) \/ exists ge_signed_half_negate_balancedecode. (((a) = 2 * ge_signed_half_negate_balancedecode + 1 /\ (ge_balance_positive_negate_balance) = 0) /\ (ge_balance_negative_negate_balance) = S ge_signed_half_negate_balancedecode))) /\ ((p) + ge_balance_negative_negate_balance = (n) + ge_balance_positive_negate_balance))) -> (exists mps_positive_negate_graph mps_negative_negate_graph. (((((a) = 2 * (mps_positive_negate_graph) /\ (mps_negative_negate_graph) = 0) \/ exists ge_signed_half_negate_graphsource. (((a) = 2 * ge_signed_half_negate_graphsource + 1 /\ (mps_positive_negate_graph) = 0) /\ (mps_negative_negate_graph) = S ge_signed_half_negate_graphsource))) /\ ((((b) = 2 * (mps_negative_negate_graph) /\ (mps_positive_negate_graph) = 0) \/ exists ge_signed_half_negate_graphtarget. (((b) = 2 * ge_signed_half_negate_graphtarget + 1 /\ (mps_negative_negate_graph) = 0) /\ (mps_positive_negate_graph) = S ge_signed_half_negate_graphtarget))))) -> (exists ge_balance_positive_negate_result ge_balance_negative_negate_result. (((((b) = 2 * (ge_balance_positive_negate_result) /\ (ge_balance_negative_negate_result) = 0) \/ exists ge_signed_half_negate_resultdecode. (((b) = 2 * ge_signed_half_negate_resultdecode + 1 /\ (ge_balance_positive_negate_result) = 0) /\ (ge_balance_negative_negate_result) = S ge_signed_half_negate_resultdecode))) /\ ((n) + ge_balance_negative_negate_result = (p) + ge_balance_positive_negate_result)))

• divisor_signed_negate_fixed_zero · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall a. (exists mps_positive_fixed_negation mps_negative_fixed_negation. (((((a) = 2 * (mps_positive_fixed_negation) /\ (mps_negative_fixed_negation) = 0) \/ exists ge_signed_half_fixed_negationsource. (((a) = 2 * ge_signed_half_fixed_negationsource + 1 /\ (mps_positive_fixed_negation) = 0) /\ (mps_negative_fixed_negation) = S ge_signed_half_fixed_negationsource))) /\ ((((a) = 2 * (mps_negative_fixed_negation) /\ (mps_positive_fixed_negation) = 0) \/ exists ge_signed_half_fixed_negationtarget. (((a) = 2 * ge_signed_half_fixed_negationtarget + 1 /\ (mps_negative_fixed_negation) = 0) /\ (mps_positive_fixed_negation) = S ge_signed_half_fixed_negationtarget))))) -> a = 0

• divisor_signed_sum_extensional · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G l a b. (forall dst_index_sum_ext_entries dst_first_sum_ext_entries dst_second_sum_ext_entries. (exists pvs_gap_sum_ext_entriesbound. pvs_gap_sum_ext_entriesbound + S (dst_index_sum_ext_entries) = (l)) -> (exists dst_positive_code_sum_ext_entriesfirst dst_positive_scale_sum_ext_entriesfirst dst_negative_code_sum_ext_entriesfirst dst_negative_scale_sum_ext_entriesfirst dst_positive_sum_ext_entriesfirst dst_negative_sum_ext_entriesfirst. (((F) = (((((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) * S ((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) + ((dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))) * S ((((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) * S ((dst_positive_code_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst)) + ((dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))) + ((((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst))) + (((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) * S ((dst_negative_code_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)) + ((dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_scale_sum_ext_entriesfirst)))))) /\ (((((exists ff_h_pvs_sum_ext_entriesfirstpositive. ff_h_pvs_sum_ext_entriesfirstpositive + S (dst_positive_sum_ext_entriesfirst) = S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriesfirst)) /\ exists ff_q_pvs_sum_ext_entriesfirstpositive. dst_positive_code_sum_ext_entriesfirst = ff_q_pvs_sum_ext_entriesfirstpositive * S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriesfirst) + (dst_positive_sum_ext_entriesfirst))) /\ (((((exists ff_h_pvs_sum_ext_entriesfirstnegative. ff_h_pvs_sum_ext_entriesfirstnegative + S (dst_negative_sum_ext_entriesfirst) = S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriesfirst)) /\ exists ff_q_pvs_sum_ext_entriesfirstnegative. dst_negative_code_sum_ext_entriesfirst = ff_q_pvs_sum_ext_entriesfirstnegative * S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriesfirst) + (dst_negative_sum_ext_entriesfirst))) /\ (exists ge_balance_positive_sum_ext_entriesfirstvalue ge_balance_negative_sum_ext_entriesfirstvalue. (((((dst_first_sum_ext_entries) = 2 * (ge_balance_positive_sum_ext_entriesfirstvalue) /\ (ge_balance_negative_sum_ext_entriesfirstvalue) = 0) \/ exists ge_signed_half_sum_ext_entriesfirstvaluedecode. (((dst_first_sum_ext_entries) = 2 * ge_signed_half_sum_ext_entriesfirstvaluedecode + 1 /\ (ge_balance_positive_sum_ext_entriesfirstvalue) = 0) /\ (ge_balance_negative_sum_ext_entriesfirstvalue) = S ge_signed_half_sum_ext_entriesfirstvaluedecode))) /\ ((dst_positive_sum_ext_entriesfirst) + ge_balance_negative_sum_ext_entriesfirstvalue = (dst_negative_sum_ext_entriesfirst) + ge_balance_positive_sum_ext_entriesfirstvalue))))))))) -> (exists dst_positive_code_sum_ext_entriessecond dst_positive_scale_sum_ext_entriessecond dst_negative_code_sum_ext_entriessecond dst_negative_scale_sum_ext_entriessecond dst_positive_sum_ext_entriessecond dst_negative_sum_ext_entriessecond. (((G) = (((((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) * S ((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) + ((dst_positive_scale_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))) * S ((((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) * S ((dst_positive_code_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond)) + ((dst_positive_scale_sum_ext_entriessecond) + (dst_positive_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))) + ((((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond))) + (((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) * S ((dst_negative_code_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)) + ((dst_negative_scale_sum_ext_entriessecond) + (dst_negative_scale_sum_ext_entriessecond)))))) /\ (((((exists ff_h_pvs_sum_ext_entriessecondpositive. ff_h_pvs_sum_ext_entriessecondpositive + S (dst_positive_sum_ext_entriessecond) = S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriessecond)) /\ exists ff_q_pvs_sum_ext_entriessecondpositive. dst_positive_code_sum_ext_entriessecond = ff_q_pvs_sum_ext_entriessecondpositive * S ((S (dst_index_sum_ext_entries)) * dst_positive_scale_sum_ext_entriessecond) + (dst_positive_sum_ext_entriessecond))) /\ (((((exists ff_h_pvs_sum_ext_entriessecondnegative. ff_h_pvs_sum_ext_entriessecondnegative + S (dst_negative_sum_ext_entriessecond) = S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriessecond)) /\ exists ff_q_pvs_sum_ext_entriessecondnegative. dst_negative_code_sum_ext_entriessecond = ff_q_pvs_sum_ext_entriessecondnegative * S ((S (dst_index_sum_ext_entries)) * dst_negative_scale_sum_ext_entriessecond) + (dst_negative_sum_ext_entriessecond))) /\ (exists ge_balance_positive_sum_ext_entriessecondvalue ge_balance_negative_sum_ext_entriessecondvalue. (((((dst_second_sum_ext_entries) = 2 * (ge_balance_positive_sum_ext_entriessecondvalue) /\ (ge_balance_negative_sum_ext_entriessecondvalue) = 0) \/ exists ge_signed_half_sum_ext_entriessecondvaluedecode. (((dst_second_sum_ext_entries) = 2 * ge_signed_half_sum_ext_entriessecondvaluedecode + 1 /\ (ge_balance_positive_sum_ext_entriessecondvalue) = 0) /\ (ge_balance_negative_sum_ext_entriessecondvalue) = S ge_signed_half_sum_ext_entriessecondvaluedecode))) /\ ((dst_positive_sum_ext_entriessecond) + ge_balance_negative_sum_ext_entriessecondvalue = (dst_negative_sum_ext_entriessecond) + ge_balance_positive_sum_ext_entriessecondvalue))))))))) -> dst_first_sum_ext_entries = dst_second_sum_ext_entries) -> (exists dst_positive_code_sum_ext_first dst_positive_scale_sum_ext_first dst_negative_code_sum_ext_first dst_negative_scale_sum_ext_first dst_positive_sum_sum_ext_first dst_negative_sum_sum_ext_first. (((F) = (((((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) * S ((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) + ((dst_positive_scale_sum_ext_first) + (dst_positive_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))) * S ((((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) * S ((dst_positive_code_sum_ext_first) + (dst_positive_scale_sum_ext_first)) + ((dst_positive_scale_sum_ext_first) + (dst_positive_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))) + ((((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first))) + (((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) * S ((dst_negative_code_sum_ext_first) + (dst_negative_scale_sum_ext_first)) + ((dst_negative_scale_sum_ext_first) + (dst_negative_scale_sum_ext_first)))))) /\ (((exists fs_u_dst_sum_ext_firstpositive fs_v_dst_sum_ext_firstpositive. ((((exists fs_h_dst_sum_ext_firstpositive_body_start. fs_h_dst_sum_ext_firstpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_start. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_start * S ((S (0)) * fs_v_dst_sum_ext_firstpositive) + (0))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_terminal. fs_h_dst_sum_ext_firstpositive_body_terminal + S (dst_positive_sum_sum_ext_first) = S ((S (l)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_terminal. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_firstpositive) + (dst_positive_sum_sum_ext_first))) /\ forall fs_i_dst_sum_ext_firstpositive_body_steps. (exists fs_lt_dst_sum_ext_firstpositive_body_steps_bound. fs_lt_dst_sum_ext_firstpositive_body_steps_bound + S fs_i_dst_sum_ext_firstpositive_body_steps = l) -> exists fs_a_dst_sum_ext_firstpositive_body_steps fs_r_dst_sum_ext_firstpositive_body_steps fs_s_dst_sum_ext_firstpositive_body_steps. ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_summand. fs_h_dst_sum_ext_firstpositive_body_steps_summand + S (fs_a_dst_sum_ext_firstpositive_body_steps) = S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * dst_positive_scale_sum_ext_first)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_summand. dst_positive_code_sum_ext_first = fs_q_dst_sum_ext_firstpositive_body_steps_summand * S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * dst_positive_scale_sum_ext_first) + (fs_a_dst_sum_ext_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_partial. fs_h_dst_sum_ext_firstpositive_body_steps_partial + S (fs_r_dst_sum_ext_firstpositive_body_steps) = S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_partial. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_steps_partial * S ((S (fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive) + (fs_r_dst_sum_ext_firstpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstpositive_body_steps_successor. fs_h_dst_sum_ext_firstpositive_body_steps_successor + S (fs_s_dst_sum_ext_firstpositive_body_steps) = S ((S (S fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive)) /\ exists fs_q_dst_sum_ext_firstpositive_body_steps_successor. fs_u_dst_sum_ext_firstpositive = fs_q_dst_sum_ext_firstpositive_body_steps_successor * S ((S (S fs_i_dst_sum_ext_firstpositive_body_steps)) * fs_v_dst_sum_ext_firstpositive) + (fs_s_dst_sum_ext_firstpositive_body_steps))) /\ fs_s_dst_sum_ext_firstpositive_body_steps = fs_r_dst_sum_ext_firstpositive_body_steps + fs_a_dst_sum_ext_firstpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_ext_firstnegative fs_v_dst_sum_ext_firstnegative. ((((exists fs_h_dst_sum_ext_firstnegative_body_start. fs_h_dst_sum_ext_firstnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_start. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_start * S ((S (0)) * fs_v_dst_sum_ext_firstnegative) + (0))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_terminal. fs_h_dst_sum_ext_firstnegative_body_terminal + S (dst_negative_sum_sum_ext_first) = S ((S (l)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_terminal. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_firstnegative) + (dst_negative_sum_sum_ext_first))) /\ forall fs_i_dst_sum_ext_firstnegative_body_steps. (exists fs_lt_dst_sum_ext_firstnegative_body_steps_bound. fs_lt_dst_sum_ext_firstnegative_body_steps_bound + S fs_i_dst_sum_ext_firstnegative_body_steps = l) -> exists fs_a_dst_sum_ext_firstnegative_body_steps fs_r_dst_sum_ext_firstnegative_body_steps fs_s_dst_sum_ext_firstnegative_body_steps. ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_summand. fs_h_dst_sum_ext_firstnegative_body_steps_summand + S (fs_a_dst_sum_ext_firstnegative_body_steps) = S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * dst_negative_scale_sum_ext_first)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_summand. dst_negative_code_sum_ext_first = fs_q_dst_sum_ext_firstnegative_body_steps_summand * S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * dst_negative_scale_sum_ext_first) + (fs_a_dst_sum_ext_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_partial. fs_h_dst_sum_ext_firstnegative_body_steps_partial + S (fs_r_dst_sum_ext_firstnegative_body_steps) = S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_partial. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_steps_partial * S ((S (fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative) + (fs_r_dst_sum_ext_firstnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_firstnegative_body_steps_successor. fs_h_dst_sum_ext_firstnegative_body_steps_successor + S (fs_s_dst_sum_ext_firstnegative_body_steps) = S ((S (S fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative)) /\ exists fs_q_dst_sum_ext_firstnegative_body_steps_successor. fs_u_dst_sum_ext_firstnegative = fs_q_dst_sum_ext_firstnegative_body_steps_successor * S ((S (S fs_i_dst_sum_ext_firstnegative_body_steps)) * fs_v_dst_sum_ext_firstnegative) + (fs_s_dst_sum_ext_firstnegative_body_steps))) /\ fs_s_dst_sum_ext_firstnegative_body_steps = fs_r_dst_sum_ext_firstnegative_body_steps + fs_a_dst_sum_ext_firstnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_ext_firstresult ge_balance_negative_sum_ext_firstresult. (((((a) = 2 * (ge_balance_positive_sum_ext_firstresult) /\ (ge_balance_negative_sum_ext_firstresult) = 0) \/ exists ge_signed_half_sum_ext_firstresultdecode. (((a) = 2 * ge_signed_half_sum_ext_firstresultdecode + 1 /\ (ge_balance_positive_sum_ext_firstresult) = 0) /\ (ge_balance_negative_sum_ext_firstresult) = S ge_signed_half_sum_ext_firstresultdecode))) /\ ((dst_positive_sum_sum_ext_first) + ge_balance_negative_sum_ext_firstresult = (dst_negative_sum_sum_ext_first) + ge_balance_positive_sum_ext_firstresult))))))))) -> (exists dst_positive_code_sum_ext_second dst_positive_scale_sum_ext_second dst_negative_code_sum_ext_second dst_negative_scale_sum_ext_second dst_positive_sum_sum_ext_second dst_negative_sum_sum_ext_second. (((G) = (((((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) * S ((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) + ((dst_positive_scale_sum_ext_second) + (dst_positive_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))) * S ((((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) * S ((dst_positive_code_sum_ext_second) + (dst_positive_scale_sum_ext_second)) + ((dst_positive_scale_sum_ext_second) + (dst_positive_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))) + ((((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second))) + (((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) * S ((dst_negative_code_sum_ext_second) + (dst_negative_scale_sum_ext_second)) + ((dst_negative_scale_sum_ext_second) + (dst_negative_scale_sum_ext_second)))))) /\ (((exists fs_u_dst_sum_ext_secondpositive fs_v_dst_sum_ext_secondpositive. ((((exists fs_h_dst_sum_ext_secondpositive_body_start. fs_h_dst_sum_ext_secondpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_start. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_start * S ((S (0)) * fs_v_dst_sum_ext_secondpositive) + (0))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_terminal. fs_h_dst_sum_ext_secondpositive_body_terminal + S (dst_positive_sum_sum_ext_second) = S ((S (l)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_terminal. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_secondpositive) + (dst_positive_sum_sum_ext_second))) /\ forall fs_i_dst_sum_ext_secondpositive_body_steps. (exists fs_lt_dst_sum_ext_secondpositive_body_steps_bound. fs_lt_dst_sum_ext_secondpositive_body_steps_bound + S fs_i_dst_sum_ext_secondpositive_body_steps = l) -> exists fs_a_dst_sum_ext_secondpositive_body_steps fs_r_dst_sum_ext_secondpositive_body_steps fs_s_dst_sum_ext_secondpositive_body_steps. ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_summand. fs_h_dst_sum_ext_secondpositive_body_steps_summand + S (fs_a_dst_sum_ext_secondpositive_body_steps) = S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * dst_positive_scale_sum_ext_second)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_summand. dst_positive_code_sum_ext_second = fs_q_dst_sum_ext_secondpositive_body_steps_summand * S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * dst_positive_scale_sum_ext_second) + (fs_a_dst_sum_ext_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_partial. fs_h_dst_sum_ext_secondpositive_body_steps_partial + S (fs_r_dst_sum_ext_secondpositive_body_steps) = S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_partial. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_steps_partial * S ((S (fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive) + (fs_r_dst_sum_ext_secondpositive_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondpositive_body_steps_successor. fs_h_dst_sum_ext_secondpositive_body_steps_successor + S (fs_s_dst_sum_ext_secondpositive_body_steps) = S ((S (S fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive)) /\ exists fs_q_dst_sum_ext_secondpositive_body_steps_successor. fs_u_dst_sum_ext_secondpositive = fs_q_dst_sum_ext_secondpositive_body_steps_successor * S ((S (S fs_i_dst_sum_ext_secondpositive_body_steps)) * fs_v_dst_sum_ext_secondpositive) + (fs_s_dst_sum_ext_secondpositive_body_steps))) /\ fs_s_dst_sum_ext_secondpositive_body_steps = fs_r_dst_sum_ext_secondpositive_body_steps + fs_a_dst_sum_ext_secondpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_ext_secondnegative fs_v_dst_sum_ext_secondnegative. ((((exists fs_h_dst_sum_ext_secondnegative_body_start. fs_h_dst_sum_ext_secondnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_start. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_start * S ((S (0)) * fs_v_dst_sum_ext_secondnegative) + (0))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_terminal. fs_h_dst_sum_ext_secondnegative_body_terminal + S (dst_negative_sum_sum_ext_second) = S ((S (l)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_terminal. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_terminal * S ((S (l)) * fs_v_dst_sum_ext_secondnegative) + (dst_negative_sum_sum_ext_second))) /\ forall fs_i_dst_sum_ext_secondnegative_body_steps. (exists fs_lt_dst_sum_ext_secondnegative_body_steps_bound. fs_lt_dst_sum_ext_secondnegative_body_steps_bound + S fs_i_dst_sum_ext_secondnegative_body_steps = l) -> exists fs_a_dst_sum_ext_secondnegative_body_steps fs_r_dst_sum_ext_secondnegative_body_steps fs_s_dst_sum_ext_secondnegative_body_steps. ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_summand. fs_h_dst_sum_ext_secondnegative_body_steps_summand + S (fs_a_dst_sum_ext_secondnegative_body_steps) = S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * dst_negative_scale_sum_ext_second)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_summand. dst_negative_code_sum_ext_second = fs_q_dst_sum_ext_secondnegative_body_steps_summand * S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * dst_negative_scale_sum_ext_second) + (fs_a_dst_sum_ext_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_partial. fs_h_dst_sum_ext_secondnegative_body_steps_partial + S (fs_r_dst_sum_ext_secondnegative_body_steps) = S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_partial. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_steps_partial * S ((S (fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative) + (fs_r_dst_sum_ext_secondnegative_body_steps))) /\ ((((exists fs_h_dst_sum_ext_secondnegative_body_steps_successor. fs_h_dst_sum_ext_secondnegative_body_steps_successor + S (fs_s_dst_sum_ext_secondnegative_body_steps) = S ((S (S fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative)) /\ exists fs_q_dst_sum_ext_secondnegative_body_steps_successor. fs_u_dst_sum_ext_secondnegative = fs_q_dst_sum_ext_secondnegative_body_steps_successor * S ((S (S fs_i_dst_sum_ext_secondnegative_body_steps)) * fs_v_dst_sum_ext_secondnegative) + (fs_s_dst_sum_ext_secondnegative_body_steps))) /\ fs_s_dst_sum_ext_secondnegative_body_steps = fs_r_dst_sum_ext_secondnegative_body_steps + fs_a_dst_sum_ext_secondnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_ext_secondresult ge_balance_negative_sum_ext_secondresult. (((((b) = 2 * (ge_balance_positive_sum_ext_secondresult) /\ (ge_balance_negative_sum_ext_secondresult) = 0) \/ exists ge_signed_half_sum_ext_secondresultdecode. (((b) = 2 * ge_signed_half_sum_ext_secondresultdecode + 1 /\ (ge_balance_positive_sum_ext_secondresult) = 0) /\ (ge_balance_negative_sum_ext_secondresult) = S ge_signed_half_sum_ext_secondresultdecode))) /\ ((dst_positive_sum_sum_ext_second) + ge_balance_negative_sum_ext_secondresult = (dst_negative_sum_sum_ext_second) + ge_balance_positive_sum_ext_secondresult))))))))) -> a = b

• divisor_signed_sum_negation_transport · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G pb pc nb nc l a b. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> ((G) = (((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc)))) * S ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc)))) + ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc)))))) -> (exists dst_positive_code_negation_source_sum dst_positive_scale_negation_source_sum dst_negative_code_negation_source_sum dst_negative_scale_negation_source_sum dst_positive_sum_negation_source_sum dst_negative_sum_negation_source_sum. (((F) = (((((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) * S ((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) + ((dst_positive_scale_negation_source_sum) + (dst_positive_scale_negation_source_sum))) + (((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum)))) * S ((((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) * S ((dst_positive_code_negation_source_sum) + (dst_positive_scale_negation_source_sum)) + ((dst_positive_scale_negation_source_sum) + (dst_positive_scale_negation_source_sum))) + (((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum)))) + ((((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum))) + (((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) * S ((dst_negative_code_negation_source_sum) + (dst_negative_scale_negation_source_sum)) + ((dst_negative_scale_negation_source_sum) + (dst_negative_scale_negation_source_sum)))))) /\ (((exists fs_u_dst_negation_source_sumpositive fs_v_dst_negation_source_sumpositive. ((((exists fs_h_dst_negation_source_sumpositive_body_start. fs_h_dst_negation_source_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_start. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_start * S ((S (0)) * fs_v_dst_negation_source_sumpositive) + (0))) /\ ((((exists fs_h_dst_negation_source_sumpositive_body_terminal. fs_h_dst_negation_source_sumpositive_body_terminal + S (dst_positive_sum_negation_source_sum) = S ((S (l)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_terminal. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_negation_source_sumpositive) + (dst_positive_sum_negation_source_sum))) /\ forall fs_i_dst_negation_source_sumpositive_body_steps. (exists fs_lt_dst_negation_source_sumpositive_body_steps_bound. fs_lt_dst_negation_source_sumpositive_body_steps_bound + S fs_i_dst_negation_source_sumpositive_body_steps = l) -> exists fs_a_dst_negation_source_sumpositive_body_steps fs_r_dst_negation_source_sumpositive_body_steps fs_s_dst_negation_source_sumpositive_body_steps. ((((exists fs_h_dst_negation_source_sumpositive_body_steps_summand. fs_h_dst_negation_source_sumpositive_body_steps_summand + S (fs_a_dst_negation_source_sumpositive_body_steps) = S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * dst_positive_scale_negation_source_sum)) /\ exists fs_q_dst_negation_source_sumpositive_body_steps_summand. dst_positive_code_negation_source_sum = fs_q_dst_negation_source_sumpositive_body_steps_summand * S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * dst_positive_scale_negation_source_sum) + (fs_a_dst_negation_source_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumpositive_body_steps_partial. fs_h_dst_negation_source_sumpositive_body_steps_partial + S (fs_r_dst_negation_source_sumpositive_body_steps) = S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_steps_partial. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_steps_partial * S ((S (fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive) + (fs_r_dst_negation_source_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumpositive_body_steps_successor. fs_h_dst_negation_source_sumpositive_body_steps_successor + S (fs_s_dst_negation_source_sumpositive_body_steps) = S ((S (S fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive)) /\ exists fs_q_dst_negation_source_sumpositive_body_steps_successor. fs_u_dst_negation_source_sumpositive = fs_q_dst_negation_source_sumpositive_body_steps_successor * S ((S (S fs_i_dst_negation_source_sumpositive_body_steps)) * fs_v_dst_negation_source_sumpositive) + (fs_s_dst_negation_source_sumpositive_body_steps))) /\ fs_s_dst_negation_source_sumpositive_body_steps = fs_r_dst_negation_source_sumpositive_body_steps + fs_a_dst_negation_source_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_negation_source_sumnegative fs_v_dst_negation_source_sumnegative. ((((exists fs_h_dst_negation_source_sumnegative_body_start. fs_h_dst_negation_source_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_start. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_start * S ((S (0)) * fs_v_dst_negation_source_sumnegative) + (0))) /\ ((((exists fs_h_dst_negation_source_sumnegative_body_terminal. fs_h_dst_negation_source_sumnegative_body_terminal + S (dst_negative_sum_negation_source_sum) = S ((S (l)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_terminal. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_negation_source_sumnegative) + (dst_negative_sum_negation_source_sum))) /\ forall fs_i_dst_negation_source_sumnegative_body_steps. (exists fs_lt_dst_negation_source_sumnegative_body_steps_bound. fs_lt_dst_negation_source_sumnegative_body_steps_bound + S fs_i_dst_negation_source_sumnegative_body_steps = l) -> exists fs_a_dst_negation_source_sumnegative_body_steps fs_r_dst_negation_source_sumnegative_body_steps fs_s_dst_negation_source_sumnegative_body_steps. ((((exists fs_h_dst_negation_source_sumnegative_body_steps_summand. fs_h_dst_negation_source_sumnegative_body_steps_summand + S (fs_a_dst_negation_source_sumnegative_body_steps) = S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * dst_negative_scale_negation_source_sum)) /\ exists fs_q_dst_negation_source_sumnegative_body_steps_summand. dst_negative_code_negation_source_sum = fs_q_dst_negation_source_sumnegative_body_steps_summand * S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * dst_negative_scale_negation_source_sum) + (fs_a_dst_negation_source_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumnegative_body_steps_partial. fs_h_dst_negation_source_sumnegative_body_steps_partial + S (fs_r_dst_negation_source_sumnegative_body_steps) = S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_steps_partial. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_steps_partial * S ((S (fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative) + (fs_r_dst_negation_source_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_source_sumnegative_body_steps_successor. fs_h_dst_negation_source_sumnegative_body_steps_successor + S (fs_s_dst_negation_source_sumnegative_body_steps) = S ((S (S fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative)) /\ exists fs_q_dst_negation_source_sumnegative_body_steps_successor. fs_u_dst_negation_source_sumnegative = fs_q_dst_negation_source_sumnegative_body_steps_successor * S ((S (S fs_i_dst_negation_source_sumnegative_body_steps)) * fs_v_dst_negation_source_sumnegative) + (fs_s_dst_negation_source_sumnegative_body_steps))) /\ fs_s_dst_negation_source_sumnegative_body_steps = fs_r_dst_negation_source_sumnegative_body_steps + fs_a_dst_negation_source_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_negation_source_sumresult ge_balance_negative_negation_source_sumresult. (((((a) = 2 * (ge_balance_positive_negation_source_sumresult) /\ (ge_balance_negative_negation_source_sumresult) = 0) \/ exists ge_signed_half_negation_source_sumresultdecode. (((a) = 2 * ge_signed_half_negation_source_sumresultdecode + 1 /\ (ge_balance_positive_negation_source_sumresult) = 0) /\ (ge_balance_negative_negation_source_sumresult) = S ge_signed_half_negation_source_sumresultdecode))) /\ ((dst_positive_sum_negation_source_sum) + ge_balance_negative_negation_source_sumresult = (dst_negative_sum_negation_source_sum) + ge_balance_positive_negation_source_sumresult))))))))) -> (exists mps_positive_negation_relation mps_negative_negation_relation. (((((a) = 2 * (mps_positive_negation_relation) /\ (mps_negative_negation_relation) = 0) \/ exists ge_signed_half_negation_relationsource. (((a) = 2 * ge_signed_half_negation_relationsource + 1 /\ (mps_positive_negation_relation) = 0) /\ (mps_negative_negation_relation) = S ge_signed_half_negation_relationsource))) /\ ((((b) = 2 * (mps_negative_negation_relation) /\ (mps_positive_negation_relation) = 0) \/ exists ge_signed_half_negation_relationtarget. (((b) = 2 * ge_signed_half_negation_relationtarget + 1 /\ (mps_negative_negation_relation) = 0) /\ (mps_positive_negation_relation) = S ge_signed_half_negation_relationtarget))))) -> (exists dst_positive_code_negation_target_sum dst_positive_scale_negation_target_sum dst_negative_code_negation_target_sum dst_negative_scale_negation_target_sum dst_positive_sum_negation_target_sum dst_negative_sum_negation_target_sum. (((G) = (((((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) * S ((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) + ((dst_positive_scale_negation_target_sum) + (dst_positive_scale_negation_target_sum))) + (((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum)))) * S ((((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) * S ((dst_positive_code_negation_target_sum) + (dst_positive_scale_negation_target_sum)) + ((dst_positive_scale_negation_target_sum) + (dst_positive_scale_negation_target_sum))) + (((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum)))) + ((((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum))) + (((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) * S ((dst_negative_code_negation_target_sum) + (dst_negative_scale_negation_target_sum)) + ((dst_negative_scale_negation_target_sum) + (dst_negative_scale_negation_target_sum)))))) /\ (((exists fs_u_dst_negation_target_sumpositive fs_v_dst_negation_target_sumpositive. ((((exists fs_h_dst_negation_target_sumpositive_body_start. fs_h_dst_negation_target_sumpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_start. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_start * S ((S (0)) * fs_v_dst_negation_target_sumpositive) + (0))) /\ ((((exists fs_h_dst_negation_target_sumpositive_body_terminal. fs_h_dst_negation_target_sumpositive_body_terminal + S (dst_positive_sum_negation_target_sum) = S ((S (l)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_terminal. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_terminal * S ((S (l)) * fs_v_dst_negation_target_sumpositive) + (dst_positive_sum_negation_target_sum))) /\ forall fs_i_dst_negation_target_sumpositive_body_steps. (exists fs_lt_dst_negation_target_sumpositive_body_steps_bound. fs_lt_dst_negation_target_sumpositive_body_steps_bound + S fs_i_dst_negation_target_sumpositive_body_steps = l) -> exists fs_a_dst_negation_target_sumpositive_body_steps fs_r_dst_negation_target_sumpositive_body_steps fs_s_dst_negation_target_sumpositive_body_steps. ((((exists fs_h_dst_negation_target_sumpositive_body_steps_summand. fs_h_dst_negation_target_sumpositive_body_steps_summand + S (fs_a_dst_negation_target_sumpositive_body_steps) = S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * dst_positive_scale_negation_target_sum)) /\ exists fs_q_dst_negation_target_sumpositive_body_steps_summand. dst_positive_code_negation_target_sum = fs_q_dst_negation_target_sumpositive_body_steps_summand * S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * dst_positive_scale_negation_target_sum) + (fs_a_dst_negation_target_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumpositive_body_steps_partial. fs_h_dst_negation_target_sumpositive_body_steps_partial + S (fs_r_dst_negation_target_sumpositive_body_steps) = S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_steps_partial. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_steps_partial * S ((S (fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive) + (fs_r_dst_negation_target_sumpositive_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumpositive_body_steps_successor. fs_h_dst_negation_target_sumpositive_body_steps_successor + S (fs_s_dst_negation_target_sumpositive_body_steps) = S ((S (S fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive)) /\ exists fs_q_dst_negation_target_sumpositive_body_steps_successor. fs_u_dst_negation_target_sumpositive = fs_q_dst_negation_target_sumpositive_body_steps_successor * S ((S (S fs_i_dst_negation_target_sumpositive_body_steps)) * fs_v_dst_negation_target_sumpositive) + (fs_s_dst_negation_target_sumpositive_body_steps))) /\ fs_s_dst_negation_target_sumpositive_body_steps = fs_r_dst_negation_target_sumpositive_body_steps + fs_a_dst_negation_target_sumpositive_body_steps)))))) /\ (((exists fs_u_dst_negation_target_sumnegative fs_v_dst_negation_target_sumnegative. ((((exists fs_h_dst_negation_target_sumnegative_body_start. fs_h_dst_negation_target_sumnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_start. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_start * S ((S (0)) * fs_v_dst_negation_target_sumnegative) + (0))) /\ ((((exists fs_h_dst_negation_target_sumnegative_body_terminal. fs_h_dst_negation_target_sumnegative_body_terminal + S (dst_negative_sum_negation_target_sum) = S ((S (l)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_terminal. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_terminal * S ((S (l)) * fs_v_dst_negation_target_sumnegative) + (dst_negative_sum_negation_target_sum))) /\ forall fs_i_dst_negation_target_sumnegative_body_steps. (exists fs_lt_dst_negation_target_sumnegative_body_steps_bound. fs_lt_dst_negation_target_sumnegative_body_steps_bound + S fs_i_dst_negation_target_sumnegative_body_steps = l) -> exists fs_a_dst_negation_target_sumnegative_body_steps fs_r_dst_negation_target_sumnegative_body_steps fs_s_dst_negation_target_sumnegative_body_steps. ((((exists fs_h_dst_negation_target_sumnegative_body_steps_summand. fs_h_dst_negation_target_sumnegative_body_steps_summand + S (fs_a_dst_negation_target_sumnegative_body_steps) = S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * dst_negative_scale_negation_target_sum)) /\ exists fs_q_dst_negation_target_sumnegative_body_steps_summand. dst_negative_code_negation_target_sum = fs_q_dst_negation_target_sumnegative_body_steps_summand * S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * dst_negative_scale_negation_target_sum) + (fs_a_dst_negation_target_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumnegative_body_steps_partial. fs_h_dst_negation_target_sumnegative_body_steps_partial + S (fs_r_dst_negation_target_sumnegative_body_steps) = S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_steps_partial. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_steps_partial * S ((S (fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative) + (fs_r_dst_negation_target_sumnegative_body_steps))) /\ ((((exists fs_h_dst_negation_target_sumnegative_body_steps_successor. fs_h_dst_negation_target_sumnegative_body_steps_successor + S (fs_s_dst_negation_target_sumnegative_body_steps) = S ((S (S fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative)) /\ exists fs_q_dst_negation_target_sumnegative_body_steps_successor. fs_u_dst_negation_target_sumnegative = fs_q_dst_negation_target_sumnegative_body_steps_successor * S ((S (S fs_i_dst_negation_target_sumnegative_body_steps)) * fs_v_dst_negation_target_sumnegative) + (fs_s_dst_negation_target_sumnegative_body_steps))) /\ fs_s_dst_negation_target_sumnegative_body_steps = fs_r_dst_negation_target_sumnegative_body_steps + fs_a_dst_negation_target_sumnegative_body_steps)))))) /\ (exists ge_balance_positive_negation_target_sumresult ge_balance_negative_negation_target_sumresult. (((((b) = 2 * (ge_balance_positive_negation_target_sumresult) /\ (ge_balance_negative_negation_target_sumresult) = 0) \/ exists ge_signed_half_negation_target_sumresultdecode. (((b) = 2 * ge_signed_half_negation_target_sumresultdecode + 1 /\ (ge_balance_positive_negation_target_sumresult) = 0) /\ (ge_balance_negative_negation_target_sumresult) = S ge_signed_half_negation_target_sumresultdecode))) /\ ((dst_positive_sum_negation_target_sum) + ge_balance_negative_negation_target_sumresult = (dst_negative_sum_negation_target_sum) + ge_balance_positive_negation_target_sumresult)))))))))

• divisor_signed_sum_permutation_invariant · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G r s l u v. (forall pfp_i_permutation_bound. (exists pfp_gap_permutation_boundindex. pfp_gap_permutation_boundindex + S (pfp_i_permutation_bound) = (l)) -> exists pfp_a_permutation_bound. (((exists ff_h_pfp_permutation_boundentry. ff_h_pfp_permutation_boundentry + S (pfp_a_permutation_bound) = S ((S (pfp_i_permutation_bound)) * s)) /\ exists ff_q_pfp_permutation_boundentry. r = ff_q_pfp_permutation_boundentry * S ((S (pfp_i_permutation_bound)) * s) + (pfp_a_permutation_bound))) /\ (exists pfp_gap_permutation_boundvalue. pfp_gap_permutation_boundvalue + S (pfp_a_permutation_bound) = (l))) -> (forall pfp_i_permutation_injective pfp_j_permutation_injective pfp_a_permutation_injective. (exists pfp_gap_permutation_injectivefirst. pfp_gap_permutation_injectivefirst + S (pfp_i_permutation_injective) = (l)) -> (exists pfp_gap_permutation_injectivesecond. pfp_gap_permutation_injectivesecond + S (pfp_j_permutation_injective) = (l)) -> (((exists ff_h_pfp_permutation_injectiveleft. ff_h_pfp_permutation_injectiveleft + S (pfp_a_permutation_injective) = S ((S (pfp_i_permutation_injective)) * s)) /\ exists ff_q_pfp_permutation_injectiveleft. r = ff_q_pfp_permutation_injectiveleft * S ((S (pfp_i_permutation_injective)) * s) + (pfp_a_permutation_injective))) -> (((exists ff_h_pfp_permutation_injectiveright. ff_h_pfp_permutation_injectiveright + S (pfp_a_permutation_injective) = S ((S (pfp_j_permutation_injective)) * s)) /\ exists ff_q_pfp_permutation_injectiveright. r = ff_q_pfp_permutation_injectiveright * S ((S (pfp_j_permutation_injective)) * s) + (pfp_a_permutation_injective))) -> pfp_i_permutation_injective = pfp_j_permutation_injective) -> (forall dsr_index_permutation_pullback dsr_image_permutation_pullback dsr_value_permutation_pullback. (exists pvs_gap_permutation_pullbackbound. pvs_gap_permutation_pullbackbound + S (dsr_index_permutation_pullback) = (l)) -> (((exists ff_h_pvs_permutation_pullbackmap. ff_h_pvs_permutation_pullbackmap + S (dsr_image_permutation_pullback) = S ((S (dsr_index_permutation_pullback)) * s)) /\ exists ff_q_pvs_permutation_pullbackmap. r = ff_q_pvs_permutation_pullbackmap * S ((S (dsr_index_permutation_pullback)) * s) + (dsr_image_permutation_pullback))) -> (exists dst_positive_code_permutation_pullbacksource dst_positive_scale_permutation_pullbacksource dst_negative_code_permutation_pullbacksource dst_negative_scale_permutation_pullbacksource dst_positive_permutation_pullbacksource dst_negative_permutation_pullbacksource. (((F) = (((((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) * S ((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) + ((dst_positive_scale_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource))) + (((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)))) * S ((((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) * S ((dst_positive_code_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource)) + ((dst_positive_scale_permutation_pullbacksource) + (dst_positive_scale_permutation_pullbacksource))) + (((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)))) + ((((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource))) + (((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) * S ((dst_negative_code_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)) + ((dst_negative_scale_permutation_pullbacksource) + (dst_negative_scale_permutation_pullbacksource)))))) /\ (((((exists ff_h_pvs_permutation_pullbacksourcepositive. ff_h_pvs_permutation_pullbacksourcepositive + S (dst_positive_permutation_pullbacksource) = S ((S (dsr_image_permutation_pullback)) * dst_positive_scale_permutation_pullbacksource)) /\ exists ff_q_pvs_permutation_pullbacksourcepositive. dst_positive_code_permutation_pullbacksource = ff_q_pvs_permutation_pullbacksourcepositive * S ((S (dsr_image_permutation_pullback)) * dst_positive_scale_permutation_pullbacksource) + (dst_positive_permutation_pullbacksource))) /\ (((((exists ff_h_pvs_permutation_pullbacksourcenegative. ff_h_pvs_permutation_pullbacksourcenegative + S (dst_negative_permutation_pullbacksource) = S ((S (dsr_image_permutation_pullback)) * dst_negative_scale_permutation_pullbacksource)) /\ exists ff_q_pvs_permutation_pullbacksourcenegative. dst_negative_code_permutation_pullbacksource = ff_q_pvs_permutation_pullbacksourcenegative * S ((S (dsr_image_permutation_pullback)) * dst_negative_scale_permutation_pullbacksource) + (dst_negative_permutation_pullbacksource))) /\ (exists ge_balance_positive_permutation_pullbacksourcevalue ge_balance_negative_permutation_pullbacksourcevalue. (((((dsr_value_permutation_pullback) = 2 * (ge_balance_positive_permutation_pullbacksourcevalue) /\ (ge_balance_negative_permutation_pullbacksourcevalue) = 0) \/ exists ge_signed_half_permutation_pullbacksourcevaluedecode. (((dsr_value_permutation_pullback) = 2 * ge_signed_half_permutation_pullbacksourcevaluedecode + 1 /\ (ge_balance_positive_permutation_pullbacksourcevalue) = 0) /\ (ge_balance_negative_permutation_pullbacksourcevalue) = S ge_signed_half_permutation_pullbacksourcevaluedecode))) /\ ((dst_positive_permutation_pullbacksource) + ge_balance_negative_permutation_pullbacksourcevalue = (dst_negative_permutation_pullbacksource) + ge_balance_positive_permutation_pullbacksourcevalue))))))))) -> (exists dst_positive_code_permutation_pullbacktarget dst_positive_scale_permutation_pullbacktarget dst_negative_code_permutation_pullbacktarget dst_negative_scale_permutation_pullbacktarget dst_positive_permutation_pullbacktarget dst_negative_permutation_pullbacktarget. (((G) = (((((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) * S ((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) + ((dst_positive_scale_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget))) + (((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)))) * S ((((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) * S ((dst_positive_code_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget)) + ((dst_positive_scale_permutation_pullbacktarget) + (dst_positive_scale_permutation_pullbacktarget))) + (((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)))) + ((((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget))) + (((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) * S ((dst_negative_code_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)) + ((dst_negative_scale_permutation_pullbacktarget) + (dst_negative_scale_permutation_pullbacktarget)))))) /\ (((((exists ff_h_pvs_permutation_pullbacktargetpositive. ff_h_pvs_permutation_pullbacktargetpositive + S (dst_positive_permutation_pullbacktarget) = S ((S (dsr_index_permutation_pullback)) * dst_positive_scale_permutation_pullbacktarget)) /\ exists ff_q_pvs_permutation_pullbacktargetpositive. dst_positive_code_permutation_pullbacktarget = ff_q_pvs_permutation_pullbacktargetpositive * S ((S (dsr_index_permutation_pullback)) * dst_positive_scale_permutation_pullbacktarget) + (dst_positive_permutation_pullbacktarget))) /\ (((((exists ff_h_pvs_permutation_pullbacktargetnegative. ff_h_pvs_permutation_pullbacktargetnegative + S (dst_negative_permutation_pullbacktarget) = S ((S (dsr_index_permutation_pullback)) * dst_negative_scale_permutation_pullbacktarget)) /\ exists ff_q_pvs_permutation_pullbacktargetnegative. dst_negative_code_permutation_pullbacktarget = ff_q_pvs_permutation_pullbacktargetnegative * S ((S (dsr_index_permutation_pullback)) * dst_negative_scale_permutation_pullbacktarget) + (dst_negative_permutation_pullbacktarget))) /\ (exists ge_balance_positive_permutation_pullbacktargetvalue ge_balance_negative_permutation_pullbacktargetvalue. (((((dsr_value_permutation_pullback) = 2 * (ge_balance_positive_permutation_pullbacktargetvalue) /\ (ge_balance_negative_permutation_pullbacktargetvalue) = 0) \/ exists ge_signed_half_permutation_pullbacktargetvaluedecode. (((dsr_value_permutation_pullback) = 2 * ge_signed_half_permutation_pullbacktargetvaluedecode + 1 /\ (ge_balance_positive_permutation_pullbacktargetvalue) = 0) /\ (ge_balance_negative_permutation_pullbacktargetvalue) = S ge_signed_half_permutation_pullbacktargetvaluedecode))) /\ ((dst_positive_permutation_pullbacktarget) + ge_balance_negative_permutation_pullbacktargetvalue = (dst_negative_permutation_pullbacktarget) + ge_balance_positive_permutation_pullbacktargetvalue)))))))))) -> (exists dst_positive_code_permutation_source dst_positive_scale_permutation_source dst_negative_code_permutation_source dst_negative_scale_permutation_source dst_positive_sum_permutation_source dst_negative_sum_permutation_source. (((F) = (((((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) * S ((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) + ((dst_positive_scale_permutation_source) + (dst_positive_scale_permutation_source))) + (((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source)))) * S ((((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) * S ((dst_positive_code_permutation_source) + (dst_positive_scale_permutation_source)) + ((dst_positive_scale_permutation_source) + (dst_positive_scale_permutation_source))) + (((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source)))) + ((((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source))) + (((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) * S ((dst_negative_code_permutation_source) + (dst_negative_scale_permutation_source)) + ((dst_negative_scale_permutation_source) + (dst_negative_scale_permutation_source)))))) /\ (((exists fs_u_dst_permutation_sourcepositive fs_v_dst_permutation_sourcepositive. ((((exists fs_h_dst_permutation_sourcepositive_body_start. fs_h_dst_permutation_sourcepositive_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_start. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_start * S ((S (0)) * fs_v_dst_permutation_sourcepositive) + (0))) /\ ((((exists fs_h_dst_permutation_sourcepositive_body_terminal. fs_h_dst_permutation_sourcepositive_body_terminal + S (dst_positive_sum_permutation_source) = S ((S (l)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_terminal. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_terminal * S ((S (l)) * fs_v_dst_permutation_sourcepositive) + (dst_positive_sum_permutation_source))) /\ forall fs_i_dst_permutation_sourcepositive_body_steps. (exists fs_lt_dst_permutation_sourcepositive_body_steps_bound. fs_lt_dst_permutation_sourcepositive_body_steps_bound + S fs_i_dst_permutation_sourcepositive_body_steps = l) -> exists fs_a_dst_permutation_sourcepositive_body_steps fs_r_dst_permutation_sourcepositive_body_steps fs_s_dst_permutation_sourcepositive_body_steps. ((((exists fs_h_dst_permutation_sourcepositive_body_steps_summand. fs_h_dst_permutation_sourcepositive_body_steps_summand + S (fs_a_dst_permutation_sourcepositive_body_steps) = S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * dst_positive_scale_permutation_source)) /\ exists fs_q_dst_permutation_sourcepositive_body_steps_summand. dst_positive_code_permutation_source = fs_q_dst_permutation_sourcepositive_body_steps_summand * S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * dst_positive_scale_permutation_source) + (fs_a_dst_permutation_sourcepositive_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcepositive_body_steps_partial. fs_h_dst_permutation_sourcepositive_body_steps_partial + S (fs_r_dst_permutation_sourcepositive_body_steps) = S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_steps_partial. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_steps_partial * S ((S (fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive) + (fs_r_dst_permutation_sourcepositive_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcepositive_body_steps_successor. fs_h_dst_permutation_sourcepositive_body_steps_successor + S (fs_s_dst_permutation_sourcepositive_body_steps) = S ((S (S fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive)) /\ exists fs_q_dst_permutation_sourcepositive_body_steps_successor. fs_u_dst_permutation_sourcepositive = fs_q_dst_permutation_sourcepositive_body_steps_successor * S ((S (S fs_i_dst_permutation_sourcepositive_body_steps)) * fs_v_dst_permutation_sourcepositive) + (fs_s_dst_permutation_sourcepositive_body_steps))) /\ fs_s_dst_permutation_sourcepositive_body_steps = fs_r_dst_permutation_sourcepositive_body_steps + fs_a_dst_permutation_sourcepositive_body_steps)))))) /\ (((exists fs_u_dst_permutation_sourcenegative fs_v_dst_permutation_sourcenegative. ((((exists fs_h_dst_permutation_sourcenegative_body_start. fs_h_dst_permutation_sourcenegative_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_start. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_start * S ((S (0)) * fs_v_dst_permutation_sourcenegative) + (0))) /\ ((((exists fs_h_dst_permutation_sourcenegative_body_terminal. fs_h_dst_permutation_sourcenegative_body_terminal + S (dst_negative_sum_permutation_source) = S ((S (l)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_terminal. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_terminal * S ((S (l)) * fs_v_dst_permutation_sourcenegative) + (dst_negative_sum_permutation_source))) /\ forall fs_i_dst_permutation_sourcenegative_body_steps. (exists fs_lt_dst_permutation_sourcenegative_body_steps_bound. fs_lt_dst_permutation_sourcenegative_body_steps_bound + S fs_i_dst_permutation_sourcenegative_body_steps = l) -> exists fs_a_dst_permutation_sourcenegative_body_steps fs_r_dst_permutation_sourcenegative_body_steps fs_s_dst_permutation_sourcenegative_body_steps. ((((exists fs_h_dst_permutation_sourcenegative_body_steps_summand. fs_h_dst_permutation_sourcenegative_body_steps_summand + S (fs_a_dst_permutation_sourcenegative_body_steps) = S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * dst_negative_scale_permutation_source)) /\ exists fs_q_dst_permutation_sourcenegative_body_steps_summand. dst_negative_code_permutation_source = fs_q_dst_permutation_sourcenegative_body_steps_summand * S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * dst_negative_scale_permutation_source) + (fs_a_dst_permutation_sourcenegative_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcenegative_body_steps_partial. fs_h_dst_permutation_sourcenegative_body_steps_partial + S (fs_r_dst_permutation_sourcenegative_body_steps) = S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_steps_partial. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_steps_partial * S ((S (fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative) + (fs_r_dst_permutation_sourcenegative_body_steps))) /\ ((((exists fs_h_dst_permutation_sourcenegative_body_steps_successor. fs_h_dst_permutation_sourcenegative_body_steps_successor + S (fs_s_dst_permutation_sourcenegative_body_steps) = S ((S (S fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative)) /\ exists fs_q_dst_permutation_sourcenegative_body_steps_successor. fs_u_dst_permutation_sourcenegative = fs_q_dst_permutation_sourcenegative_body_steps_successor * S ((S (S fs_i_dst_permutation_sourcenegative_body_steps)) * fs_v_dst_permutation_sourcenegative) + (fs_s_dst_permutation_sourcenegative_body_steps))) /\ fs_s_dst_permutation_sourcenegative_body_steps = fs_r_dst_permutation_sourcenegative_body_steps + fs_a_dst_permutation_sourcenegative_body_steps)))))) /\ (exists ge_balance_positive_permutation_sourceresult ge_balance_negative_permutation_sourceresult. (((((u) = 2 * (ge_balance_positive_permutation_sourceresult) /\ (ge_balance_negative_permutation_sourceresult) = 0) \/ exists ge_signed_half_permutation_sourceresultdecode. (((u) = 2 * ge_signed_half_permutation_sourceresultdecode + 1 /\ (ge_balance_positive_permutation_sourceresult) = 0) /\ (ge_balance_negative_permutation_sourceresult) = S ge_signed_half_permutation_sourceresultdecode))) /\ ((dst_positive_sum_permutation_source) + ge_balance_negative_permutation_sourceresult = (dst_negative_sum_permutation_source) + ge_balance_positive_permutation_sourceresult))))))))) -> (exists dst_positive_code_permutation_target dst_positive_scale_permutation_target dst_negative_code_permutation_target dst_negative_scale_permutation_target dst_positive_sum_permutation_target dst_negative_sum_permutation_target. (((G) = (((((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) * S ((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) + ((dst_positive_scale_permutation_target) + (dst_positive_scale_permutation_target))) + (((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target)))) * S ((((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) * S ((dst_positive_code_permutation_target) + (dst_positive_scale_permutation_target)) + ((dst_positive_scale_permutation_target) + (dst_positive_scale_permutation_target))) + (((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target)))) + ((((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target))) + (((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) * S ((dst_negative_code_permutation_target) + (dst_negative_scale_permutation_target)) + ((dst_negative_scale_permutation_target) + (dst_negative_scale_permutation_target)))))) /\ (((exists fs_u_dst_permutation_targetpositive fs_v_dst_permutation_targetpositive. ((((exists fs_h_dst_permutation_targetpositive_body_start. fs_h_dst_permutation_targetpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_start. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_start * S ((S (0)) * fs_v_dst_permutation_targetpositive) + (0))) /\ ((((exists fs_h_dst_permutation_targetpositive_body_terminal. fs_h_dst_permutation_targetpositive_body_terminal + S (dst_positive_sum_permutation_target) = S ((S (l)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_terminal. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_terminal * S ((S (l)) * fs_v_dst_permutation_targetpositive) + (dst_positive_sum_permutation_target))) /\ forall fs_i_dst_permutation_targetpositive_body_steps. (exists fs_lt_dst_permutation_targetpositive_body_steps_bound. fs_lt_dst_permutation_targetpositive_body_steps_bound + S fs_i_dst_permutation_targetpositive_body_steps = l) -> exists fs_a_dst_permutation_targetpositive_body_steps fs_r_dst_permutation_targetpositive_body_steps fs_s_dst_permutation_targetpositive_body_steps. ((((exists fs_h_dst_permutation_targetpositive_body_steps_summand. fs_h_dst_permutation_targetpositive_body_steps_summand + S (fs_a_dst_permutation_targetpositive_body_steps) = S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * dst_positive_scale_permutation_target)) /\ exists fs_q_dst_permutation_targetpositive_body_steps_summand. dst_positive_code_permutation_target = fs_q_dst_permutation_targetpositive_body_steps_summand * S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * dst_positive_scale_permutation_target) + (fs_a_dst_permutation_targetpositive_body_steps))) /\ ((((exists fs_h_dst_permutation_targetpositive_body_steps_partial. fs_h_dst_permutation_targetpositive_body_steps_partial + S (fs_r_dst_permutation_targetpositive_body_steps) = S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_steps_partial. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_steps_partial * S ((S (fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive) + (fs_r_dst_permutation_targetpositive_body_steps))) /\ ((((exists fs_h_dst_permutation_targetpositive_body_steps_successor. fs_h_dst_permutation_targetpositive_body_steps_successor + S (fs_s_dst_permutation_targetpositive_body_steps) = S ((S (S fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive)) /\ exists fs_q_dst_permutation_targetpositive_body_steps_successor. fs_u_dst_permutation_targetpositive = fs_q_dst_permutation_targetpositive_body_steps_successor * S ((S (S fs_i_dst_permutation_targetpositive_body_steps)) * fs_v_dst_permutation_targetpositive) + (fs_s_dst_permutation_targetpositive_body_steps))) /\ fs_s_dst_permutation_targetpositive_body_steps = fs_r_dst_permutation_targetpositive_body_steps + fs_a_dst_permutation_targetpositive_body_steps)))))) /\ (((exists fs_u_dst_permutation_targetnegative fs_v_dst_permutation_targetnegative. ((((exists fs_h_dst_permutation_targetnegative_body_start. fs_h_dst_permutation_targetnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_start. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_start * S ((S (0)) * fs_v_dst_permutation_targetnegative) + (0))) /\ ((((exists fs_h_dst_permutation_targetnegative_body_terminal. fs_h_dst_permutation_targetnegative_body_terminal + S (dst_negative_sum_permutation_target) = S ((S (l)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_terminal. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_terminal * S ((S (l)) * fs_v_dst_permutation_targetnegative) + (dst_negative_sum_permutation_target))) /\ forall fs_i_dst_permutation_targetnegative_body_steps. (exists fs_lt_dst_permutation_targetnegative_body_steps_bound. fs_lt_dst_permutation_targetnegative_body_steps_bound + S fs_i_dst_permutation_targetnegative_body_steps = l) -> exists fs_a_dst_permutation_targetnegative_body_steps fs_r_dst_permutation_targetnegative_body_steps fs_s_dst_permutation_targetnegative_body_steps. ((((exists fs_h_dst_permutation_targetnegative_body_steps_summand. fs_h_dst_permutation_targetnegative_body_steps_summand + S (fs_a_dst_permutation_targetnegative_body_steps) = S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * dst_negative_scale_permutation_target)) /\ exists fs_q_dst_permutation_targetnegative_body_steps_summand. dst_negative_code_permutation_target = fs_q_dst_permutation_targetnegative_body_steps_summand * S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * dst_negative_scale_permutation_target) + (fs_a_dst_permutation_targetnegative_body_steps))) /\ ((((exists fs_h_dst_permutation_targetnegative_body_steps_partial. fs_h_dst_permutation_targetnegative_body_steps_partial + S (fs_r_dst_permutation_targetnegative_body_steps) = S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_steps_partial. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_steps_partial * S ((S (fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative) + (fs_r_dst_permutation_targetnegative_body_steps))) /\ ((((exists fs_h_dst_permutation_targetnegative_body_steps_successor. fs_h_dst_permutation_targetnegative_body_steps_successor + S (fs_s_dst_permutation_targetnegative_body_steps) = S ((S (S fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative)) /\ exists fs_q_dst_permutation_targetnegative_body_steps_successor. fs_u_dst_permutation_targetnegative = fs_q_dst_permutation_targetnegative_body_steps_successor * S ((S (S fs_i_dst_permutation_targetnegative_body_steps)) * fs_v_dst_permutation_targetnegative) + (fs_s_dst_permutation_targetnegative_body_steps))) /\ fs_s_dst_permutation_targetnegative_body_steps = fs_r_dst_permutation_targetnegative_body_steps + fs_a_dst_permutation_targetnegative_body_steps)))))) /\ (exists ge_balance_positive_permutation_targetresult ge_balance_negative_permutation_targetresult. (((((v) = 2 * (ge_balance_positive_permutation_targetresult) /\ (ge_balance_negative_permutation_targetresult) = 0) \/ exists ge_signed_half_permutation_targetresultdecode. (((v) = 2 * ge_signed_half_permutation_targetresultdecode + 1 /\ (ge_balance_positive_permutation_targetresult) = 0) /\ (ge_balance_negative_permutation_targetresult) = S ge_signed_half_permutation_targetresultdecode))) /\ ((dst_positive_sum_permutation_target) + ge_balance_negative_permutation_targetresult = (dst_negative_sum_permutation_target) + ge_balance_positive_permutation_targetresult))))))))) -> u = v

• divisor_signed_table_at_from_components · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F pb pc nb nc i p n z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (((exists ff_h_pvs_entry_positive. ff_h_pvs_entry_positive + S (p) = S ((S (i)) * pc)) /\ exists ff_q_pvs_entry_positive. pb = ff_q_pvs_entry_positive * S ((S (i)) * pc) + (p))) -> (((exists ff_h_pvs_entry_negative. ff_h_pvs_entry_negative + S (n) = S ((S (i)) * nc)) /\ exists ff_q_pvs_entry_negative. nb = ff_q_pvs_entry_negative * S ((S (i)) * nc) + (n))) -> (exists ge_balance_positive_entry_balance ge_balance_negative_entry_balance. (((((z) = 2 * (ge_balance_positive_entry_balance) /\ (ge_balance_negative_entry_balance) = 0) \/ exists ge_signed_half_entry_balancedecode. (((z) = 2 * ge_signed_half_entry_balancedecode + 1 /\ (ge_balance_positive_entry_balance) = 0) /\ (ge_balance_negative_entry_balance) = S ge_signed_half_entry_balancedecode))) /\ ((p) + ge_balance_negative_entry_balance = (n) + ge_balance_positive_entry_balance))) -> (exists dst_positive_code_entry_result dst_positive_scale_entry_result dst_negative_code_entry_result dst_negative_scale_entry_result dst_positive_entry_result dst_negative_entry_result. (((F) = (((((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) * S ((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) + ((dst_positive_scale_entry_result) + (dst_positive_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))) * S ((((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) * S ((dst_positive_code_entry_result) + (dst_positive_scale_entry_result)) + ((dst_positive_scale_entry_result) + (dst_positive_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))) + ((((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result))) + (((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) * S ((dst_negative_code_entry_result) + (dst_negative_scale_entry_result)) + ((dst_negative_scale_entry_result) + (dst_negative_scale_entry_result)))))) /\ (((((exists ff_h_pvs_entry_resultpositive. ff_h_pvs_entry_resultpositive + S (dst_positive_entry_result) = S ((S (i)) * dst_positive_scale_entry_result)) /\ exists ff_q_pvs_entry_resultpositive. dst_positive_code_entry_result = ff_q_pvs_entry_resultpositive * S ((S (i)) * dst_positive_scale_entry_result) + (dst_positive_entry_result))) /\ (((((exists ff_h_pvs_entry_resultnegative. ff_h_pvs_entry_resultnegative + S (dst_negative_entry_result) = S ((S (i)) * dst_negative_scale_entry_result)) /\ exists ff_q_pvs_entry_resultnegative. dst_negative_code_entry_result = ff_q_pvs_entry_resultnegative * S ((S (i)) * dst_negative_scale_entry_result) + (dst_negative_entry_result))) /\ (exists ge_balance_positive_entry_resultvalue ge_balance_negative_entry_resultvalue. (((((z) = 2 * (ge_balance_positive_entry_resultvalue) /\ (ge_balance_negative_entry_resultvalue) = 0) \/ exists ge_signed_half_entry_resultvaluedecode. (((z) = 2 * ge_signed_half_entry_resultvaluedecode + 1 /\ (ge_balance_positive_entry_resultvalue) = 0) /\ (ge_balance_negative_entry_resultvalue) = S ge_signed_half_entry_resultvaluedecode))) /\ ((dst_positive_entry_result) + ge_balance_negative_entry_resultvalue = (dst_negative_entry_result) + ge_balance_positive_entry_resultvalue)))))))))

• 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_at_to_components · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F pb pc nb nc i z. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> (exists dst_positive_code_unpack_entry dst_positive_scale_unpack_entry dst_negative_code_unpack_entry dst_negative_scale_unpack_entry dst_positive_unpack_entry dst_negative_unpack_entry. (((F) = (((((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) * S ((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) + ((dst_positive_scale_unpack_entry) + (dst_positive_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))) * S ((((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) * S ((dst_positive_code_unpack_entry) + (dst_positive_scale_unpack_entry)) + ((dst_positive_scale_unpack_entry) + (dst_positive_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))) + ((((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry))) + (((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) * S ((dst_negative_code_unpack_entry) + (dst_negative_scale_unpack_entry)) + ((dst_negative_scale_unpack_entry) + (dst_negative_scale_unpack_entry)))))) /\ (((((exists ff_h_pvs_unpack_entrypositive. ff_h_pvs_unpack_entrypositive + S (dst_positive_unpack_entry) = S ((S (i)) * dst_positive_scale_unpack_entry)) /\ exists ff_q_pvs_unpack_entrypositive. dst_positive_code_unpack_entry = ff_q_pvs_unpack_entrypositive * S ((S (i)) * dst_positive_scale_unpack_entry) + (dst_positive_unpack_entry))) /\ (((((exists ff_h_pvs_unpack_entrynegative. ff_h_pvs_unpack_entrynegative + S (dst_negative_unpack_entry) = S ((S (i)) * dst_negative_scale_unpack_entry)) /\ exists ff_q_pvs_unpack_entrynegative. dst_negative_code_unpack_entry = ff_q_pvs_unpack_entrynegative * S ((S (i)) * dst_negative_scale_unpack_entry) + (dst_negative_unpack_entry))) /\ (exists ge_balance_positive_unpack_entryvalue ge_balance_negative_unpack_entryvalue. (((((z) = 2 * (ge_balance_positive_unpack_entryvalue) /\ (ge_balance_negative_unpack_entryvalue) = 0) \/ exists ge_signed_half_unpack_entryvaluedecode. (((z) = 2 * ge_signed_half_unpack_entryvaluedecode + 1 /\ (ge_balance_positive_unpack_entryvalue) = 0) /\ (ge_balance_negative_unpack_entryvalue) = S ge_signed_half_unpack_entryvaluedecode))) /\ ((dst_positive_unpack_entry) + ge_balance_negative_unpack_entryvalue = (dst_negative_unpack_entry) + ge_balance_positive_unpack_entryvalue))))))))) -> exists p n. (((((exists ff_h_pvs_unpack_resultpositive. ff_h_pvs_unpack_resultpositive + S (p) = S ((S (i)) * pc)) /\ exists ff_q_pvs_unpack_resultpositive. pb = ff_q_pvs_unpack_resultpositive * S ((S (i)) * pc) + (p))) /\ (((((exists ff_h_pvs_unpack_resultnegative. ff_h_pvs_unpack_resultnegative + S (n) = S ((S (i)) * nc)) /\ exists ff_q_pvs_unpack_resultnegative. nb = ff_q_pvs_unpack_resultnegative * S ((S (i)) * nc) + (n))) /\ (exists ge_balance_positive_unpack_resultvalue ge_balance_negative_unpack_resultvalue. (((((z) = 2 * (ge_balance_positive_unpack_resultvalue) /\ (ge_balance_negative_unpack_resultvalue) = 0) \/ exists ge_signed_half_unpack_resultvaluedecode. (((z) = 2 * ge_signed_half_unpack_resultvaluedecode + 1 /\ (ge_balance_positive_unpack_resultvalue) = 0) /\ (ge_balance_negative_unpack_resultvalue) = S ge_signed_half_unpack_resultvaluedecode))) /\ ((p) + ge_balance_negative_unpack_resultvalue = (n) + ge_balance_positive_unpack_resultvalue)))))))

• 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)))))))))

• divisor_signed_table_lookup_from_components · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F pb pc nb nc i. ((F) = (((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) * S ((((pb) + (pc)) * S ((pb) + (pc)) + ((pc) + (pc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))) + ((((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc))) + (((nb) + (nc)) * S ((nb) + (nc)) + ((nc) + (nc)))))) -> 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)))))))))

• divisor_signed_table_reindex_exists · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall N F r s l. (exists dst_positive_code_constructed_source dst_positive_scale_constructed_source dst_negative_code_constructed_source dst_negative_scale_constructed_source. (((F) = (((((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) * S ((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) + ((dst_positive_scale_constructed_source) + (dst_positive_scale_constructed_source))) + (((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source)))) * S ((((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) * S ((dst_positive_code_constructed_source) + (dst_positive_scale_constructed_source)) + ((dst_positive_scale_constructed_source) + (dst_positive_scale_constructed_source))) + (((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source)))) + ((((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source))) + (((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) * S ((dst_negative_code_constructed_source) + (dst_negative_scale_constructed_source)) + ((dst_negative_scale_constructed_source) + (dst_negative_scale_constructed_source)))))) /\ (forall dst_index_constructed_source. (exists pvs_le_gap_constructed_sourcedomain. pvs_le_gap_constructed_sourcedomain + (dst_index_constructed_source) = (N)) -> exists dst_positive_constructed_source dst_negative_constructed_source dst_value_constructed_source. ((((exists ff_h_pvs_constructed_sourceentrypositive. ff_h_pvs_constructed_sourceentrypositive + S (dst_positive_constructed_source) = S ((S (dst_index_constructed_source)) * dst_positive_scale_constructed_source)) /\ exists ff_q_pvs_constructed_sourceentrypositive. dst_positive_code_constructed_source = ff_q_pvs_constructed_sourceentrypositive * S ((S (dst_index_constructed_source)) * dst_positive_scale_constructed_source) + (dst_positive_constructed_source))) /\ (((((exists ff_h_pvs_constructed_sourceentrynegative. ff_h_pvs_constructed_sourceentrynegative + S (dst_negative_constructed_source) = S ((S (dst_index_constructed_source)) * dst_negative_scale_constructed_source)) /\ exists ff_q_pvs_constructed_sourceentrynegative. dst_negative_code_constructed_source = ff_q_pvs_constructed_sourceentrynegative * S ((S (dst_index_constructed_source)) * dst_negative_scale_constructed_source) + (dst_negative_constructed_source))) /\ (exists ge_balance_positive_constructed_sourceentryvalue ge_balance_negative_constructed_sourceentryvalue. (((((dst_value_constructed_source) = 2 * (ge_balance_positive_constructed_sourceentryvalue) /\ (ge_balance_negative_constructed_sourceentryvalue) = 0) \/ exists ge_signed_half_constructed_sourceentryvaluedecode. (((dst_value_constructed_source) = 2 * ge_signed_half_constructed_sourceentryvaluedecode + 1 /\ (ge_balance_positive_constructed_sourceentryvalue) = 0) /\ (ge_balance_negative_constructed_sourceentryvalue) = S ge_signed_half_constructed_sourceentryvaluedecode))) /\ ((dst_positive_constructed_source) + ge_balance_negative_constructed_sourceentryvalue = (dst_negative_constructed_source) + ge_balance_positive_constructed_sourceentryvalue))))))))) -> exists G. (exists dst_positive_code_constructed_target dst_positive_scale_constructed_target dst_negative_code_constructed_target dst_negative_scale_constructed_target. (((G) = (((((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) * S ((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) + ((dst_positive_scale_constructed_target) + (dst_positive_scale_constructed_target))) + (((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target)))) * S ((((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) * S ((dst_positive_code_constructed_target) + (dst_positive_scale_constructed_target)) + ((dst_positive_scale_constructed_target) + (dst_positive_scale_constructed_target))) + (((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target)))) + ((((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target))) + (((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) * S ((dst_negative_code_constructed_target) + (dst_negative_scale_constructed_target)) + ((dst_negative_scale_constructed_target) + (dst_negative_scale_constructed_target)))))) /\ (forall dst_index_constructed_target. (exists pvs_le_gap_constructed_targetdomain. pvs_le_gap_constructed_targetdomain + (dst_index_constructed_target) = (l)) -> exists dst_positive_constructed_target dst_negative_constructed_target dst_value_constructed_target. ((((exists ff_h_pvs_constructed_targetentrypositive. ff_h_pvs_constructed_targetentrypositive + S (dst_positive_constructed_target) = S ((S (dst_index_constructed_target)) * dst_positive_scale_constructed_target)) /\ exists ff_q_pvs_constructed_targetentrypositive. dst_positive_code_constructed_target = ff_q_pvs_constructed_targetentrypositive * S ((S (dst_index_constructed_target)) * dst_positive_scale_constructed_target) + (dst_positive_constructed_target))) /\ (((((exists ff_h_pvs_constructed_targetentrynegative. ff_h_pvs_constructed_targetentrynegative + S (dst_negative_constructed_target) = S ((S (dst_index_constructed_target)) * dst_negative_scale_constructed_target)) /\ exists ff_q_pvs_constructed_targetentrynegative. dst_negative_code_constructed_target = ff_q_pvs_constructed_targetentrynegative * S ((S (dst_index_constructed_target)) * dst_negative_scale_constructed_target) + (dst_negative_constructed_target))) /\ (exists ge_balance_positive_constructed_targetentryvalue ge_balance_negative_constructed_targetentryvalue. (((((dst_value_constructed_target) = 2 * (ge_balance_positive_constructed_targetentryvalue) /\ (ge_balance_negative_constructed_targetentryvalue) = 0) \/ exists ge_signed_half_constructed_targetentryvaluedecode. (((dst_value_constructed_target) = 2 * ge_signed_half_constructed_targetentryvaluedecode + 1 /\ (ge_balance_positive_constructed_targetentryvalue) = 0) /\ (ge_balance_negative_constructed_targetentryvalue) = S ge_signed_half_constructed_targetentryvaluedecode))) /\ ((dst_positive_constructed_target) + ge_balance_negative_constructed_targetentryvalue = (dst_negative_constructed_target) + ge_balance_positive_constructed_targetentryvalue))))))))) /\ (forall dsr_index_constructed_reindex dsr_image_constructed_reindex dsr_value_constructed_reindex. (exists pvs_gap_constructed_reindexbound. pvs_gap_constructed_reindexbound + S (dsr_index_constructed_reindex) = (l)) -> (((exists ff_h_pvs_constructed_reindexmap. ff_h_pvs_constructed_reindexmap + S (dsr_image_constructed_reindex) = S ((S (dsr_index_constructed_reindex)) * s)) /\ exists ff_q_pvs_constructed_reindexmap. r = ff_q_pvs_constructed_reindexmap * S ((S (dsr_index_constructed_reindex)) * s) + (dsr_image_constructed_reindex))) -> (exists dst_positive_code_constructed_reindexsource dst_positive_scale_constructed_reindexsource dst_negative_code_constructed_reindexsource dst_negative_scale_constructed_reindexsource dst_positive_constructed_reindexsource dst_negative_constructed_reindexsource. (((F) = (((((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) * S ((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) + ((dst_positive_scale_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource))) + (((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)))) * S ((((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) * S ((dst_positive_code_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource)) + ((dst_positive_scale_constructed_reindexsource) + (dst_positive_scale_constructed_reindexsource))) + (((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)))) + ((((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource))) + (((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) * S ((dst_negative_code_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)) + ((dst_negative_scale_constructed_reindexsource) + (dst_negative_scale_constructed_reindexsource)))))) /\ (((((exists ff_h_pvs_constructed_reindexsourcepositive. ff_h_pvs_constructed_reindexsourcepositive + S (dst_positive_constructed_reindexsource) = S ((S (dsr_image_constructed_reindex)) * dst_positive_scale_constructed_reindexsource)) /\ exists ff_q_pvs_constructed_reindexsourcepositive. dst_positive_code_constructed_reindexsource = ff_q_pvs_constructed_reindexsourcepositive * S ((S (dsr_image_constructed_reindex)) * dst_positive_scale_constructed_reindexsource) + (dst_positive_constructed_reindexsource))) /\ (((((exists ff_h_pvs_constructed_reindexsourcenegative. ff_h_pvs_constructed_reindexsourcenegative + S (dst_negative_constructed_reindexsource) = S ((S (dsr_image_constructed_reindex)) * dst_negative_scale_constructed_reindexsource)) /\ exists ff_q_pvs_constructed_reindexsourcenegative. dst_negative_code_constructed_reindexsource = ff_q_pvs_constructed_reindexsourcenegative * S ((S (dsr_image_constructed_reindex)) * dst_negative_scale_constructed_reindexsource) + (dst_negative_constructed_reindexsource))) /\ (exists ge_balance_positive_constructed_reindexsourcevalue ge_balance_negative_constructed_reindexsourcevalue. (((((dsr_value_constructed_reindex) = 2 * (ge_balance_positive_constructed_reindexsourcevalue) /\ (ge_balance_negative_constructed_reindexsourcevalue) = 0) \/ exists ge_signed_half_constructed_reindexsourcevaluedecode. (((dsr_value_constructed_reindex) = 2 * ge_signed_half_constructed_reindexsourcevaluedecode + 1 /\ (ge_balance_positive_constructed_reindexsourcevalue) = 0) /\ (ge_balance_negative_constructed_reindexsourcevalue) = S ge_signed_half_constructed_reindexsourcevaluedecode))) /\ ((dst_positive_constructed_reindexsource) + ge_balance_negative_constructed_reindexsourcevalue = (dst_negative_constructed_reindexsource) + ge_balance_positive_constructed_reindexsourcevalue))))))))) -> (exists dst_positive_code_constructed_reindextarget dst_positive_scale_constructed_reindextarget dst_negative_code_constructed_reindextarget dst_negative_scale_constructed_reindextarget dst_positive_constructed_reindextarget dst_negative_constructed_reindextarget. (((G) = (((((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) * S ((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) + ((dst_positive_scale_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget))) + (((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)))) * S ((((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) * S ((dst_positive_code_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget)) + ((dst_positive_scale_constructed_reindextarget) + (dst_positive_scale_constructed_reindextarget))) + (((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)))) + ((((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget))) + (((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) * S ((dst_negative_code_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)) + ((dst_negative_scale_constructed_reindextarget) + (dst_negative_scale_constructed_reindextarget)))))) /\ (((((exists ff_h_pvs_constructed_reindextargetpositive. ff_h_pvs_constructed_reindextargetpositive + S (dst_positive_constructed_reindextarget) = S ((S (dsr_index_constructed_reindex)) * dst_positive_scale_constructed_reindextarget)) /\ exists ff_q_pvs_constructed_reindextargetpositive. dst_positive_code_constructed_reindextarget = ff_q_pvs_constructed_reindextargetpositive * S ((S (dsr_index_constructed_reindex)) * dst_positive_scale_constructed_reindextarget) + (dst_positive_constructed_reindextarget))) /\ (((((exists ff_h_pvs_constructed_reindextargetnegative. ff_h_pvs_constructed_reindextargetnegative + S (dst_negative_constructed_reindextarget) = S ((S (dsr_index_constructed_reindex)) * dst_negative_scale_constructed_reindextarget)) /\ exists ff_q_pvs_constructed_reindextargetnegative. dst_negative_code_constructed_reindextarget = ff_q_pvs_constructed_reindextargetnegative * S ((S (dsr_index_constructed_reindex)) * dst_negative_scale_constructed_reindextarget) + (dst_negative_constructed_reindextarget))) /\ (exists ge_balance_positive_constructed_reindextargetvalue ge_balance_negative_constructed_reindextargetvalue. (((((dsr_value_constructed_reindex) = 2 * (ge_balance_positive_constructed_reindextargetvalue) /\ (ge_balance_negative_constructed_reindextargetvalue) = 0) \/ exists ge_signed_half_constructed_reindextargetvaluedecode. (((dsr_value_constructed_reindex) = 2 * ge_signed_half_constructed_reindextargetvaluedecode + 1 /\ (ge_balance_positive_constructed_reindextargetvalue) = 0) /\ (ge_balance_negative_constructed_reindextargetvalue) = S ge_signed_half_constructed_reindextargetvaluedecode))) /\ ((dst_positive_constructed_reindextarget) + ge_balance_negative_constructed_reindextargetvalue = (dst_negative_constructed_reindextarget) + ge_balance_positive_constructed_reindextargetvalue))))))))))

• 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)

• factor_permutation_below_zero_impossible · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall i. (exists pfp_gap_empty. pfp_gap_empty + S (i) = (0)) -> false

• finite_bounded_injective_surjective · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n b c. (forall fp_i_pigeon_bounded. (exists fp_gap_pigeon_bounded_index. fp_gap_pigeon_bounded_index + S fp_i_pigeon_bounded = n) -> exists fp_value_pigeon_bounded. ((((exists ff_h_pigeon_bounded_entry. ff_h_pigeon_bounded_entry + S (fp_value_pigeon_bounded) = S ((S (fp_i_pigeon_bounded)) * c)) /\ exists ff_q_pigeon_bounded_entry. b = ff_q_pigeon_bounded_entry * S ((S (fp_i_pigeon_bounded)) * c) + (fp_value_pigeon_bounded))) /\ (exists fp_gap_pigeon_bounded_value. fp_gap_pigeon_bounded_value + S fp_value_pigeon_bounded = n))) -> (forall fp_i_pigeon_injective fp_j_pigeon_injective fp_value_pigeon_injective. (exists fp_gap_pigeon_injective_i. fp_gap_pigeon_injective_i + S fp_i_pigeon_injective = n) -> (exists fp_gap_pigeon_injective_j. fp_gap_pigeon_injective_j + S fp_j_pigeon_injective = n) -> (((exists ff_h_pigeon_injective_left. ff_h_pigeon_injective_left + S (fp_value_pigeon_injective) = S ((S (fp_i_pigeon_injective)) * c)) /\ exists ff_q_pigeon_injective_left. b = ff_q_pigeon_injective_left * S ((S (fp_i_pigeon_injective)) * c) + (fp_value_pigeon_injective))) -> (((exists ff_h_pigeon_injective_right. ff_h_pigeon_injective_right + S (fp_value_pigeon_injective) = S ((S (fp_j_pigeon_injective)) * c)) /\ exists ff_q_pigeon_injective_right. b = ff_q_pigeon_injective_right * S ((S (fp_j_pigeon_injective)) * c) + (fp_value_pigeon_injective))) -> fp_i_pigeon_injective = fp_j_pigeon_injective) -> (forall fp_value_pigeon_surjective. (exists fp_gap_pigeon_surjective_value. fp_gap_pigeon_surjective_value + S fp_value_pigeon_surjective = n) -> exists fp_i_pigeon_surjective. ((exists fp_gap_pigeon_surjective_index. fp_gap_pigeon_surjective_index + S fp_i_pigeon_surjective = n) /\ (((exists ff_h_pigeon_surjective_entry. ff_h_pigeon_surjective_entry + S (fp_value_pigeon_surjective) = S ((S (fp_i_pigeon_surjective)) * c)) /\ exists ff_q_pigeon_surjective_entry. b = ff_q_pigeon_surjective_entry * S ((S (fp_i_pigeon_surjective)) * c) + (fp_value_pigeon_surjective)))))

• finite_lt_succ_eq_or_lt · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n x. (exists h. h + S x = S n) -> x = n \/ exists h. h + S x = n

• gauss_coprime_cancel · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall a b z. (forall d. (exists x. a = d * x) -> (exists y. b = d * y) -> d = 1) -> (exists q. b * z = a * q) -> exists w. z = a * w

• 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_refl · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n. n <= n

• le_trans · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n m k. n <= m -> m <= k -> n <= k

• mobius_fresh_prime_negates · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall p n a b. (~((p) = 1) /\ forall pvs_left_step_prime pvs_right_step_prime. (p) = pvs_left_step_prime * pvs_right_step_prime -> pvs_left_step_prime = 1 \/ pvs_right_step_prime = 1) -> ~(exists pvs_factor_step_fresh. (n) = (p) * pvs_factor_step_fresh) -> (((~((n) = 0)) /\ ((((exists mv_square_prime_step_sourcesquare. ((~((mv_square_prime_step_sourcesquare) = 1) /\ forall pvs_left_step_sourcesquareprime pvs_right_step_sourcesquareprime. (mv_square_prime_step_sourcesquare) = pvs_left_step_sourcesquareprime * pvs_right_step_sourcesquareprime -> pvs_left_step_sourcesquareprime = 1 \/ pvs_right_step_sourcesquareprime = 1) /\ (exists pvs_factor_step_sourcesquaredivisor. (n) = (mv_square_prime_step_sourcesquare * mv_square_prime_step_sourcesquare) * pvs_factor_step_sourcesquaredivisor))) /\ ((a) = 0))) \/ (((((~((n) = 0)) /\ (forall sfd_prime_step_sourcesquarefree. (~((sfd_prime_step_sourcesquarefree) = 1) /\ forall pvs_left_step_sourcesquarefreedomain pvs_right_step_sourcesquarefreedomain. (sfd_prime_step_sourcesquarefree) = pvs_left_step_sourcesquarefreedomain * pvs_right_step_sourcesquarefreedomain -> pvs_left_step_sourcesquarefreedomain = 1 \/ pvs_right_step_sourcesquarefreedomain = 1) -> (exists pvs_le_gap_step_sourcesquarefreebound. pvs_le_gap_step_sourcesquarefreebound + (sfd_prime_step_sourcesquarefree) = (n)) -> ~(exists pvs_factor_step_sourcesquarefreesquare. (n) = (sfd_prime_step_sourcesquarefree * sfd_prime_step_sourcesquarefree) * pvs_factor_step_sourcesquarefreesquare)))) /\ (exists mv_factor_code_step_sourcefactors mv_factor_scale_step_sourcefactors mv_factor_count_step_sourcefactors. (((~(n = 0) /\ ((exists ff_u_fsat_step_sourcefactorsfactorization_product ff_v_fsat_step_sourcefactorsfactorization_product. ((((exists ff_h_fsat_step_sourcefactorsfactorization_product_start. ff_h_fsat_step_sourcefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_step_sourcefactorsfactorization_product)) /\ exists ff_q_fsat_step_sourcefactorsfactorization_product_start. ff_u_fsat_step_sourcefactorsfactorization_product = ff_q_fsat_step_sourcefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_step_sourcefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_step_sourcefactorsfactorization_product_terminal. ff_h_fsat_step_sourcefactorsfactorization_product_terminal + S (n) = S ((S (mv_factor_count_step_sourcefactors)) * ff_v_fsat_step_sourcefactorsfactorization_product)) /\ exists ff_q_fsat_step_sourcefactorsfactorization_product_terminal. ff_u_fsat_step_sourcefactorsfactorization_product = ff_q_fsat_step_sourcefactorsfactorization_product_terminal * S ((S (mv_factor_count_step_sourcefactors)) * ff_v_fsat_step_sourcefactorsfactorization_product) + (n))) /\ forall ff_i_fsat_step_sourcefactorsfactorization_product. (exists ff_lt_fsat_step_sourcefactorsfactorization_product_bound. ff_lt_fsat_step_sourcefactorsfactorization_product_bound + S ff_i_fsat_step_sourcefactorsfactorization_product = mv_factor_count_step_sourcefactors) -> exists ff_p_fsat_step_sourcefactorsfactorization_product ff_r_fsat_step_sourcefactorsfactorization_product ff_s_fsat_step_sourcefactorsfactorization_product. ((((exists ff_h_fsat_step_sourcefactorsfactorization_product_factor. ff_h_fsat_step_sourcefactorsfactorization_product_factor + S (ff_p_fsat_step_sourcefactorsfactorization_product) = S ((S (ff_i_fsat_step_sourcefactorsfactorization_product)) * mv_factor_scale_step_sourcefactors)) /\ exists ff_q_fsat_step_sourcefactorsfactorization_product_factor. mv_factor_code_step_sourcefactors = ff_q_fsat_step_sourcefactorsfactorization_product_factor * S ((S (ff_i_fsat_step_sourcefactorsfactorization_product)) * mv_factor_scale_step_sourcefactors) + (ff_p_fsat_step_sourcefactorsfactorization_product))) /\ ((((exists ff_h_fsat_step_sourcefactorsfactorization_product_partial. ff_h_fsat_step_sourcefactorsfactorization_product_partial + S (ff_r_fsat_step_sourcefactorsfactorization_product) = S ((S (ff_i_fsat_step_sourcefactorsfactorization_product)) * ff_v_fsat_step_sourcefactorsfactorization_product)) /\ exists ff_q_fsat_step_sourcefactorsfactorization_product_partial. ff_u_fsat_step_sourcefactorsfactorization_product = ff_q_fsat_step_sourcefactorsfactorization_product_partial * S ((S (ff_i_fsat_step_sourcefactorsfactorization_product)) * ff_v_fsat_step_sourcefactorsfactorization_product) + (ff_r_fsat_step_sourcefactorsfactorization_product))) /\ ((((exists ff_h_fsat_step_sourcefactorsfactorization_product_successor. ff_h_fsat_step_sourcefactorsfactorization_product_successor + S (ff_s_fsat_step_sourcefactorsfactorization_product) = S ((S (S ff_i_fsat_step_sourcefactorsfactorization_product)) * ff_v_fsat_step_sourcefactorsfactorization_product)) /\ exists ff_q_fsat_step_sourcefactorsfactorization_product_successor. ff_u_fsat_step_sourcefactorsfactorization_product = ff_q_fsat_step_sourcefactorsfactorization_product_successor * S ((S (S ff_i_fsat_step_sourcefactorsfactorization_product)) * ff_v_fsat_step_sourcefactorsfactorization_product) + (ff_s_fsat_step_sourcefactorsfactorization_product))) /\ ff_s_fsat_step_sourcefactorsfactorization_product = ff_r_fsat_step_sourcefactorsfactorization_product * ff_p_fsat_step_sourcefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_step_sourcefactorsfactorization_primes. (exists ftsf_gap_fsat_step_sourcefactorsfactorization_primes_bound. ftsf_gap_fsat_step_sourcefactorsfactorization_primes_bound + S ftsf_index_fsat_step_sourcefactorsfactorization_primes = (mv_factor_count_step_sourcefactors)) -> exists ftsf_factor_fsat_step_sourcefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_step_sourcefactorsfactorization_primes_entry. ff_h_ftsf_fsat_step_sourcefactorsfactorization_primes_entry + S (ftsf_factor_fsat_step_sourcefactorsfactorization_primes) = S ((S (ftsf_index_fsat_step_sourcefactorsfactorization_primes)) * mv_factor_scale_step_sourcefactors)) /\ exists ff_q_ftsf_fsat_step_sourcefactorsfactorization_primes_entry. mv_factor_code_step_sourcefactors = ff_q_ftsf_fsat_step_sourcefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_step_sourcefactorsfactorization_primes)) * mv_factor_scale_step_sourcefactors) + (ftsf_factor_fsat_step_sourcefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_step_sourcefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_step_sourcefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_step_sourcefactorsfactorization_primes_prime. ftsf_factor_fsat_step_sourcefactorsfactorization_primes = frm_prime_left_ftsf_fsat_step_sourcefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_step_sourcefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_step_sourcefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_step_sourcefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_step_sourcefactorsparityeven. (mv_factor_count_step_sourcefactors) = 2 * mv_even_half_step_sourcefactorsparityeven) /\ ((a) = 2))) \/ (((exists mv_odd_half_step_sourcefactorsparityodd. (mv_factor_count_step_sourcefactors) = 2 * mv_odd_half_step_sourcefactorsparityodd + 1) /\ ((a) = 1))))))))))) -> (((~((p * n) = 0)) /\ ((((exists mv_square_prime_step_targetsquare. ((~((mv_square_prime_step_targetsquare) = 1) /\ forall pvs_left_step_targetsquareprime pvs_right_step_targetsquareprime. (mv_square_prime_step_targetsquare) = pvs_left_step_targetsquareprime * pvs_right_step_targetsquareprime -> pvs_left_step_targetsquareprime = 1 \/ pvs_right_step_targetsquareprime = 1) /\ (exists pvs_factor_step_targetsquaredivisor. (p * n) = (mv_square_prime_step_targetsquare * mv_square_prime_step_targetsquare) * pvs_factor_step_targetsquaredivisor))) /\ ((b) = 0))) \/ (((((~((p * n) = 0)) /\ (forall sfd_prime_step_targetsquarefree. (~((sfd_prime_step_targetsquarefree) = 1) /\ forall pvs_left_step_targetsquarefreedomain pvs_right_step_targetsquarefreedomain. (sfd_prime_step_targetsquarefree) = pvs_left_step_targetsquarefreedomain * pvs_right_step_targetsquarefreedomain -> pvs_left_step_targetsquarefreedomain = 1 \/ pvs_right_step_targetsquarefreedomain = 1) -> (exists pvs_le_gap_step_targetsquarefreebound. pvs_le_gap_step_targetsquarefreebound + (sfd_prime_step_targetsquarefree) = (p * n)) -> ~(exists pvs_factor_step_targetsquarefreesquare. (p * n) = (sfd_prime_step_targetsquarefree * sfd_prime_step_targetsquarefree) * pvs_factor_step_targetsquarefreesquare)))) /\ (exists mv_factor_code_step_targetfactors mv_factor_scale_step_targetfactors mv_factor_count_step_targetfactors. (((~(p * n = 0) /\ ((exists ff_u_fsat_step_targetfactorsfactorization_product ff_v_fsat_step_targetfactorsfactorization_product. ((((exists ff_h_fsat_step_targetfactorsfactorization_product_start. ff_h_fsat_step_targetfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_step_targetfactorsfactorization_product)) /\ exists ff_q_fsat_step_targetfactorsfactorization_product_start. ff_u_fsat_step_targetfactorsfactorization_product = ff_q_fsat_step_targetfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_step_targetfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_step_targetfactorsfactorization_product_terminal. ff_h_fsat_step_targetfactorsfactorization_product_terminal + S (p * n) = S ((S (mv_factor_count_step_targetfactors)) * ff_v_fsat_step_targetfactorsfactorization_product)) /\ exists ff_q_fsat_step_targetfactorsfactorization_product_terminal. ff_u_fsat_step_targetfactorsfactorization_product = ff_q_fsat_step_targetfactorsfactorization_product_terminal * S ((S (mv_factor_count_step_targetfactors)) * ff_v_fsat_step_targetfactorsfactorization_product) + (p * n))) /\ forall ff_i_fsat_step_targetfactorsfactorization_product. (exists ff_lt_fsat_step_targetfactorsfactorization_product_bound. ff_lt_fsat_step_targetfactorsfactorization_product_bound + S ff_i_fsat_step_targetfactorsfactorization_product = mv_factor_count_step_targetfactors) -> exists ff_p_fsat_step_targetfactorsfactorization_product ff_r_fsat_step_targetfactorsfactorization_product ff_s_fsat_step_targetfactorsfactorization_product. ((((exists ff_h_fsat_step_targetfactorsfactorization_product_factor. ff_h_fsat_step_targetfactorsfactorization_product_factor + S (ff_p_fsat_step_targetfactorsfactorization_product) = S ((S (ff_i_fsat_step_targetfactorsfactorization_product)) * mv_factor_scale_step_targetfactors)) /\ exists ff_q_fsat_step_targetfactorsfactorization_product_factor. mv_factor_code_step_targetfactors = ff_q_fsat_step_targetfactorsfactorization_product_factor * S ((S (ff_i_fsat_step_targetfactorsfactorization_product)) * mv_factor_scale_step_targetfactors) + (ff_p_fsat_step_targetfactorsfactorization_product))) /\ ((((exists ff_h_fsat_step_targetfactorsfactorization_product_partial. ff_h_fsat_step_targetfactorsfactorization_product_partial + S (ff_r_fsat_step_targetfactorsfactorization_product) = S ((S (ff_i_fsat_step_targetfactorsfactorization_product)) * ff_v_fsat_step_targetfactorsfactorization_product)) /\ exists ff_q_fsat_step_targetfactorsfactorization_product_partial. ff_u_fsat_step_targetfactorsfactorization_product = ff_q_fsat_step_targetfactorsfactorization_product_partial * S ((S (ff_i_fsat_step_targetfactorsfactorization_product)) * ff_v_fsat_step_targetfactorsfactorization_product) + (ff_r_fsat_step_targetfactorsfactorization_product))) /\ ((((exists ff_h_fsat_step_targetfactorsfactorization_product_successor. ff_h_fsat_step_targetfactorsfactorization_product_successor + S (ff_s_fsat_step_targetfactorsfactorization_product) = S ((S (S ff_i_fsat_step_targetfactorsfactorization_product)) * ff_v_fsat_step_targetfactorsfactorization_product)) /\ exists ff_q_fsat_step_targetfactorsfactorization_product_successor. ff_u_fsat_step_targetfactorsfactorization_product = ff_q_fsat_step_targetfactorsfactorization_product_successor * S ((S (S ff_i_fsat_step_targetfactorsfactorization_product)) * ff_v_fsat_step_targetfactorsfactorization_product) + (ff_s_fsat_step_targetfactorsfactorization_product))) /\ ff_s_fsat_step_targetfactorsfactorization_product = ff_r_fsat_step_targetfactorsfactorization_product * ff_p_fsat_step_targetfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_step_targetfactorsfactorization_primes. (exists ftsf_gap_fsat_step_targetfactorsfactorization_primes_bound. ftsf_gap_fsat_step_targetfactorsfactorization_primes_bound + S ftsf_index_fsat_step_targetfactorsfactorization_primes = (mv_factor_count_step_targetfactors)) -> exists ftsf_factor_fsat_step_targetfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_step_targetfactorsfactorization_primes_entry. ff_h_ftsf_fsat_step_targetfactorsfactorization_primes_entry + S (ftsf_factor_fsat_step_targetfactorsfactorization_primes) = S ((S (ftsf_index_fsat_step_targetfactorsfactorization_primes)) * mv_factor_scale_step_targetfactors)) /\ exists ff_q_ftsf_fsat_step_targetfactorsfactorization_primes_entry. mv_factor_code_step_targetfactors = ff_q_ftsf_fsat_step_targetfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_step_targetfactorsfactorization_primes)) * mv_factor_scale_step_targetfactors) + (ftsf_factor_fsat_step_targetfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_step_targetfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_step_targetfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_step_targetfactorsfactorization_primes_prime. ftsf_factor_fsat_step_targetfactorsfactorization_primes = frm_prime_left_ftsf_fsat_step_targetfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_step_targetfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_step_targetfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_step_targetfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_step_targetfactorsparityeven. (mv_factor_count_step_targetfactors) = 2 * mv_even_half_step_targetfactorsparityeven) /\ ((b) = 2))) \/ (((exists mv_odd_half_step_targetfactorsparityodd. (mv_factor_count_step_targetfactors) = 2 * mv_odd_half_step_targetfactorsparityodd + 1) /\ ((b) = 1))))))))))) -> (exists mps_positive_step_result mps_negative_step_result. (((((a) = 2 * (mps_positive_step_result) /\ (mps_negative_step_result) = 0) \/ exists ge_signed_half_step_resultsource. (((a) = 2 * ge_signed_half_step_resultsource + 1 /\ (mps_positive_step_result) = 0) /\ (mps_negative_step_result) = S ge_signed_half_step_resultsource))) /\ ((((b) = 2 * (mps_negative_step_result) /\ (mps_positive_step_result) = 0) \/ exists ge_signed_half_step_resulttarget. (((b) = 2 * ge_signed_half_step_resulttarget + 1 /\ (mps_negative_step_result) = 0) /\ (mps_positive_step_result) = S ge_signed_half_step_resulttarget)))))

• mobius_prime_square_value_zero · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n p z. (~((p) = 1) /\ forall pvs_left_square_value_prime pvs_right_square_value_prime. (p) = pvs_left_square_value_prime * pvs_right_square_value_prime -> pvs_left_square_value_prime = 1 \/ pvs_right_square_value_prime = 1) -> (exists pvs_factor_square_value_divisor. (n) = (p * p) * pvs_factor_square_value_divisor) -> (((~((n) = 0)) /\ ((((exists mv_square_prime_square_value_inputsquare. ((~((mv_square_prime_square_value_inputsquare) = 1) /\ forall pvs_left_square_value_inputsquareprime pvs_right_square_value_inputsquareprime. (mv_square_prime_square_value_inputsquare) = pvs_left_square_value_inputsquareprime * pvs_right_square_value_inputsquareprime -> pvs_left_square_value_inputsquareprime = 1 \/ pvs_right_square_value_inputsquareprime = 1) /\ (exists pvs_factor_square_value_inputsquaredivisor. (n) = (mv_square_prime_square_value_inputsquare * mv_square_prime_square_value_inputsquare) * pvs_factor_square_value_inputsquaredivisor))) /\ ((z) = 0))) \/ (((((~((n) = 0)) /\ (forall sfd_prime_square_value_inputsquarefree. (~((sfd_prime_square_value_inputsquarefree) = 1) /\ forall pvs_left_square_value_inputsquarefreedomain pvs_right_square_value_inputsquarefreedomain. (sfd_prime_square_value_inputsquarefree) = pvs_left_square_value_inputsquarefreedomain * pvs_right_square_value_inputsquarefreedomain -> pvs_left_square_value_inputsquarefreedomain = 1 \/ pvs_right_square_value_inputsquarefreedomain = 1) -> (exists pvs_le_gap_square_value_inputsquarefreebound. pvs_le_gap_square_value_inputsquarefreebound + (sfd_prime_square_value_inputsquarefree) = (n)) -> ~(exists pvs_factor_square_value_inputsquarefreesquare. (n) = (sfd_prime_square_value_inputsquarefree * sfd_prime_square_value_inputsquarefree) * pvs_factor_square_value_inputsquarefreesquare)))) /\ (exists mv_factor_code_square_value_inputfactors mv_factor_scale_square_value_inputfactors mv_factor_count_square_value_inputfactors. (((~(n = 0) /\ ((exists ff_u_fsat_square_value_inputfactorsfactorization_product ff_v_fsat_square_value_inputfactorsfactorization_product. ((((exists ff_h_fsat_square_value_inputfactorsfactorization_product_start. ff_h_fsat_square_value_inputfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_square_value_inputfactorsfactorization_product)) /\ exists ff_q_fsat_square_value_inputfactorsfactorization_product_start. ff_u_fsat_square_value_inputfactorsfactorization_product = ff_q_fsat_square_value_inputfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_square_value_inputfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_square_value_inputfactorsfactorization_product_terminal. ff_h_fsat_square_value_inputfactorsfactorization_product_terminal + S (n) = S ((S (mv_factor_count_square_value_inputfactors)) * ff_v_fsat_square_value_inputfactorsfactorization_product)) /\ exists ff_q_fsat_square_value_inputfactorsfactorization_product_terminal. ff_u_fsat_square_value_inputfactorsfactorization_product = ff_q_fsat_square_value_inputfactorsfactorization_product_terminal * S ((S (mv_factor_count_square_value_inputfactors)) * ff_v_fsat_square_value_inputfactorsfactorization_product) + (n))) /\ forall ff_i_fsat_square_value_inputfactorsfactorization_product. (exists ff_lt_fsat_square_value_inputfactorsfactorization_product_bound. ff_lt_fsat_square_value_inputfactorsfactorization_product_bound + S ff_i_fsat_square_value_inputfactorsfactorization_product = mv_factor_count_square_value_inputfactors) -> exists ff_p_fsat_square_value_inputfactorsfactorization_product ff_r_fsat_square_value_inputfactorsfactorization_product ff_s_fsat_square_value_inputfactorsfactorization_product. ((((exists ff_h_fsat_square_value_inputfactorsfactorization_product_factor. ff_h_fsat_square_value_inputfactorsfactorization_product_factor + S (ff_p_fsat_square_value_inputfactorsfactorization_product) = S ((S (ff_i_fsat_square_value_inputfactorsfactorization_product)) * mv_factor_scale_square_value_inputfactors)) /\ exists ff_q_fsat_square_value_inputfactorsfactorization_product_factor. mv_factor_code_square_value_inputfactors = ff_q_fsat_square_value_inputfactorsfactorization_product_factor * S ((S (ff_i_fsat_square_value_inputfactorsfactorization_product)) * mv_factor_scale_square_value_inputfactors) + (ff_p_fsat_square_value_inputfactorsfactorization_product))) /\ ((((exists ff_h_fsat_square_value_inputfactorsfactorization_product_partial. ff_h_fsat_square_value_inputfactorsfactorization_product_partial + S (ff_r_fsat_square_value_inputfactorsfactorization_product) = S ((S (ff_i_fsat_square_value_inputfactorsfactorization_product)) * ff_v_fsat_square_value_inputfactorsfactorization_product)) /\ exists ff_q_fsat_square_value_inputfactorsfactorization_product_partial. ff_u_fsat_square_value_inputfactorsfactorization_product = ff_q_fsat_square_value_inputfactorsfactorization_product_partial * S ((S (ff_i_fsat_square_value_inputfactorsfactorization_product)) * ff_v_fsat_square_value_inputfactorsfactorization_product) + (ff_r_fsat_square_value_inputfactorsfactorization_product))) /\ ((((exists ff_h_fsat_square_value_inputfactorsfactorization_product_successor. ff_h_fsat_square_value_inputfactorsfactorization_product_successor + S (ff_s_fsat_square_value_inputfactorsfactorization_product) = S ((S (S ff_i_fsat_square_value_inputfactorsfactorization_product)) * ff_v_fsat_square_value_inputfactorsfactorization_product)) /\ exists ff_q_fsat_square_value_inputfactorsfactorization_product_successor. ff_u_fsat_square_value_inputfactorsfactorization_product = ff_q_fsat_square_value_inputfactorsfactorization_product_successor * S ((S (S ff_i_fsat_square_value_inputfactorsfactorization_product)) * ff_v_fsat_square_value_inputfactorsfactorization_product) + (ff_s_fsat_square_value_inputfactorsfactorization_product))) /\ ff_s_fsat_square_value_inputfactorsfactorization_product = ff_r_fsat_square_value_inputfactorsfactorization_product * ff_p_fsat_square_value_inputfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_square_value_inputfactorsfactorization_primes. (exists ftsf_gap_fsat_square_value_inputfactorsfactorization_primes_bound. ftsf_gap_fsat_square_value_inputfactorsfactorization_primes_bound + S ftsf_index_fsat_square_value_inputfactorsfactorization_primes = (mv_factor_count_square_value_inputfactors)) -> exists ftsf_factor_fsat_square_value_inputfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_square_value_inputfactorsfactorization_primes_entry. ff_h_ftsf_fsat_square_value_inputfactorsfactorization_primes_entry + S (ftsf_factor_fsat_square_value_inputfactorsfactorization_primes) = S ((S (ftsf_index_fsat_square_value_inputfactorsfactorization_primes)) * mv_factor_scale_square_value_inputfactors)) /\ exists ff_q_ftsf_fsat_square_value_inputfactorsfactorization_primes_entry. mv_factor_code_square_value_inputfactors = ff_q_ftsf_fsat_square_value_inputfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_square_value_inputfactorsfactorization_primes)) * mv_factor_scale_square_value_inputfactors) + (ftsf_factor_fsat_square_value_inputfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_square_value_inputfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_square_value_inputfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_square_value_inputfactorsfactorization_primes_prime. ftsf_factor_fsat_square_value_inputfactorsfactorization_primes = frm_prime_left_ftsf_fsat_square_value_inputfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_square_value_inputfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_square_value_inputfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_square_value_inputfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_square_value_inputfactorsparityeven. (mv_factor_count_square_value_inputfactors) = 2 * mv_even_half_square_value_inputfactorsparityeven) /\ ((z) = 2))) \/ (((exists mv_odd_half_square_value_inputfactorsparityodd. (mv_factor_count_square_value_inputfactors) = 2 * mv_odd_half_square_value_inputfactorsparityodd + 1) /\ ((z) = 1))))))))))) -> z = 0

• mobius_table_exists · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall N. 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) = (N)) -> 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))))))))) /\ (((exists dst_positive_code_exists_resultzero dst_positive_scale_exists_resultzero dst_negative_code_exists_resultzero dst_negative_scale_exists_resultzero dst_positive_exists_resultzero dst_negative_exists_resultzero. (((M) = (((((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) * S ((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) + ((dst_positive_scale_exists_resultzero) + (dst_positive_scale_exists_resultzero))) + (((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero)))) * S ((((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) * S ((dst_positive_code_exists_resultzero) + (dst_positive_scale_exists_resultzero)) + ((dst_positive_scale_exists_resultzero) + (dst_positive_scale_exists_resultzero))) + (((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero)))) + ((((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero))) + (((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) * S ((dst_negative_code_exists_resultzero) + (dst_negative_scale_exists_resultzero)) + ((dst_negative_scale_exists_resultzero) + (dst_negative_scale_exists_resultzero)))))) /\ (((((exists ff_h_pvs_exists_resultzeropositive. ff_h_pvs_exists_resultzeropositive + S (dst_positive_exists_resultzero) = S ((S (0)) * dst_positive_scale_exists_resultzero)) /\ exists ff_q_pvs_exists_resultzeropositive. dst_positive_code_exists_resultzero = ff_q_pvs_exists_resultzeropositive * S ((S (0)) * dst_positive_scale_exists_resultzero) + (dst_positive_exists_resultzero))) /\ (((((exists ff_h_pvs_exists_resultzeronegative. ff_h_pvs_exists_resultzeronegative + S (dst_negative_exists_resultzero) = S ((S (0)) * dst_negative_scale_exists_resultzero)) /\ exists ff_q_pvs_exists_resultzeronegative. dst_negative_code_exists_resultzero = ff_q_pvs_exists_resultzeronegative * S ((S (0)) * dst_negative_scale_exists_resultzero) + (dst_negative_exists_resultzero))) /\ (exists ge_balance_positive_exists_resultzerovalue ge_balance_negative_exists_resultzerovalue. (((((0) = 2 * (ge_balance_positive_exists_resultzerovalue) /\ (ge_balance_negative_exists_resultzerovalue) = 0) \/ exists ge_signed_half_exists_resultzerovaluedecode. (((0) = 2 * ge_signed_half_exists_resultzerovaluedecode + 1 /\ (ge_balance_positive_exists_resultzerovalue) = 0) /\ (ge_balance_negative_exists_resultzerovalue) = S ge_signed_half_exists_resultzerovaluedecode))) /\ ((dst_positive_exists_resultzero) + ge_balance_negative_exists_resultzerovalue = (dst_negative_exists_resultzero) + ge_balance_positive_exists_resultzerovalue))))))))) /\ (forall mt_index_exists_result mt_value_exists_result. ~(mt_index_exists_result=0) -> (exists pvs_le_gap_exists_resultdomain. pvs_le_gap_exists_resultdomain + (mt_index_exists_result) = (N)) -> (exists dst_positive_code_exists_resultentry dst_positive_scale_exists_resultentry dst_negative_code_exists_resultentry dst_negative_scale_exists_resultentry dst_positive_exists_resultentry dst_negative_exists_resultentry. (((M) = (((((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) * S ((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) + ((dst_positive_scale_exists_resultentry) + (dst_positive_scale_exists_resultentry))) + (((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry)))) * S ((((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) * S ((dst_positive_code_exists_resultentry) + (dst_positive_scale_exists_resultentry)) + ((dst_positive_scale_exists_resultentry) + (dst_positive_scale_exists_resultentry))) + (((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry)))) + ((((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry))) + (((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) * S ((dst_negative_code_exists_resultentry) + (dst_negative_scale_exists_resultentry)) + ((dst_negative_scale_exists_resultentry) + (dst_negative_scale_exists_resultentry)))))) /\ (((((exists ff_h_pvs_exists_resultentrypositive. ff_h_pvs_exists_resultentrypositive + S (dst_positive_exists_resultentry) = S ((S (mt_index_exists_result)) * dst_positive_scale_exists_resultentry)) /\ exists ff_q_pvs_exists_resultentrypositive. dst_positive_code_exists_resultentry = ff_q_pvs_exists_resultentrypositive * S ((S (mt_index_exists_result)) * dst_positive_scale_exists_resultentry) + (dst_positive_exists_resultentry))) /\ (((((exists ff_h_pvs_exists_resultentrynegative. ff_h_pvs_exists_resultentrynegative + S (dst_negative_exists_resultentry) = S ((S (mt_index_exists_result)) * dst_negative_scale_exists_resultentry)) /\ exists ff_q_pvs_exists_resultentrynegative. dst_negative_code_exists_resultentry = ff_q_pvs_exists_resultentrynegative * S ((S (mt_index_exists_result)) * dst_negative_scale_exists_resultentry) + (dst_negative_exists_resultentry))) /\ (exists ge_balance_positive_exists_resultentryvalue ge_balance_negative_exists_resultentryvalue. (((((mt_value_exists_result) = 2 * (ge_balance_positive_exists_resultentryvalue) /\ (ge_balance_negative_exists_resultentryvalue) = 0) \/ exists ge_signed_half_exists_resultentryvaluedecode. (((mt_value_exists_result) = 2 * ge_signed_half_exists_resultentryvaluedecode + 1 /\ (ge_balance_positive_exists_resultentryvalue) = 0) /\ (ge_balance_negative_exists_resultentryvalue) = S ge_signed_half_exists_resultentryvaluedecode))) /\ ((dst_positive_exists_resultentry) + ge_balance_negative_exists_resultentryvalue = (dst_negative_exists_resultentry) + ge_balance_positive_exists_resultentryvalue))))))))) -> (((~((mt_index_exists_result) = 0)) /\ ((((exists mv_square_prime_exists_resultvaluesquare. ((~((mv_square_prime_exists_resultvaluesquare) = 1) /\ forall pvs_left_exists_resultvaluesquareprime pvs_right_exists_resultvaluesquareprime. (mv_square_prime_exists_resultvaluesquare) = pvs_left_exists_resultvaluesquareprime * pvs_right_exists_resultvaluesquareprime -> pvs_left_exists_resultvaluesquareprime = 1 \/ pvs_right_exists_resultvaluesquareprime = 1) /\ (exists pvs_factor_exists_resultvaluesquaredivisor. (mt_index_exists_result) = (mv_square_prime_exists_resultvaluesquare * mv_square_prime_exists_resultvaluesquare) * pvs_factor_exists_resultvaluesquaredivisor))) /\ ((mt_value_exists_result) = 0))) \/ (((((~((mt_index_exists_result) = 0)) /\ (forall sfd_prime_exists_resultvaluesquarefree. (~((sfd_prime_exists_resultvaluesquarefree) = 1) /\ forall pvs_left_exists_resultvaluesquarefreedomain pvs_right_exists_resultvaluesquarefreedomain. (sfd_prime_exists_resultvaluesquarefree) = pvs_left_exists_resultvaluesquarefreedomain * pvs_right_exists_resultvaluesquarefreedomain -> pvs_left_exists_resultvaluesquarefreedomain = 1 \/ pvs_right_exists_resultvaluesquarefreedomain = 1) -> (exists pvs_le_gap_exists_resultvaluesquarefreebound. pvs_le_gap_exists_resultvaluesquarefreebound + (sfd_prime_exists_resultvaluesquarefree) = (mt_index_exists_result)) -> ~(exists pvs_factor_exists_resultvaluesquarefreesquare. (mt_index_exists_result) = (sfd_prime_exists_resultvaluesquarefree * sfd_prime_exists_resultvaluesquarefree) * pvs_factor_exists_resultvaluesquarefreesquare)))) /\ (exists mv_factor_code_exists_resultvaluefactors mv_factor_scale_exists_resultvaluefactors mv_factor_count_exists_resultvaluefactors. (((~(mt_index_exists_result = 0) /\ ((exists ff_u_fsat_exists_resultvaluefactorsfactorization_product ff_v_fsat_exists_resultvaluefactorsfactorization_product. ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_start. ff_h_fsat_exists_resultvaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_start. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_terminal. ff_h_fsat_exists_resultvaluefactorsfactorization_product_terminal + S (mt_index_exists_result) = S ((S (mv_factor_count_exists_resultvaluefactors)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_terminal. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_exists_resultvaluefactors)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (mt_index_exists_result))) /\ forall ff_i_fsat_exists_resultvaluefactorsfactorization_product. (exists ff_lt_fsat_exists_resultvaluefactorsfactorization_product_bound. ff_lt_fsat_exists_resultvaluefactorsfactorization_product_bound + S ff_i_fsat_exists_resultvaluefactorsfactorization_product = mv_factor_count_exists_resultvaluefactors) -> exists ff_p_fsat_exists_resultvaluefactorsfactorization_product ff_r_fsat_exists_resultvaluefactorsfactorization_product ff_s_fsat_exists_resultvaluefactorsfactorization_product. ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_factor. ff_h_fsat_exists_resultvaluefactorsfactorization_product_factor + S (ff_p_fsat_exists_resultvaluefactorsfactorization_product) = S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * mv_factor_scale_exists_resultvaluefactors)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_factor. mv_factor_code_exists_resultvaluefactors = ff_q_fsat_exists_resultvaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * mv_factor_scale_exists_resultvaluefactors) + (ff_p_fsat_exists_resultvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_partial. ff_h_fsat_exists_resultvaluefactorsfactorization_product_partial + S (ff_r_fsat_exists_resultvaluefactorsfactorization_product) = S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_partial. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (ff_r_fsat_exists_resultvaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_exists_resultvaluefactorsfactorization_product_successor. ff_h_fsat_exists_resultvaluefactorsfactorization_product_successor + S (ff_s_fsat_exists_resultvaluefactorsfactorization_product) = S ((S (S ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product)) /\ exists ff_q_fsat_exists_resultvaluefactorsfactorization_product_successor. ff_u_fsat_exists_resultvaluefactorsfactorization_product = ff_q_fsat_exists_resultvaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_exists_resultvaluefactorsfactorization_product)) * ff_v_fsat_exists_resultvaluefactorsfactorization_product) + (ff_s_fsat_exists_resultvaluefactorsfactorization_product))) /\ ff_s_fsat_exists_resultvaluefactorsfactorization_product = ff_r_fsat_exists_resultvaluefactorsfactorization_product * ff_p_fsat_exists_resultvaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes. (exists ftsf_gap_fsat_exists_resultvaluefactorsfactorization_primes_bound. ftsf_gap_fsat_exists_resultvaluefactorsfactorization_primes_bound + S ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes = (mv_factor_count_exists_resultvaluefactors)) -> exists ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes)) * mv_factor_scale_exists_resultvaluefactors)) /\ exists ff_q_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry. mv_factor_code_exists_resultvaluefactors = ff_q_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_exists_resultvaluefactorsfactorization_primes)) * mv_factor_scale_exists_resultvaluefactors) + (ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime. ftsf_factor_fsat_exists_resultvaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_exists_resultvaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_exists_resultvaluefactorsparityeven. (mv_factor_count_exists_resultvaluefactors) = 2 * mv_even_half_exists_resultvaluefactorsparityeven) /\ ((mt_value_exists_result) = 2))) \/ (((exists mv_odd_half_exists_resultvaluefactorsparityodd. (mv_factor_count_exists_resultvaluefactors) = 2 * mv_odd_half_exists_resultvaluefactorsparityodd + 1) /\ ((mt_value_exists_result) = 1))))))))))))))))

• mobius_table_one_entry · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall N M. (((exists dst_positive_code_unit_tabletable dst_positive_scale_unit_tabletable dst_negative_code_unit_tabletable dst_negative_scale_unit_tabletable. (((M) = (((((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) * S ((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) + ((dst_positive_scale_unit_tabletable) + (dst_positive_scale_unit_tabletable))) + (((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable)))) * S ((((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) * S ((dst_positive_code_unit_tabletable) + (dst_positive_scale_unit_tabletable)) + ((dst_positive_scale_unit_tabletable) + (dst_positive_scale_unit_tabletable))) + (((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable)))) + ((((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable))) + (((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) * S ((dst_negative_code_unit_tabletable) + (dst_negative_scale_unit_tabletable)) + ((dst_negative_scale_unit_tabletable) + (dst_negative_scale_unit_tabletable)))))) /\ (forall dst_index_unit_tabletable. (exists pvs_le_gap_unit_tabletabledomain. pvs_le_gap_unit_tabletabledomain + (dst_index_unit_tabletable) = (N)) -> exists dst_positive_unit_tabletable dst_negative_unit_tabletable dst_value_unit_tabletable. ((((exists ff_h_pvs_unit_tabletableentrypositive. ff_h_pvs_unit_tabletableentrypositive + S (dst_positive_unit_tabletable) = S ((S (dst_index_unit_tabletable)) * dst_positive_scale_unit_tabletable)) /\ exists ff_q_pvs_unit_tabletableentrypositive. dst_positive_code_unit_tabletable = ff_q_pvs_unit_tabletableentrypositive * S ((S (dst_index_unit_tabletable)) * dst_positive_scale_unit_tabletable) + (dst_positive_unit_tabletable))) /\ (((((exists ff_h_pvs_unit_tabletableentrynegative. ff_h_pvs_unit_tabletableentrynegative + S (dst_negative_unit_tabletable) = S ((S (dst_index_unit_tabletable)) * dst_negative_scale_unit_tabletable)) /\ exists ff_q_pvs_unit_tabletableentrynegative. dst_negative_code_unit_tabletable = ff_q_pvs_unit_tabletableentrynegative * S ((S (dst_index_unit_tabletable)) * dst_negative_scale_unit_tabletable) + (dst_negative_unit_tabletable))) /\ (exists ge_balance_positive_unit_tabletableentryvalue ge_balance_negative_unit_tabletableentryvalue. (((((dst_value_unit_tabletable) = 2 * (ge_balance_positive_unit_tabletableentryvalue) /\ (ge_balance_negative_unit_tabletableentryvalue) = 0) \/ exists ge_signed_half_unit_tabletableentryvaluedecode. (((dst_value_unit_tabletable) = 2 * ge_signed_half_unit_tabletableentryvaluedecode + 1 /\ (ge_balance_positive_unit_tabletableentryvalue) = 0) /\ (ge_balance_negative_unit_tabletableentryvalue) = S ge_signed_half_unit_tabletableentryvaluedecode))) /\ ((dst_positive_unit_tabletable) + ge_balance_negative_unit_tabletableentryvalue = (dst_negative_unit_tabletable) + ge_balance_positive_unit_tabletableentryvalue))))))))) /\ (((exists dst_positive_code_unit_tablezero dst_positive_scale_unit_tablezero dst_negative_code_unit_tablezero dst_negative_scale_unit_tablezero dst_positive_unit_tablezero dst_negative_unit_tablezero. (((M) = (((((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) * S ((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) + ((dst_positive_scale_unit_tablezero) + (dst_positive_scale_unit_tablezero))) + (((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero)))) * S ((((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) * S ((dst_positive_code_unit_tablezero) + (dst_positive_scale_unit_tablezero)) + ((dst_positive_scale_unit_tablezero) + (dst_positive_scale_unit_tablezero))) + (((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero)))) + ((((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero))) + (((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) * S ((dst_negative_code_unit_tablezero) + (dst_negative_scale_unit_tablezero)) + ((dst_negative_scale_unit_tablezero) + (dst_negative_scale_unit_tablezero)))))) /\ (((((exists ff_h_pvs_unit_tablezeropositive. ff_h_pvs_unit_tablezeropositive + S (dst_positive_unit_tablezero) = S ((S (0)) * dst_positive_scale_unit_tablezero)) /\ exists ff_q_pvs_unit_tablezeropositive. dst_positive_code_unit_tablezero = ff_q_pvs_unit_tablezeropositive * S ((S (0)) * dst_positive_scale_unit_tablezero) + (dst_positive_unit_tablezero))) /\ (((((exists ff_h_pvs_unit_tablezeronegative. ff_h_pvs_unit_tablezeronegative + S (dst_negative_unit_tablezero) = S ((S (0)) * dst_negative_scale_unit_tablezero)) /\ exists ff_q_pvs_unit_tablezeronegative. dst_negative_code_unit_tablezero = ff_q_pvs_unit_tablezeronegative * S ((S (0)) * dst_negative_scale_unit_tablezero) + (dst_negative_unit_tablezero))) /\ (exists ge_balance_positive_unit_tablezerovalue ge_balance_negative_unit_tablezerovalue. (((((0) = 2 * (ge_balance_positive_unit_tablezerovalue) /\ (ge_balance_negative_unit_tablezerovalue) = 0) \/ exists ge_signed_half_unit_tablezerovaluedecode. (((0) = 2 * ge_signed_half_unit_tablezerovaluedecode + 1 /\ (ge_balance_positive_unit_tablezerovalue) = 0) /\ (ge_balance_negative_unit_tablezerovalue) = S ge_signed_half_unit_tablezerovaluedecode))) /\ ((dst_positive_unit_tablezero) + ge_balance_negative_unit_tablezerovalue = (dst_negative_unit_tablezero) + ge_balance_positive_unit_tablezerovalue))))))))) /\ (forall mt_index_unit_table mt_value_unit_table. ~(mt_index_unit_table=0) -> (exists pvs_le_gap_unit_tabledomain. pvs_le_gap_unit_tabledomain + (mt_index_unit_table) = (N)) -> (exists dst_positive_code_unit_tableentry dst_positive_scale_unit_tableentry dst_negative_code_unit_tableentry dst_negative_scale_unit_tableentry dst_positive_unit_tableentry dst_negative_unit_tableentry. (((M) = (((((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) * S ((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) + ((dst_positive_scale_unit_tableentry) + (dst_positive_scale_unit_tableentry))) + (((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry)))) * S ((((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) * S ((dst_positive_code_unit_tableentry) + (dst_positive_scale_unit_tableentry)) + ((dst_positive_scale_unit_tableentry) + (dst_positive_scale_unit_tableentry))) + (((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry)))) + ((((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry))) + (((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) * S ((dst_negative_code_unit_tableentry) + (dst_negative_scale_unit_tableentry)) + ((dst_negative_scale_unit_tableentry) + (dst_negative_scale_unit_tableentry)))))) /\ (((((exists ff_h_pvs_unit_tableentrypositive. ff_h_pvs_unit_tableentrypositive + S (dst_positive_unit_tableentry) = S ((S (mt_index_unit_table)) * dst_positive_scale_unit_tableentry)) /\ exists ff_q_pvs_unit_tableentrypositive. dst_positive_code_unit_tableentry = ff_q_pvs_unit_tableentrypositive * S ((S (mt_index_unit_table)) * dst_positive_scale_unit_tableentry) + (dst_positive_unit_tableentry))) /\ (((((exists ff_h_pvs_unit_tableentrynegative. ff_h_pvs_unit_tableentrynegative + S (dst_negative_unit_tableentry) = S ((S (mt_index_unit_table)) * dst_negative_scale_unit_tableentry)) /\ exists ff_q_pvs_unit_tableentrynegative. dst_negative_code_unit_tableentry = ff_q_pvs_unit_tableentrynegative * S ((S (mt_index_unit_table)) * dst_negative_scale_unit_tableentry) + (dst_negative_unit_tableentry))) /\ (exists ge_balance_positive_unit_tableentryvalue ge_balance_negative_unit_tableentryvalue. (((((mt_value_unit_table) = 2 * (ge_balance_positive_unit_tableentryvalue) /\ (ge_balance_negative_unit_tableentryvalue) = 0) \/ exists ge_signed_half_unit_tableentryvaluedecode. (((mt_value_unit_table) = 2 * ge_signed_half_unit_tableentryvaluedecode + 1 /\ (ge_balance_positive_unit_tableentryvalue) = 0) /\ (ge_balance_negative_unit_tableentryvalue) = S ge_signed_half_unit_tableentryvaluedecode))) /\ ((dst_positive_unit_tableentry) + ge_balance_negative_unit_tableentryvalue = (dst_negative_unit_tableentry) + ge_balance_positive_unit_tableentryvalue))))))))) -> (((~((mt_index_unit_table) = 0)) /\ ((((exists mv_square_prime_unit_tablevaluesquare. ((~((mv_square_prime_unit_tablevaluesquare) = 1) /\ forall pvs_left_unit_tablevaluesquareprime pvs_right_unit_tablevaluesquareprime. (mv_square_prime_unit_tablevaluesquare) = pvs_left_unit_tablevaluesquareprime * pvs_right_unit_tablevaluesquareprime -> pvs_left_unit_tablevaluesquareprime = 1 \/ pvs_right_unit_tablevaluesquareprime = 1) /\ (exists pvs_factor_unit_tablevaluesquaredivisor. (mt_index_unit_table) = (mv_square_prime_unit_tablevaluesquare * mv_square_prime_unit_tablevaluesquare) * pvs_factor_unit_tablevaluesquaredivisor))) /\ ((mt_value_unit_table) = 0))) \/ (((((~((mt_index_unit_table) = 0)) /\ (forall sfd_prime_unit_tablevaluesquarefree. (~((sfd_prime_unit_tablevaluesquarefree) = 1) /\ forall pvs_left_unit_tablevaluesquarefreedomain pvs_right_unit_tablevaluesquarefreedomain. (sfd_prime_unit_tablevaluesquarefree) = pvs_left_unit_tablevaluesquarefreedomain * pvs_right_unit_tablevaluesquarefreedomain -> pvs_left_unit_tablevaluesquarefreedomain = 1 \/ pvs_right_unit_tablevaluesquarefreedomain = 1) -> (exists pvs_le_gap_unit_tablevaluesquarefreebound. pvs_le_gap_unit_tablevaluesquarefreebound + (sfd_prime_unit_tablevaluesquarefree) = (mt_index_unit_table)) -> ~(exists pvs_factor_unit_tablevaluesquarefreesquare. (mt_index_unit_table) = (sfd_prime_unit_tablevaluesquarefree * sfd_prime_unit_tablevaluesquarefree) * pvs_factor_unit_tablevaluesquarefreesquare)))) /\ (exists mv_factor_code_unit_tablevaluefactors mv_factor_scale_unit_tablevaluefactors mv_factor_count_unit_tablevaluefactors. (((~(mt_index_unit_table = 0) /\ ((exists ff_u_fsat_unit_tablevaluefactorsfactorization_product ff_v_fsat_unit_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_start. ff_h_fsat_unit_tablevaluefactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_start. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_terminal. ff_h_fsat_unit_tablevaluefactorsfactorization_product_terminal + S (mt_index_unit_table) = S ((S (mv_factor_count_unit_tablevaluefactors)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_terminal. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_terminal * S ((S (mv_factor_count_unit_tablevaluefactors)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (mt_index_unit_table))) /\ forall ff_i_fsat_unit_tablevaluefactorsfactorization_product. (exists ff_lt_fsat_unit_tablevaluefactorsfactorization_product_bound. ff_lt_fsat_unit_tablevaluefactorsfactorization_product_bound + S ff_i_fsat_unit_tablevaluefactorsfactorization_product = mv_factor_count_unit_tablevaluefactors) -> exists ff_p_fsat_unit_tablevaluefactorsfactorization_product ff_r_fsat_unit_tablevaluefactorsfactorization_product ff_s_fsat_unit_tablevaluefactorsfactorization_product. ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_factor. ff_h_fsat_unit_tablevaluefactorsfactorization_product_factor + S (ff_p_fsat_unit_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * mv_factor_scale_unit_tablevaluefactors)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_factor. mv_factor_code_unit_tablevaluefactors = ff_q_fsat_unit_tablevaluefactorsfactorization_product_factor * S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * mv_factor_scale_unit_tablevaluefactors) + (ff_p_fsat_unit_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_partial. ff_h_fsat_unit_tablevaluefactorsfactorization_product_partial + S (ff_r_fsat_unit_tablevaluefactorsfactorization_product) = S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_partial. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_partial * S ((S (ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (ff_r_fsat_unit_tablevaluefactorsfactorization_product))) /\ ((((exists ff_h_fsat_unit_tablevaluefactorsfactorization_product_successor. ff_h_fsat_unit_tablevaluefactorsfactorization_product_successor + S (ff_s_fsat_unit_tablevaluefactorsfactorization_product) = S ((S (S ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product)) /\ exists ff_q_fsat_unit_tablevaluefactorsfactorization_product_successor. ff_u_fsat_unit_tablevaluefactorsfactorization_product = ff_q_fsat_unit_tablevaluefactorsfactorization_product_successor * S ((S (S ff_i_fsat_unit_tablevaluefactorsfactorization_product)) * ff_v_fsat_unit_tablevaluefactorsfactorization_product) + (ff_s_fsat_unit_tablevaluefactorsfactorization_product))) /\ ff_s_fsat_unit_tablevaluefactorsfactorization_product = ff_r_fsat_unit_tablevaluefactorsfactorization_product * ff_p_fsat_unit_tablevaluefactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes. (exists ftsf_gap_fsat_unit_tablevaluefactorsfactorization_primes_bound. ftsf_gap_fsat_unit_tablevaluefactorsfactorization_primes_bound + S ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes = (mv_factor_count_unit_tablevaluefactors)) -> exists ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry. ff_h_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry + S (ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes) = S ((S (ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes)) * mv_factor_scale_unit_tablevaluefactors)) /\ exists ff_q_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry. mv_factor_code_unit_tablevaluefactors = ff_q_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_unit_tablevaluefactorsfactorization_primes)) * mv_factor_scale_unit_tablevaluefactors) + (ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime. ftsf_factor_fsat_unit_tablevaluefactorsfactorization_primes = frm_prime_left_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_unit_tablevaluefactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_unit_tablevaluefactorsparityeven. (mv_factor_count_unit_tablevaluefactors) = 2 * mv_even_half_unit_tablevaluefactorsparityeven) /\ ((mt_value_unit_table) = 2))) \/ (((exists mv_odd_half_unit_tablevaluefactorsparityodd. (mv_factor_count_unit_tablevaluefactors) = 2 * mv_odd_half_unit_tablevaluefactorsparityodd + 1) /\ ((mt_value_unit_table) = 1)))))))))))))))) -> (exists pvs_le_gap_unit_bound. pvs_le_gap_unit_bound + (1) = (N)) -> (exists dst_positive_code_unit_entry dst_positive_scale_unit_entry dst_negative_code_unit_entry dst_negative_scale_unit_entry dst_positive_unit_entry dst_negative_unit_entry. (((M) = (((((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) * S ((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) + ((dst_positive_scale_unit_entry) + (dst_positive_scale_unit_entry))) + (((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry)))) * S ((((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) * S ((dst_positive_code_unit_entry) + (dst_positive_scale_unit_entry)) + ((dst_positive_scale_unit_entry) + (dst_positive_scale_unit_entry))) + (((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry)))) + ((((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry))) + (((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) * S ((dst_negative_code_unit_entry) + (dst_negative_scale_unit_entry)) + ((dst_negative_scale_unit_entry) + (dst_negative_scale_unit_entry)))))) /\ (((((exists ff_h_pvs_unit_entrypositive. ff_h_pvs_unit_entrypositive + S (dst_positive_unit_entry) = S ((S (1)) * dst_positive_scale_unit_entry)) /\ exists ff_q_pvs_unit_entrypositive. dst_positive_code_unit_entry = ff_q_pvs_unit_entrypositive * S ((S (1)) * dst_positive_scale_unit_entry) + (dst_positive_unit_entry))) /\ (((((exists ff_h_pvs_unit_entrynegative. ff_h_pvs_unit_entrynegative + S (dst_negative_unit_entry) = S ((S (1)) * dst_negative_scale_unit_entry)) /\ exists ff_q_pvs_unit_entrynegative. dst_negative_code_unit_entry = ff_q_pvs_unit_entrynegative * S ((S (1)) * dst_negative_scale_unit_entry) + (dst_negative_unit_entry))) /\ (exists ge_balance_positive_unit_entryvalue ge_balance_negative_unit_entryvalue. (((((2) = 2 * (ge_balance_positive_unit_entryvalue) /\ (ge_balance_negative_unit_entryvalue) = 0) \/ exists ge_signed_half_unit_entryvaluedecode. (((2) = 2 * ge_signed_half_unit_entryvaluedecode + 1 /\ (ge_balance_positive_unit_entryvalue) = 0) /\ (ge_balance_negative_unit_entryvalue) = S ge_signed_half_unit_entryvaluedecode))) /\ ((dst_positive_unit_entry) + ge_balance_negative_unit_entryvalue = (dst_negative_unit_entry) + ge_balance_positive_unit_entryvalue)))))))))

• mobius_value_functional · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n a b. (((~((n) = 0)) /\ ((((exists mv_square_prime_functional_firstsquare. ((~((mv_square_prime_functional_firstsquare) = 1) /\ forall pvs_left_functional_firstsquareprime pvs_right_functional_firstsquareprime. (mv_square_prime_functional_firstsquare) = pvs_left_functional_firstsquareprime * pvs_right_functional_firstsquareprime -> pvs_left_functional_firstsquareprime = 1 \/ pvs_right_functional_firstsquareprime = 1) /\ (exists pvs_factor_functional_firstsquaredivisor. (n) = (mv_square_prime_functional_firstsquare * mv_square_prime_functional_firstsquare) * pvs_factor_functional_firstsquaredivisor))) /\ ((a) = 0))) \/ (((((~((n) = 0)) /\ (forall sfd_prime_functional_firstsquarefree. (~((sfd_prime_functional_firstsquarefree) = 1) /\ forall pvs_left_functional_firstsquarefreedomain pvs_right_functional_firstsquarefreedomain. (sfd_prime_functional_firstsquarefree) = pvs_left_functional_firstsquarefreedomain * pvs_right_functional_firstsquarefreedomain -> pvs_left_functional_firstsquarefreedomain = 1 \/ pvs_right_functional_firstsquarefreedomain = 1) -> (exists pvs_le_gap_functional_firstsquarefreebound. pvs_le_gap_functional_firstsquarefreebound + (sfd_prime_functional_firstsquarefree) = (n)) -> ~(exists pvs_factor_functional_firstsquarefreesquare. (n) = (sfd_prime_functional_firstsquarefree * sfd_prime_functional_firstsquarefree) * pvs_factor_functional_firstsquarefreesquare)))) /\ (exists mv_factor_code_functional_firstfactors mv_factor_scale_functional_firstfactors mv_factor_count_functional_firstfactors. (((~(n = 0) /\ ((exists ff_u_fsat_functional_firstfactorsfactorization_product ff_v_fsat_functional_firstfactorsfactorization_product. ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_start. ff_h_fsat_functional_firstfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_start. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_terminal. ff_h_fsat_functional_firstfactorsfactorization_product_terminal + S (n) = S ((S (mv_factor_count_functional_firstfactors)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_terminal. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_terminal * S ((S (mv_factor_count_functional_firstfactors)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (n))) /\ forall ff_i_fsat_functional_firstfactorsfactorization_product. (exists ff_lt_fsat_functional_firstfactorsfactorization_product_bound. ff_lt_fsat_functional_firstfactorsfactorization_product_bound + S ff_i_fsat_functional_firstfactorsfactorization_product = mv_factor_count_functional_firstfactors) -> exists ff_p_fsat_functional_firstfactorsfactorization_product ff_r_fsat_functional_firstfactorsfactorization_product ff_s_fsat_functional_firstfactorsfactorization_product. ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_factor. ff_h_fsat_functional_firstfactorsfactorization_product_factor + S (ff_p_fsat_functional_firstfactorsfactorization_product) = S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * mv_factor_scale_functional_firstfactors)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_factor. mv_factor_code_functional_firstfactors = ff_q_fsat_functional_firstfactorsfactorization_product_factor * S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * mv_factor_scale_functional_firstfactors) + (ff_p_fsat_functional_firstfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_partial. ff_h_fsat_functional_firstfactorsfactorization_product_partial + S (ff_r_fsat_functional_firstfactorsfactorization_product) = S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_partial. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_partial * S ((S (ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (ff_r_fsat_functional_firstfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_firstfactorsfactorization_product_successor. ff_h_fsat_functional_firstfactorsfactorization_product_successor + S (ff_s_fsat_functional_firstfactorsfactorization_product) = S ((S (S ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product)) /\ exists ff_q_fsat_functional_firstfactorsfactorization_product_successor. ff_u_fsat_functional_firstfactorsfactorization_product = ff_q_fsat_functional_firstfactorsfactorization_product_successor * S ((S (S ff_i_fsat_functional_firstfactorsfactorization_product)) * ff_v_fsat_functional_firstfactorsfactorization_product) + (ff_s_fsat_functional_firstfactorsfactorization_product))) /\ ff_s_fsat_functional_firstfactorsfactorization_product = ff_r_fsat_functional_firstfactorsfactorization_product * ff_p_fsat_functional_firstfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_functional_firstfactorsfactorization_primes. (exists ftsf_gap_fsat_functional_firstfactorsfactorization_primes_bound. ftsf_gap_fsat_functional_firstfactorsfactorization_primes_bound + S ftsf_index_fsat_functional_firstfactorsfactorization_primes = (mv_factor_count_functional_firstfactors)) -> exists ftsf_factor_fsat_functional_firstfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_functional_firstfactorsfactorization_primes_entry. ff_h_ftsf_fsat_functional_firstfactorsfactorization_primes_entry + S (ftsf_factor_fsat_functional_firstfactorsfactorization_primes) = S ((S (ftsf_index_fsat_functional_firstfactorsfactorization_primes)) * mv_factor_scale_functional_firstfactors)) /\ exists ff_q_ftsf_fsat_functional_firstfactorsfactorization_primes_entry. mv_factor_code_functional_firstfactors = ff_q_ftsf_fsat_functional_firstfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_functional_firstfactorsfactorization_primes)) * mv_factor_scale_functional_firstfactors) + (ftsf_factor_fsat_functional_firstfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_functional_firstfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_functional_firstfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_functional_firstfactorsfactorization_primes_prime. ftsf_factor_fsat_functional_firstfactorsfactorization_primes = frm_prime_left_ftsf_fsat_functional_firstfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_functional_firstfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_functional_firstfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_functional_firstfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_functional_firstfactorsparityeven. (mv_factor_count_functional_firstfactors) = 2 * mv_even_half_functional_firstfactorsparityeven) /\ ((a) = 2))) \/ (((exists mv_odd_half_functional_firstfactorsparityodd. (mv_factor_count_functional_firstfactors) = 2 * mv_odd_half_functional_firstfactorsparityodd + 1) /\ ((a) = 1))))))))))) -> (((~((n) = 0)) /\ ((((exists mv_square_prime_functional_secondsquare. ((~((mv_square_prime_functional_secondsquare) = 1) /\ forall pvs_left_functional_secondsquareprime pvs_right_functional_secondsquareprime. (mv_square_prime_functional_secondsquare) = pvs_left_functional_secondsquareprime * pvs_right_functional_secondsquareprime -> pvs_left_functional_secondsquareprime = 1 \/ pvs_right_functional_secondsquareprime = 1) /\ (exists pvs_factor_functional_secondsquaredivisor. (n) = (mv_square_prime_functional_secondsquare * mv_square_prime_functional_secondsquare) * pvs_factor_functional_secondsquaredivisor))) /\ ((b) = 0))) \/ (((((~((n) = 0)) /\ (forall sfd_prime_functional_secondsquarefree. (~((sfd_prime_functional_secondsquarefree) = 1) /\ forall pvs_left_functional_secondsquarefreedomain pvs_right_functional_secondsquarefreedomain. (sfd_prime_functional_secondsquarefree) = pvs_left_functional_secondsquarefreedomain * pvs_right_functional_secondsquarefreedomain -> pvs_left_functional_secondsquarefreedomain = 1 \/ pvs_right_functional_secondsquarefreedomain = 1) -> (exists pvs_le_gap_functional_secondsquarefreebound. pvs_le_gap_functional_secondsquarefreebound + (sfd_prime_functional_secondsquarefree) = (n)) -> ~(exists pvs_factor_functional_secondsquarefreesquare. (n) = (sfd_prime_functional_secondsquarefree * sfd_prime_functional_secondsquarefree) * pvs_factor_functional_secondsquarefreesquare)))) /\ (exists mv_factor_code_functional_secondfactors mv_factor_scale_functional_secondfactors mv_factor_count_functional_secondfactors. (((~(n = 0) /\ ((exists ff_u_fsat_functional_secondfactorsfactorization_product ff_v_fsat_functional_secondfactorsfactorization_product. ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_start. ff_h_fsat_functional_secondfactorsfactorization_product_start + S (1) = S ((S (0)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_start. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_start * S ((S (0)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (1))) /\ ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_terminal. ff_h_fsat_functional_secondfactorsfactorization_product_terminal + S (n) = S ((S (mv_factor_count_functional_secondfactors)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_terminal. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_terminal * S ((S (mv_factor_count_functional_secondfactors)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (n))) /\ forall ff_i_fsat_functional_secondfactorsfactorization_product. (exists ff_lt_fsat_functional_secondfactorsfactorization_product_bound. ff_lt_fsat_functional_secondfactorsfactorization_product_bound + S ff_i_fsat_functional_secondfactorsfactorization_product = mv_factor_count_functional_secondfactors) -> exists ff_p_fsat_functional_secondfactorsfactorization_product ff_r_fsat_functional_secondfactorsfactorization_product ff_s_fsat_functional_secondfactorsfactorization_product. ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_factor. ff_h_fsat_functional_secondfactorsfactorization_product_factor + S (ff_p_fsat_functional_secondfactorsfactorization_product) = S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * mv_factor_scale_functional_secondfactors)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_factor. mv_factor_code_functional_secondfactors = ff_q_fsat_functional_secondfactorsfactorization_product_factor * S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * mv_factor_scale_functional_secondfactors) + (ff_p_fsat_functional_secondfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_partial. ff_h_fsat_functional_secondfactorsfactorization_product_partial + S (ff_r_fsat_functional_secondfactorsfactorization_product) = S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_partial. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_partial * S ((S (ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (ff_r_fsat_functional_secondfactorsfactorization_product))) /\ ((((exists ff_h_fsat_functional_secondfactorsfactorization_product_successor. ff_h_fsat_functional_secondfactorsfactorization_product_successor + S (ff_s_fsat_functional_secondfactorsfactorization_product) = S ((S (S ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product)) /\ exists ff_q_fsat_functional_secondfactorsfactorization_product_successor. ff_u_fsat_functional_secondfactorsfactorization_product = ff_q_fsat_functional_secondfactorsfactorization_product_successor * S ((S (S ff_i_fsat_functional_secondfactorsfactorization_product)) * ff_v_fsat_functional_secondfactorsfactorization_product) + (ff_s_fsat_functional_secondfactorsfactorization_product))) /\ ff_s_fsat_functional_secondfactorsfactorization_product = ff_r_fsat_functional_secondfactorsfactorization_product * ff_p_fsat_functional_secondfactorsfactorization_product)))))) /\ (forall ftsf_index_fsat_functional_secondfactorsfactorization_primes. (exists ftsf_gap_fsat_functional_secondfactorsfactorization_primes_bound. ftsf_gap_fsat_functional_secondfactorsfactorization_primes_bound + S ftsf_index_fsat_functional_secondfactorsfactorization_primes = (mv_factor_count_functional_secondfactors)) -> exists ftsf_factor_fsat_functional_secondfactorsfactorization_primes. ((((exists ff_h_ftsf_fsat_functional_secondfactorsfactorization_primes_entry. ff_h_ftsf_fsat_functional_secondfactorsfactorization_primes_entry + S (ftsf_factor_fsat_functional_secondfactorsfactorization_primes) = S ((S (ftsf_index_fsat_functional_secondfactorsfactorization_primes)) * mv_factor_scale_functional_secondfactors)) /\ exists ff_q_ftsf_fsat_functional_secondfactorsfactorization_primes_entry. mv_factor_code_functional_secondfactors = ff_q_ftsf_fsat_functional_secondfactorsfactorization_primes_entry * S ((S (ftsf_index_fsat_functional_secondfactorsfactorization_primes)) * mv_factor_scale_functional_secondfactors) + (ftsf_factor_fsat_functional_secondfactorsfactorization_primes))) /\ ((~(ftsf_factor_fsat_functional_secondfactorsfactorization_primes = 1) /\ forall frm_prime_left_ftsf_fsat_functional_secondfactorsfactorization_primes_prime frm_prime_right_ftsf_fsat_functional_secondfactorsfactorization_primes_prime. ftsf_factor_fsat_functional_secondfactorsfactorization_primes = frm_prime_left_ftsf_fsat_functional_secondfactorsfactorization_primes_prime * frm_prime_right_ftsf_fsat_functional_secondfactorsfactorization_primes_prime -> frm_prime_left_ftsf_fsat_functional_secondfactorsfactorization_primes_prime = 1 \/ frm_prime_right_ftsf_fsat_functional_secondfactorsfactorization_primes_prime = 1))))))) /\ ((((exists mv_even_half_functional_secondfactorsparityeven. (mv_factor_count_functional_secondfactors) = 2 * mv_even_half_functional_secondfactorsparityeven) /\ ((b) = 2))) \/ (((exists mv_odd_half_functional_secondfactorsparityodd. (mv_factor_count_functional_secondfactors) = 2 * mv_odd_half_functional_secondfactorsparityodd + 1) /\ ((b) = 1))))))))))) -> a = b

• 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)

• multiple_trans · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall a b n. (exists q. n = a * q) -> (exists r. a = b * r) -> exists s. n = b * s

• natural_mul_swap_right_tail · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall a b c. a * (b * c) = b * (a * c)

• prime_coprime_or_divides · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall p a. (~(p = 1) /\ forall c e. p = c * e -> c = 1 \/ e = 1) -> (forall d. (exists x. p = d * x) -> (exists y. a = d * y) -> d = 1) \/ exists k. a = p * k

• prime_divisor_exists · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall n. ~(n = 0) -> ~(n = 1) -> exists p. ((~(p = 1) /\ forall a b. p = a * b -> a = 1 \/ b = 1) /\ exists k. n = p * k)

• prime_nonzero · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall p. (~(p = 1) /\ forall a b. p = a * b -> a = 1 \/ b = 1) -> ~(p = 0)

• signed_divisor_sum_exists · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall N F n. (exists dst_positive_code_sum_total_input dst_positive_scale_sum_total_input dst_negative_code_sum_total_input dst_negative_scale_sum_total_input. (((F) = (((((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) * S ((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) + ((dst_positive_scale_sum_total_input) + (dst_positive_scale_sum_total_input))) + (((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input)))) * S ((((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) * S ((dst_positive_code_sum_total_input) + (dst_positive_scale_sum_total_input)) + ((dst_positive_scale_sum_total_input) + (dst_positive_scale_sum_total_input))) + (((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input)))) + ((((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input))) + (((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) * S ((dst_negative_code_sum_total_input) + (dst_negative_scale_sum_total_input)) + ((dst_negative_scale_sum_total_input) + (dst_negative_scale_sum_total_input)))))) /\ (forall dst_index_sum_total_input. (exists pvs_le_gap_sum_total_inputdomain. pvs_le_gap_sum_total_inputdomain + (dst_index_sum_total_input) = (N)) -> exists dst_positive_sum_total_input dst_negative_sum_total_input dst_value_sum_total_input. ((((exists ff_h_pvs_sum_total_inputentrypositive. ff_h_pvs_sum_total_inputentrypositive + S (dst_positive_sum_total_input) = S ((S (dst_index_sum_total_input)) * dst_positive_scale_sum_total_input)) /\ exists ff_q_pvs_sum_total_inputentrypositive. dst_positive_code_sum_total_input = ff_q_pvs_sum_total_inputentrypositive * S ((S (dst_index_sum_total_input)) * dst_positive_scale_sum_total_input) + (dst_positive_sum_total_input))) /\ (((((exists ff_h_pvs_sum_total_inputentrynegative. ff_h_pvs_sum_total_inputentrynegative + S (dst_negative_sum_total_input) = S ((S (dst_index_sum_total_input)) * dst_negative_scale_sum_total_input)) /\ exists ff_q_pvs_sum_total_inputentrynegative. dst_negative_code_sum_total_input = ff_q_pvs_sum_total_inputentrynegative * S ((S (dst_index_sum_total_input)) * dst_negative_scale_sum_total_input) + (dst_negative_sum_total_input))) /\ (exists ge_balance_positive_sum_total_inputentryvalue ge_balance_negative_sum_total_inputentryvalue. (((((dst_value_sum_total_input) = 2 * (ge_balance_positive_sum_total_inputentryvalue) /\ (ge_balance_negative_sum_total_inputentryvalue) = 0) \/ exists ge_signed_half_sum_total_inputentryvaluedecode. (((dst_value_sum_total_input) = 2 * ge_signed_half_sum_total_inputentryvaluedecode + 1 /\ (ge_balance_positive_sum_total_inputentryvalue) = 0) /\ (ge_balance_negative_sum_total_inputentryvalue) = S ge_signed_half_sum_total_inputentryvaluedecode))) /\ ((dst_positive_sum_total_input) + ge_balance_negative_sum_total_inputentryvalue = (dst_negative_sum_total_input) + ge_balance_positive_sum_total_inputentryvalue))))))))) -> ~(n=0) -> (exists pvs_le_gap_sum_total_bound. pvs_le_gap_sum_total_bound + (n) = (N)) -> exists z. (((~((n)=0)) /\ (exists dm_mask_table_sum_total_result. ((((exists dst_positive_code_sum_total_resultmasktable dst_positive_scale_sum_total_resultmasktable dst_negative_code_sum_total_resultmasktable dst_negative_scale_sum_total_resultmasktable. (((dm_mask_table_sum_total_result) = (((((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) * S ((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) + ((dst_positive_scale_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable))) + (((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)))) * S ((((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) * S ((dst_positive_code_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable)) + ((dst_positive_scale_sum_total_resultmasktable) + (dst_positive_scale_sum_total_resultmasktable))) + (((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)))) + ((((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable))) + (((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) * S ((dst_negative_code_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)) + ((dst_negative_scale_sum_total_resultmasktable) + (dst_negative_scale_sum_total_resultmasktable)))))) /\ (forall dst_index_sum_total_resultmasktable. (exists pvs_le_gap_sum_total_resultmasktabledomain. pvs_le_gap_sum_total_resultmasktabledomain + (dst_index_sum_total_resultmasktable) = (n)) -> exists dst_positive_sum_total_resultmasktable dst_negative_sum_total_resultmasktable dst_value_sum_total_resultmasktable. ((((exists ff_h_pvs_sum_total_resultmasktableentrypositive. ff_h_pvs_sum_total_resultmasktableentrypositive + S (dst_positive_sum_total_resultmasktable) = S ((S (dst_index_sum_total_resultmasktable)) * dst_positive_scale_sum_total_resultmasktable)) /\ exists ff_q_pvs_sum_total_resultmasktableentrypositive. dst_positive_code_sum_total_resultmasktable = ff_q_pvs_sum_total_resultmasktableentrypositive * S ((S (dst_index_sum_total_resultmasktable)) * dst_positive_scale_sum_total_resultmasktable) + (dst_positive_sum_total_resultmasktable))) /\ (((((exists ff_h_pvs_sum_total_resultmasktableentrynegative. ff_h_pvs_sum_total_resultmasktableentrynegative + S (dst_negative_sum_total_resultmasktable) = S ((S (dst_index_sum_total_resultmasktable)) * dst_negative_scale_sum_total_resultmasktable)) /\ exists ff_q_pvs_sum_total_resultmasktableentrynegative. dst_negative_code_sum_total_resultmasktable = ff_q_pvs_sum_total_resultmasktableentrynegative * S ((S (dst_index_sum_total_resultmasktable)) * dst_negative_scale_sum_total_resultmasktable) + (dst_negative_sum_total_resultmasktable))) /\ (exists ge_balance_positive_sum_total_resultmasktableentryvalue ge_balance_negative_sum_total_resultmasktableentryvalue. (((((dst_value_sum_total_resultmasktable) = 2 * (ge_balance_positive_sum_total_resultmasktableentryvalue) /\ (ge_balance_negative_sum_total_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_total_resultmasktableentryvaluedecode. (((dst_value_sum_total_resultmasktable) = 2 * ge_signed_half_sum_total_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_total_resultmasktableentryvalue) = S ge_signed_half_sum_total_resultmasktableentryvaluedecode))) /\ ((dst_positive_sum_total_resultmasktable) + ge_balance_negative_sum_total_resultmasktableentryvalue = (dst_negative_sum_total_resultmasktable) + ge_balance_positive_sum_total_resultmasktableentryvalue))))))))) /\ (forall dm_index_sum_total_resultmask dm_value_sum_total_resultmask. (exists pvs_le_gap_sum_total_resultmaskdomain. pvs_le_gap_sum_total_resultmaskdomain + (dm_index_sum_total_resultmask) = (n)) -> (exists dst_positive_code_sum_total_resultmasklookup dst_positive_scale_sum_total_resultmasklookup dst_negative_code_sum_total_resultmasklookup dst_negative_scale_sum_total_resultmasklookup dst_positive_sum_total_resultmasklookup dst_negative_sum_total_resultmasklookup. (((dm_mask_table_sum_total_result) = (((((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) * S ((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) + ((dst_positive_scale_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup))) + (((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)))) * S ((((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) * S ((dst_positive_code_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup)) + ((dst_positive_scale_sum_total_resultmasklookup) + (dst_positive_scale_sum_total_resultmasklookup))) + (((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)))) + ((((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup))) + (((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) * S ((dst_negative_code_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)) + ((dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_scale_sum_total_resultmasklookup)))))) /\ (((((exists ff_h_pvs_sum_total_resultmasklookuppositive. ff_h_pvs_sum_total_resultmasklookuppositive + S (dst_positive_sum_total_resultmasklookup) = S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmasklookup)) /\ exists ff_q_pvs_sum_total_resultmasklookuppositive. dst_positive_code_sum_total_resultmasklookup = ff_q_pvs_sum_total_resultmasklookuppositive * S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmasklookup) + (dst_positive_sum_total_resultmasklookup))) /\ (((((exists ff_h_pvs_sum_total_resultmasklookupnegative. ff_h_pvs_sum_total_resultmasklookupnegative + S (dst_negative_sum_total_resultmasklookup) = S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmasklookup)) /\ exists ff_q_pvs_sum_total_resultmasklookupnegative. dst_negative_code_sum_total_resultmasklookup = ff_q_pvs_sum_total_resultmasklookupnegative * S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmasklookup) + (dst_negative_sum_total_resultmasklookup))) /\ (exists ge_balance_positive_sum_total_resultmasklookupvalue ge_balance_negative_sum_total_resultmasklookupvalue. (((((dm_value_sum_total_resultmask) = 2 * (ge_balance_positive_sum_total_resultmasklookupvalue) /\ (ge_balance_negative_sum_total_resultmasklookupvalue) = 0) \/ exists ge_signed_half_sum_total_resultmasklookupvaluedecode. (((dm_value_sum_total_resultmask) = 2 * ge_signed_half_sum_total_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmasklookupvalue) = 0) /\ (ge_balance_negative_sum_total_resultmasklookupvalue) = S ge_signed_half_sum_total_resultmasklookupvaluedecode))) /\ ((dst_positive_sum_total_resultmasklookup) + ge_balance_negative_sum_total_resultmasklookupvalue = (dst_negative_sum_total_resultmasklookup) + ge_balance_positive_sum_total_resultmasklookupvalue))))))))) -> ((((~((dm_index_sum_total_resultmask)=0)) /\ (exists dm_quotient_sum_total_resultmaskentry. (((n)=(dm_index_sum_total_resultmask)*dm_quotient_sum_total_resultmaskentry) /\ (exists dst_positive_code_sum_total_resultmaskentryinput dst_positive_scale_sum_total_resultmaskentryinput dst_negative_code_sum_total_resultmaskentryinput dst_negative_scale_sum_total_resultmaskentryinput dst_positive_sum_total_resultmaskentryinput dst_negative_sum_total_resultmaskentryinput. (((F) = (((((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) * S ((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) + ((dst_positive_scale_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput))) + (((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)))) * S ((((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) * S ((dst_positive_code_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput)) + ((dst_positive_scale_sum_total_resultmaskentryinput) + (dst_positive_scale_sum_total_resultmaskentryinput))) + (((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)))) + ((((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput))) + (((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) * S ((dst_negative_code_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)) + ((dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_scale_sum_total_resultmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryinputpositive. ff_h_pvs_sum_total_resultmaskentryinputpositive + S (dst_positive_sum_total_resultmaskentryinput) = S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmaskentryinput)) /\ exists ff_q_pvs_sum_total_resultmaskentryinputpositive. dst_positive_code_sum_total_resultmaskentryinput = ff_q_pvs_sum_total_resultmaskentryinputpositive * S ((S (dm_index_sum_total_resultmask)) * dst_positive_scale_sum_total_resultmaskentryinput) + (dst_positive_sum_total_resultmaskentryinput))) /\ (((((exists ff_h_pvs_sum_total_resultmaskentryinputnegative. ff_h_pvs_sum_total_resultmaskentryinputnegative + S (dst_negative_sum_total_resultmaskentryinput) = S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmaskentryinput)) /\ exists ff_q_pvs_sum_total_resultmaskentryinputnegative. dst_negative_code_sum_total_resultmaskentryinput = ff_q_pvs_sum_total_resultmaskentryinputnegative * S ((S (dm_index_sum_total_resultmask)) * dst_negative_scale_sum_total_resultmaskentryinput) + (dst_negative_sum_total_resultmaskentryinput))) /\ (exists ge_balance_positive_sum_total_resultmaskentryinputvalue ge_balance_negative_sum_total_resultmaskentryinputvalue. (((((dm_value_sum_total_resultmask) = 2 * (ge_balance_positive_sum_total_resultmaskentryinputvalue) /\ (ge_balance_negative_sum_total_resultmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_total_resultmaskentryinputvaluedecode. (((dm_value_sum_total_resultmask) = 2 * ge_signed_half_sum_total_resultmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_total_resultmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_total_resultmaskentryinputvalue) = S ge_signed_half_sum_total_resultmaskentryinputvaluedecode))) /\ ((dst_positive_sum_total_resultmaskentryinput) + ge_balance_negative_sum_total_resultmaskentryinputvalue = (dst_negative_sum_total_resultmaskentryinput) + ge_balance_positive_sum_total_resultmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_total_resultmask)=0 \/ ~(exists pvs_factor_sum_total_resultmaskentrynondivisor. (n) = (dm_index_sum_total_resultmask) * pvs_factor_sum_total_resultmaskentrynondivisor)) /\ ((dm_value_sum_total_resultmask)=0))))))) /\ (exists dst_positive_code_sum_total_resultfold dst_positive_scale_sum_total_resultfold dst_negative_code_sum_total_resultfold dst_negative_scale_sum_total_resultfold dst_positive_sum_sum_total_resultfold dst_negative_sum_sum_total_resultfold. (((dm_mask_table_sum_total_result) = (((((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) * S ((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) + ((dst_positive_scale_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold))) + (((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)))) * S ((((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) * S ((dst_positive_code_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold)) + ((dst_positive_scale_sum_total_resultfold) + (dst_positive_scale_sum_total_resultfold))) + (((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)))) + ((((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold))) + (((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) * S ((dst_negative_code_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)) + ((dst_negative_scale_sum_total_resultfold) + (dst_negative_scale_sum_total_resultfold)))))) /\ (((exists fs_u_dst_sum_total_resultfoldpositive fs_v_dst_sum_total_resultfoldpositive. ((((exists fs_h_dst_sum_total_resultfoldpositive_body_start. fs_h_dst_sum_total_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_start. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_total_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_total_resultfoldpositive_body_terminal. fs_h_dst_sum_total_resultfoldpositive_body_terminal + S (dst_positive_sum_sum_total_resultfold) = S ((S (S (n))) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_terminal. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_total_resultfoldpositive) + (dst_positive_sum_sum_total_resultfold))) /\ forall fs_i_dst_sum_total_resultfoldpositive_body_steps. (exists fs_lt_dst_sum_total_resultfoldpositive_body_steps_bound. fs_lt_dst_sum_total_resultfoldpositive_body_steps_bound + S fs_i_dst_sum_total_resultfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_total_resultfoldpositive_body_steps fs_r_dst_sum_total_resultfoldpositive_body_steps fs_s_dst_sum_total_resultfoldpositive_body_steps. ((((exists fs_h_dst_sum_total_resultfoldpositive_body_steps_summand. fs_h_dst_sum_total_resultfoldpositive_body_steps_summand + S (fs_a_dst_sum_total_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * dst_positive_scale_sum_total_resultfold)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_steps_summand. dst_positive_code_sum_total_resultfold = fs_q_dst_sum_total_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * dst_positive_scale_sum_total_resultfold) + (fs_a_dst_sum_total_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldpositive_body_steps_partial. fs_h_dst_sum_total_resultfoldpositive_body_steps_partial + S (fs_r_dst_sum_total_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_steps_partial. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive) + (fs_r_dst_sum_total_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldpositive_body_steps_successor. fs_h_dst_sum_total_resultfoldpositive_body_steps_successor + S (fs_s_dst_sum_total_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive)) /\ exists fs_q_dst_sum_total_resultfoldpositive_body_steps_successor. fs_u_dst_sum_total_resultfoldpositive = fs_q_dst_sum_total_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_total_resultfoldpositive_body_steps)) * fs_v_dst_sum_total_resultfoldpositive) + (fs_s_dst_sum_total_resultfoldpositive_body_steps))) /\ fs_s_dst_sum_total_resultfoldpositive_body_steps = fs_r_dst_sum_total_resultfoldpositive_body_steps + fs_a_dst_sum_total_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_total_resultfoldnegative fs_v_dst_sum_total_resultfoldnegative. ((((exists fs_h_dst_sum_total_resultfoldnegative_body_start. fs_h_dst_sum_total_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_start. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_total_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_total_resultfoldnegative_body_terminal. fs_h_dst_sum_total_resultfoldnegative_body_terminal + S (dst_negative_sum_sum_total_resultfold) = S ((S (S (n))) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_terminal. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_total_resultfoldnegative) + (dst_negative_sum_sum_total_resultfold))) /\ forall fs_i_dst_sum_total_resultfoldnegative_body_steps. (exists fs_lt_dst_sum_total_resultfoldnegative_body_steps_bound. fs_lt_dst_sum_total_resultfoldnegative_body_steps_bound + S fs_i_dst_sum_total_resultfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_total_resultfoldnegative_body_steps fs_r_dst_sum_total_resultfoldnegative_body_steps fs_s_dst_sum_total_resultfoldnegative_body_steps. ((((exists fs_h_dst_sum_total_resultfoldnegative_body_steps_summand. fs_h_dst_sum_total_resultfoldnegative_body_steps_summand + S (fs_a_dst_sum_total_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * dst_negative_scale_sum_total_resultfold)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_steps_summand. dst_negative_code_sum_total_resultfold = fs_q_dst_sum_total_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * dst_negative_scale_sum_total_resultfold) + (fs_a_dst_sum_total_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldnegative_body_steps_partial. fs_h_dst_sum_total_resultfoldnegative_body_steps_partial + S (fs_r_dst_sum_total_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_steps_partial. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative) + (fs_r_dst_sum_total_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_total_resultfoldnegative_body_steps_successor. fs_h_dst_sum_total_resultfoldnegative_body_steps_successor + S (fs_s_dst_sum_total_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative)) /\ exists fs_q_dst_sum_total_resultfoldnegative_body_steps_successor. fs_u_dst_sum_total_resultfoldnegative = fs_q_dst_sum_total_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_total_resultfoldnegative_body_steps)) * fs_v_dst_sum_total_resultfoldnegative) + (fs_s_dst_sum_total_resultfoldnegative_body_steps))) /\ fs_s_dst_sum_total_resultfoldnegative_body_steps = fs_r_dst_sum_total_resultfoldnegative_body_steps + fs_a_dst_sum_total_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_total_resultfoldresult ge_balance_negative_sum_total_resultfoldresult. (((((z) = 2 * (ge_balance_positive_sum_total_resultfoldresult) /\ (ge_balance_negative_sum_total_resultfoldresult) = 0) \/ exists ge_signed_half_sum_total_resultfoldresultdecode. (((z) = 2 * ge_signed_half_sum_total_resultfoldresultdecode + 1 /\ (ge_balance_positive_sum_total_resultfoldresult) = 0) /\ (ge_balance_negative_sum_total_resultfoldresult) = S ge_signed_half_sum_total_resultfoldresultdecode))) /\ ((dst_positive_sum_sum_total_resultfold) + ge_balance_negative_sum_total_resultfoldresult = (dst_negative_sum_sum_total_resultfold) + ge_balance_positive_sum_total_resultfoldresult)))))))))))))

• signed_divisor_sum_functional · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F n a b. (((~((n)=0)) /\ (exists dm_mask_table_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. (((dm_mask_table_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 dm_index_sum_unique_firstmask dm_value_sum_unique_firstmask. (exists pvs_le_gap_sum_unique_firstmaskdomain. pvs_le_gap_sum_unique_firstmaskdomain + (dm_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. (((dm_mask_table_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 (dm_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 (dm_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 (dm_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 (dm_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. (((((dm_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. (((dm_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))))))))) -> ((((~((dm_index_sum_unique_firstmask)=0)) /\ (exists dm_quotient_sum_unique_firstmaskentry. (((n)=(dm_index_sum_unique_firstmask)*dm_quotient_sum_unique_firstmaskentry) /\ (exists dst_positive_code_sum_unique_firstmaskentryinput dst_positive_scale_sum_unique_firstmaskentryinput dst_negative_code_sum_unique_firstmaskentryinput dst_negative_scale_sum_unique_firstmaskentryinput dst_positive_sum_unique_firstmaskentryinput dst_negative_sum_unique_firstmaskentryinput. (((F) = (((((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) * S ((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) + ((dst_positive_scale_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput))) + (((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)))) * S ((((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) * S ((dst_positive_code_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput)) + ((dst_positive_scale_sum_unique_firstmaskentryinput) + (dst_positive_scale_sum_unique_firstmaskentryinput))) + (((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)))) + ((((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput))) + (((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) * S ((dst_negative_code_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)) + ((dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_scale_sum_unique_firstmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryinputpositive. ff_h_pvs_sum_unique_firstmaskentryinputpositive + S (dst_positive_sum_unique_firstmaskentryinput) = S ((S (dm_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmaskentryinput)) /\ exists ff_q_pvs_sum_unique_firstmaskentryinputpositive. dst_positive_code_sum_unique_firstmaskentryinput = ff_q_pvs_sum_unique_firstmaskentryinputpositive * S ((S (dm_index_sum_unique_firstmask)) * dst_positive_scale_sum_unique_firstmaskentryinput) + (dst_positive_sum_unique_firstmaskentryinput))) /\ (((((exists ff_h_pvs_sum_unique_firstmaskentryinputnegative. ff_h_pvs_sum_unique_firstmaskentryinputnegative + S (dst_negative_sum_unique_firstmaskentryinput) = S ((S (dm_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmaskentryinput)) /\ exists ff_q_pvs_sum_unique_firstmaskentryinputnegative. dst_negative_code_sum_unique_firstmaskentryinput = ff_q_pvs_sum_unique_firstmaskentryinputnegative * S ((S (dm_index_sum_unique_firstmask)) * dst_negative_scale_sum_unique_firstmaskentryinput) + (dst_negative_sum_unique_firstmaskentryinput))) /\ (exists ge_balance_positive_sum_unique_firstmaskentryinputvalue ge_balance_negative_sum_unique_firstmaskentryinputvalue. (((((dm_value_sum_unique_firstmask) = 2 * (ge_balance_positive_sum_unique_firstmaskentryinputvalue) /\ (ge_balance_negative_sum_unique_firstmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_unique_firstmaskentryinputvaluedecode. (((dm_value_sum_unique_firstmask) = 2 * ge_signed_half_sum_unique_firstmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_unique_firstmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_unique_firstmaskentryinputvalue) = S ge_signed_half_sum_unique_firstmaskentryinputvaluedecode))) /\ ((dst_positive_sum_unique_firstmaskentryinput) + ge_balance_negative_sum_unique_firstmaskentryinputvalue = (dst_negative_sum_unique_firstmaskentryinput) + ge_balance_positive_sum_unique_firstmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_unique_firstmask)=0 \/ ~(exists pvs_factor_sum_unique_firstmaskentrynondivisor. (n) = (dm_index_sum_unique_firstmask) * pvs_factor_sum_unique_firstmaskentrynondivisor)) /\ ((dm_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. (((dm_mask_table_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 dm_mask_table_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. (((dm_mask_table_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 dm_index_sum_unique_secondmask dm_value_sum_unique_secondmask. (exists pvs_le_gap_sum_unique_secondmaskdomain. pvs_le_gap_sum_unique_secondmaskdomain + (dm_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. (((dm_mask_table_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 (dm_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 (dm_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 (dm_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 (dm_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. (((((dm_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. (((dm_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))))))))) -> ((((~((dm_index_sum_unique_secondmask)=0)) /\ (exists dm_quotient_sum_unique_secondmaskentry. (((n)=(dm_index_sum_unique_secondmask)*dm_quotient_sum_unique_secondmaskentry) /\ (exists dst_positive_code_sum_unique_secondmaskentryinput dst_positive_scale_sum_unique_secondmaskentryinput dst_negative_code_sum_unique_secondmaskentryinput dst_negative_scale_sum_unique_secondmaskentryinput dst_positive_sum_unique_secondmaskentryinput dst_negative_sum_unique_secondmaskentryinput. (((F) = (((((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) * S ((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) + ((dst_positive_scale_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput))) + (((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)))) * S ((((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) * S ((dst_positive_code_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput)) + ((dst_positive_scale_sum_unique_secondmaskentryinput) + (dst_positive_scale_sum_unique_secondmaskentryinput))) + (((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)))) + ((((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput))) + (((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) * S ((dst_negative_code_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)) + ((dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_scale_sum_unique_secondmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryinputpositive. ff_h_pvs_sum_unique_secondmaskentryinputpositive + S (dst_positive_sum_unique_secondmaskentryinput) = S ((S (dm_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmaskentryinput)) /\ exists ff_q_pvs_sum_unique_secondmaskentryinputpositive. dst_positive_code_sum_unique_secondmaskentryinput = ff_q_pvs_sum_unique_secondmaskentryinputpositive * S ((S (dm_index_sum_unique_secondmask)) * dst_positive_scale_sum_unique_secondmaskentryinput) + (dst_positive_sum_unique_secondmaskentryinput))) /\ (((((exists ff_h_pvs_sum_unique_secondmaskentryinputnegative. ff_h_pvs_sum_unique_secondmaskentryinputnegative + S (dst_negative_sum_unique_secondmaskentryinput) = S ((S (dm_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmaskentryinput)) /\ exists ff_q_pvs_sum_unique_secondmaskentryinputnegative. dst_negative_code_sum_unique_secondmaskentryinput = ff_q_pvs_sum_unique_secondmaskentryinputnegative * S ((S (dm_index_sum_unique_secondmask)) * dst_negative_scale_sum_unique_secondmaskentryinput) + (dst_negative_sum_unique_secondmaskentryinput))) /\ (exists ge_balance_positive_sum_unique_secondmaskentryinputvalue ge_balance_negative_sum_unique_secondmaskentryinputvalue. (((((dm_value_sum_unique_secondmask) = 2 * (ge_balance_positive_sum_unique_secondmaskentryinputvalue) /\ (ge_balance_negative_sum_unique_secondmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_unique_secondmaskentryinputvaluedecode. (((dm_value_sum_unique_secondmask) = 2 * ge_signed_half_sum_unique_secondmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_unique_secondmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_unique_secondmaskentryinputvalue) = S ge_signed_half_sum_unique_secondmaskentryinputvaluedecode))) /\ ((dst_positive_sum_unique_secondmaskentryinput) + ge_balance_negative_sum_unique_secondmaskentryinputvalue = (dst_negative_sum_unique_secondmaskentryinput) + ge_balance_positive_sum_unique_secondmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_unique_secondmask)=0 \/ ~(exists pvs_factor_sum_unique_secondmaskentrynondivisor. (n) = (dm_index_sum_unique_secondmask) * pvs_factor_sum_unique_secondmaskentrynondivisor)) /\ ((dm_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. (((dm_mask_table_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

• signed_divisor_sum_one · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall N F a. (exists dst_positive_code_sum_one_input dst_positive_scale_sum_one_input dst_negative_code_sum_one_input dst_negative_scale_sum_one_input. (((F) = (((((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) * S ((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) + ((dst_positive_scale_sum_one_input) + (dst_positive_scale_sum_one_input))) + (((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input)))) * S ((((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) * S ((dst_positive_code_sum_one_input) + (dst_positive_scale_sum_one_input)) + ((dst_positive_scale_sum_one_input) + (dst_positive_scale_sum_one_input))) + (((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input)))) + ((((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input))) + (((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) * S ((dst_negative_code_sum_one_input) + (dst_negative_scale_sum_one_input)) + ((dst_negative_scale_sum_one_input) + (dst_negative_scale_sum_one_input)))))) /\ (forall dst_index_sum_one_input. (exists pvs_le_gap_sum_one_inputdomain. pvs_le_gap_sum_one_inputdomain + (dst_index_sum_one_input) = (N)) -> exists dst_positive_sum_one_input dst_negative_sum_one_input dst_value_sum_one_input. ((((exists ff_h_pvs_sum_one_inputentrypositive. ff_h_pvs_sum_one_inputentrypositive + S (dst_positive_sum_one_input) = S ((S (dst_index_sum_one_input)) * dst_positive_scale_sum_one_input)) /\ exists ff_q_pvs_sum_one_inputentrypositive. dst_positive_code_sum_one_input = ff_q_pvs_sum_one_inputentrypositive * S ((S (dst_index_sum_one_input)) * dst_positive_scale_sum_one_input) + (dst_positive_sum_one_input))) /\ (((((exists ff_h_pvs_sum_one_inputentrynegative. ff_h_pvs_sum_one_inputentrynegative + S (dst_negative_sum_one_input) = S ((S (dst_index_sum_one_input)) * dst_negative_scale_sum_one_input)) /\ exists ff_q_pvs_sum_one_inputentrynegative. dst_negative_code_sum_one_input = ff_q_pvs_sum_one_inputentrynegative * S ((S (dst_index_sum_one_input)) * dst_negative_scale_sum_one_input) + (dst_negative_sum_one_input))) /\ (exists ge_balance_positive_sum_one_inputentryvalue ge_balance_negative_sum_one_inputentryvalue. (((((dst_value_sum_one_input) = 2 * (ge_balance_positive_sum_one_inputentryvalue) /\ (ge_balance_negative_sum_one_inputentryvalue) = 0) \/ exists ge_signed_half_sum_one_inputentryvaluedecode. (((dst_value_sum_one_input) = 2 * ge_signed_half_sum_one_inputentryvaluedecode + 1 /\ (ge_balance_positive_sum_one_inputentryvalue) = 0) /\ (ge_balance_negative_sum_one_inputentryvalue) = S ge_signed_half_sum_one_inputentryvaluedecode))) /\ ((dst_positive_sum_one_input) + ge_balance_negative_sum_one_inputentryvalue = (dst_negative_sum_one_input) + ge_balance_positive_sum_one_inputentryvalue))))))))) -> (exists pvs_le_gap_sum_one_bound. pvs_le_gap_sum_one_bound + (1) = (N)) -> (exists dst_positive_code_sum_one_entry dst_positive_scale_sum_one_entry dst_negative_code_sum_one_entry dst_negative_scale_sum_one_entry dst_positive_sum_one_entry dst_negative_sum_one_entry. (((F) = (((((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) * S ((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) + ((dst_positive_scale_sum_one_entry) + (dst_positive_scale_sum_one_entry))) + (((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry)))) * S ((((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) * S ((dst_positive_code_sum_one_entry) + (dst_positive_scale_sum_one_entry)) + ((dst_positive_scale_sum_one_entry) + (dst_positive_scale_sum_one_entry))) + (((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry)))) + ((((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry))) + (((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) * S ((dst_negative_code_sum_one_entry) + (dst_negative_scale_sum_one_entry)) + ((dst_negative_scale_sum_one_entry) + (dst_negative_scale_sum_one_entry)))))) /\ (((((exists ff_h_pvs_sum_one_entrypositive. ff_h_pvs_sum_one_entrypositive + S (dst_positive_sum_one_entry) = S ((S (1)) * dst_positive_scale_sum_one_entry)) /\ exists ff_q_pvs_sum_one_entrypositive. dst_positive_code_sum_one_entry = ff_q_pvs_sum_one_entrypositive * S ((S (1)) * dst_positive_scale_sum_one_entry) + (dst_positive_sum_one_entry))) /\ (((((exists ff_h_pvs_sum_one_entrynegative. ff_h_pvs_sum_one_entrynegative + S (dst_negative_sum_one_entry) = S ((S (1)) * dst_negative_scale_sum_one_entry)) /\ exists ff_q_pvs_sum_one_entrynegative. dst_negative_code_sum_one_entry = ff_q_pvs_sum_one_entrynegative * S ((S (1)) * dst_negative_scale_sum_one_entry) + (dst_negative_sum_one_entry))) /\ (exists ge_balance_positive_sum_one_entryvalue ge_balance_negative_sum_one_entryvalue. (((((a) = 2 * (ge_balance_positive_sum_one_entryvalue) /\ (ge_balance_negative_sum_one_entryvalue) = 0) \/ exists ge_signed_half_sum_one_entryvaluedecode. (((a) = 2 * ge_signed_half_sum_one_entryvaluedecode + 1 /\ (ge_balance_positive_sum_one_entryvalue) = 0) /\ (ge_balance_negative_sum_one_entryvalue) = S ge_signed_half_sum_one_entryvaluedecode))) /\ ((dst_positive_sum_one_entry) + ge_balance_negative_sum_one_entryvalue = (dst_negative_sum_one_entry) + ge_balance_positive_sum_one_entryvalue))))))))) -> (((~((1)=0)) /\ (exists dm_mask_table_sum_one_result. ((((exists dst_positive_code_sum_one_resultmasktable dst_positive_scale_sum_one_resultmasktable dst_negative_code_sum_one_resultmasktable dst_negative_scale_sum_one_resultmasktable. (((dm_mask_table_sum_one_result) = (((((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) * S ((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) + ((dst_positive_scale_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable))) + (((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)))) * S ((((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) * S ((dst_positive_code_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable)) + ((dst_positive_scale_sum_one_resultmasktable) + (dst_positive_scale_sum_one_resultmasktable))) + (((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)))) + ((((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable))) + (((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) * S ((dst_negative_code_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)) + ((dst_negative_scale_sum_one_resultmasktable) + (dst_negative_scale_sum_one_resultmasktable)))))) /\ (forall dst_index_sum_one_resultmasktable. (exists pvs_le_gap_sum_one_resultmasktabledomain. pvs_le_gap_sum_one_resultmasktabledomain + (dst_index_sum_one_resultmasktable) = (1)) -> exists dst_positive_sum_one_resultmasktable dst_negative_sum_one_resultmasktable dst_value_sum_one_resultmasktable. ((((exists ff_h_pvs_sum_one_resultmasktableentrypositive. ff_h_pvs_sum_one_resultmasktableentrypositive + S (dst_positive_sum_one_resultmasktable) = S ((S (dst_index_sum_one_resultmasktable)) * dst_positive_scale_sum_one_resultmasktable)) /\ exists ff_q_pvs_sum_one_resultmasktableentrypositive. dst_positive_code_sum_one_resultmasktable = ff_q_pvs_sum_one_resultmasktableentrypositive * S ((S (dst_index_sum_one_resultmasktable)) * dst_positive_scale_sum_one_resultmasktable) + (dst_positive_sum_one_resultmasktable))) /\ (((((exists ff_h_pvs_sum_one_resultmasktableentrynegative. ff_h_pvs_sum_one_resultmasktableentrynegative + S (dst_negative_sum_one_resultmasktable) = S ((S (dst_index_sum_one_resultmasktable)) * dst_negative_scale_sum_one_resultmasktable)) /\ exists ff_q_pvs_sum_one_resultmasktableentrynegative. dst_negative_code_sum_one_resultmasktable = ff_q_pvs_sum_one_resultmasktableentrynegative * S ((S (dst_index_sum_one_resultmasktable)) * dst_negative_scale_sum_one_resultmasktable) + (dst_negative_sum_one_resultmasktable))) /\ (exists ge_balance_positive_sum_one_resultmasktableentryvalue ge_balance_negative_sum_one_resultmasktableentryvalue. (((((dst_value_sum_one_resultmasktable) = 2 * (ge_balance_positive_sum_one_resultmasktableentryvalue) /\ (ge_balance_negative_sum_one_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_one_resultmasktableentryvaluedecode. (((dst_value_sum_one_resultmasktable) = 2 * ge_signed_half_sum_one_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_one_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_one_resultmasktableentryvalue) = S ge_signed_half_sum_one_resultmasktableentryvaluedecode))) /\ ((dst_positive_sum_one_resultmasktable) + ge_balance_negative_sum_one_resultmasktableentryvalue = (dst_negative_sum_one_resultmasktable) + ge_balance_positive_sum_one_resultmasktableentryvalue))))))))) /\ (forall dm_index_sum_one_resultmask dm_value_sum_one_resultmask. (exists pvs_le_gap_sum_one_resultmaskdomain. pvs_le_gap_sum_one_resultmaskdomain + (dm_index_sum_one_resultmask) = (1)) -> (exists dst_positive_code_sum_one_resultmasklookup dst_positive_scale_sum_one_resultmasklookup dst_negative_code_sum_one_resultmasklookup dst_negative_scale_sum_one_resultmasklookup dst_positive_sum_one_resultmasklookup dst_negative_sum_one_resultmasklookup. (((dm_mask_table_sum_one_result) = (((((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) * S ((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) + ((dst_positive_scale_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup))) + (((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)))) * S ((((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) * S ((dst_positive_code_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup)) + ((dst_positive_scale_sum_one_resultmasklookup) + (dst_positive_scale_sum_one_resultmasklookup))) + (((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)))) + ((((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup))) + (((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) * S ((dst_negative_code_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)) + ((dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_scale_sum_one_resultmasklookup)))))) /\ (((((exists ff_h_pvs_sum_one_resultmasklookuppositive. ff_h_pvs_sum_one_resultmasklookuppositive + S (dst_positive_sum_one_resultmasklookup) = S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmasklookup)) /\ exists ff_q_pvs_sum_one_resultmasklookuppositive. dst_positive_code_sum_one_resultmasklookup = ff_q_pvs_sum_one_resultmasklookuppositive * S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmasklookup) + (dst_positive_sum_one_resultmasklookup))) /\ (((((exists ff_h_pvs_sum_one_resultmasklookupnegative. ff_h_pvs_sum_one_resultmasklookupnegative + S (dst_negative_sum_one_resultmasklookup) = S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmasklookup)) /\ exists ff_q_pvs_sum_one_resultmasklookupnegative. dst_negative_code_sum_one_resultmasklookup = ff_q_pvs_sum_one_resultmasklookupnegative * S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmasklookup) + (dst_negative_sum_one_resultmasklookup))) /\ (exists ge_balance_positive_sum_one_resultmasklookupvalue ge_balance_negative_sum_one_resultmasklookupvalue. (((((dm_value_sum_one_resultmask) = 2 * (ge_balance_positive_sum_one_resultmasklookupvalue) /\ (ge_balance_negative_sum_one_resultmasklookupvalue) = 0) \/ exists ge_signed_half_sum_one_resultmasklookupvaluedecode. (((dm_value_sum_one_resultmask) = 2 * ge_signed_half_sum_one_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_one_resultmasklookupvalue) = 0) /\ (ge_balance_negative_sum_one_resultmasklookupvalue) = S ge_signed_half_sum_one_resultmasklookupvaluedecode))) /\ ((dst_positive_sum_one_resultmasklookup) + ge_balance_negative_sum_one_resultmasklookupvalue = (dst_negative_sum_one_resultmasklookup) + ge_balance_positive_sum_one_resultmasklookupvalue))))))))) -> ((((~((dm_index_sum_one_resultmask)=0)) /\ (exists dm_quotient_sum_one_resultmaskentry. (((1)=(dm_index_sum_one_resultmask)*dm_quotient_sum_one_resultmaskentry) /\ (exists dst_positive_code_sum_one_resultmaskentryinput dst_positive_scale_sum_one_resultmaskentryinput dst_negative_code_sum_one_resultmaskentryinput dst_negative_scale_sum_one_resultmaskentryinput dst_positive_sum_one_resultmaskentryinput dst_negative_sum_one_resultmaskentryinput. (((F) = (((((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) * S ((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) + ((dst_positive_scale_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput))) + (((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)))) * S ((((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) * S ((dst_positive_code_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput)) + ((dst_positive_scale_sum_one_resultmaskentryinput) + (dst_positive_scale_sum_one_resultmaskentryinput))) + (((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)))) + ((((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput))) + (((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) * S ((dst_negative_code_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)) + ((dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_scale_sum_one_resultmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_one_resultmaskentryinputpositive. ff_h_pvs_sum_one_resultmaskentryinputpositive + S (dst_positive_sum_one_resultmaskentryinput) = S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmaskentryinput)) /\ exists ff_q_pvs_sum_one_resultmaskentryinputpositive. dst_positive_code_sum_one_resultmaskentryinput = ff_q_pvs_sum_one_resultmaskentryinputpositive * S ((S (dm_index_sum_one_resultmask)) * dst_positive_scale_sum_one_resultmaskentryinput) + (dst_positive_sum_one_resultmaskentryinput))) /\ (((((exists ff_h_pvs_sum_one_resultmaskentryinputnegative. ff_h_pvs_sum_one_resultmaskentryinputnegative + S (dst_negative_sum_one_resultmaskentryinput) = S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmaskentryinput)) /\ exists ff_q_pvs_sum_one_resultmaskentryinputnegative. dst_negative_code_sum_one_resultmaskentryinput = ff_q_pvs_sum_one_resultmaskentryinputnegative * S ((S (dm_index_sum_one_resultmask)) * dst_negative_scale_sum_one_resultmaskentryinput) + (dst_negative_sum_one_resultmaskentryinput))) /\ (exists ge_balance_positive_sum_one_resultmaskentryinputvalue ge_balance_negative_sum_one_resultmaskentryinputvalue. (((((dm_value_sum_one_resultmask) = 2 * (ge_balance_positive_sum_one_resultmaskentryinputvalue) /\ (ge_balance_negative_sum_one_resultmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_one_resultmaskentryinputvaluedecode. (((dm_value_sum_one_resultmask) = 2 * ge_signed_half_sum_one_resultmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_one_resultmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_one_resultmaskentryinputvalue) = S ge_signed_half_sum_one_resultmaskentryinputvaluedecode))) /\ ((dst_positive_sum_one_resultmaskentryinput) + ge_balance_negative_sum_one_resultmaskentryinputvalue = (dst_negative_sum_one_resultmaskentryinput) + ge_balance_positive_sum_one_resultmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_one_resultmask)=0 \/ ~(exists pvs_factor_sum_one_resultmaskentrynondivisor. (1) = (dm_index_sum_one_resultmask) * pvs_factor_sum_one_resultmaskentrynondivisor)) /\ ((dm_value_sum_one_resultmask)=0))))))) /\ (exists dst_positive_code_sum_one_resultfold dst_positive_scale_sum_one_resultfold dst_negative_code_sum_one_resultfold dst_negative_scale_sum_one_resultfold dst_positive_sum_sum_one_resultfold dst_negative_sum_sum_one_resultfold. (((dm_mask_table_sum_one_result) = (((((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) * S ((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) + ((dst_positive_scale_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold))) + (((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)))) * S ((((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) * S ((dst_positive_code_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold)) + ((dst_positive_scale_sum_one_resultfold) + (dst_positive_scale_sum_one_resultfold))) + (((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)))) + ((((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold))) + (((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) * S ((dst_negative_code_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)) + ((dst_negative_scale_sum_one_resultfold) + (dst_negative_scale_sum_one_resultfold)))))) /\ (((exists fs_u_dst_sum_one_resultfoldpositive fs_v_dst_sum_one_resultfoldpositive. ((((exists fs_h_dst_sum_one_resultfoldpositive_body_start. fs_h_dst_sum_one_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_start. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_one_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_one_resultfoldpositive_body_terminal. fs_h_dst_sum_one_resultfoldpositive_body_terminal + S (dst_positive_sum_sum_one_resultfold) = S ((S (S (1))) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_terminal. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_terminal * S ((S (S (1))) * fs_v_dst_sum_one_resultfoldpositive) + (dst_positive_sum_sum_one_resultfold))) /\ forall fs_i_dst_sum_one_resultfoldpositive_body_steps. (exists fs_lt_dst_sum_one_resultfoldpositive_body_steps_bound. fs_lt_dst_sum_one_resultfoldpositive_body_steps_bound + S fs_i_dst_sum_one_resultfoldpositive_body_steps = S (1)) -> exists fs_a_dst_sum_one_resultfoldpositive_body_steps fs_r_dst_sum_one_resultfoldpositive_body_steps fs_s_dst_sum_one_resultfoldpositive_body_steps. ((((exists fs_h_dst_sum_one_resultfoldpositive_body_steps_summand. fs_h_dst_sum_one_resultfoldpositive_body_steps_summand + S (fs_a_dst_sum_one_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * dst_positive_scale_sum_one_resultfold)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_steps_summand. dst_positive_code_sum_one_resultfold = fs_q_dst_sum_one_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * dst_positive_scale_sum_one_resultfold) + (fs_a_dst_sum_one_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldpositive_body_steps_partial. fs_h_dst_sum_one_resultfoldpositive_body_steps_partial + S (fs_r_dst_sum_one_resultfoldpositive_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_steps_partial. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive) + (fs_r_dst_sum_one_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldpositive_body_steps_successor. fs_h_dst_sum_one_resultfoldpositive_body_steps_successor + S (fs_s_dst_sum_one_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive)) /\ exists fs_q_dst_sum_one_resultfoldpositive_body_steps_successor. fs_u_dst_sum_one_resultfoldpositive = fs_q_dst_sum_one_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_one_resultfoldpositive_body_steps)) * fs_v_dst_sum_one_resultfoldpositive) + (fs_s_dst_sum_one_resultfoldpositive_body_steps))) /\ fs_s_dst_sum_one_resultfoldpositive_body_steps = fs_r_dst_sum_one_resultfoldpositive_body_steps + fs_a_dst_sum_one_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_one_resultfoldnegative fs_v_dst_sum_one_resultfoldnegative. ((((exists fs_h_dst_sum_one_resultfoldnegative_body_start. fs_h_dst_sum_one_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_start. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_one_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_one_resultfoldnegative_body_terminal. fs_h_dst_sum_one_resultfoldnegative_body_terminal + S (dst_negative_sum_sum_one_resultfold) = S ((S (S (1))) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_terminal. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_terminal * S ((S (S (1))) * fs_v_dst_sum_one_resultfoldnegative) + (dst_negative_sum_sum_one_resultfold))) /\ forall fs_i_dst_sum_one_resultfoldnegative_body_steps. (exists fs_lt_dst_sum_one_resultfoldnegative_body_steps_bound. fs_lt_dst_sum_one_resultfoldnegative_body_steps_bound + S fs_i_dst_sum_one_resultfoldnegative_body_steps = S (1)) -> exists fs_a_dst_sum_one_resultfoldnegative_body_steps fs_r_dst_sum_one_resultfoldnegative_body_steps fs_s_dst_sum_one_resultfoldnegative_body_steps. ((((exists fs_h_dst_sum_one_resultfoldnegative_body_steps_summand. fs_h_dst_sum_one_resultfoldnegative_body_steps_summand + S (fs_a_dst_sum_one_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * dst_negative_scale_sum_one_resultfold)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_steps_summand. dst_negative_code_sum_one_resultfold = fs_q_dst_sum_one_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * dst_negative_scale_sum_one_resultfold) + (fs_a_dst_sum_one_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldnegative_body_steps_partial. fs_h_dst_sum_one_resultfoldnegative_body_steps_partial + S (fs_r_dst_sum_one_resultfoldnegative_body_steps) = S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_steps_partial. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative) + (fs_r_dst_sum_one_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_one_resultfoldnegative_body_steps_successor. fs_h_dst_sum_one_resultfoldnegative_body_steps_successor + S (fs_s_dst_sum_one_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative)) /\ exists fs_q_dst_sum_one_resultfoldnegative_body_steps_successor. fs_u_dst_sum_one_resultfoldnegative = fs_q_dst_sum_one_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_one_resultfoldnegative_body_steps)) * fs_v_dst_sum_one_resultfoldnegative) + (fs_s_dst_sum_one_resultfoldnegative_body_steps))) /\ fs_s_dst_sum_one_resultfoldnegative_body_steps = fs_r_dst_sum_one_resultfoldnegative_body_steps + fs_a_dst_sum_one_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_one_resultfoldresult ge_balance_negative_sum_one_resultfoldresult. (((((a) = 2 * (ge_balance_positive_sum_one_resultfoldresult) /\ (ge_balance_negative_sum_one_resultfoldresult) = 0) \/ exists ge_signed_half_sum_one_resultfoldresultdecode. (((a) = 2 * ge_signed_half_sum_one_resultfoldresultdecode + 1 /\ (ge_balance_positive_sum_one_resultfoldresult) = 0) /\ (ge_balance_negative_sum_one_resultfoldresult) = S ge_signed_half_sum_one_resultfoldresultdecode))) /\ ((dst_positive_sum_sum_one_resultfold) + ge_balance_negative_sum_one_resultfoldresult = (dst_negative_sum_sum_one_resultfold) + ge_balance_positive_sum_one_resultfoldresult)))))))))))))

• signed_divisor_sum_positive_source_extensional · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall F G n a b. (forall dm_index_sum_source_equal dm_first_value_sum_source_equal dm_second_value_sum_source_equal. ~(dm_index_sum_source_equal=0) -> (exists pvs_le_gap_sum_source_equaldomain. pvs_le_gap_sum_source_equaldomain + (dm_index_sum_source_equal) = (n)) -> (exists dst_positive_code_sum_source_equalfirst dst_positive_scale_sum_source_equalfirst dst_negative_code_sum_source_equalfirst dst_negative_scale_sum_source_equalfirst dst_positive_sum_source_equalfirst dst_negative_sum_source_equalfirst. (((F) = (((((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) * S ((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) + ((dst_positive_scale_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst))) + (((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)))) * S ((((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) * S ((dst_positive_code_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst)) + ((dst_positive_scale_sum_source_equalfirst) + (dst_positive_scale_sum_source_equalfirst))) + (((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)))) + ((((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst))) + (((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) * S ((dst_negative_code_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)) + ((dst_negative_scale_sum_source_equalfirst) + (dst_negative_scale_sum_source_equalfirst)))))) /\ (((((exists ff_h_pvs_sum_source_equalfirstpositive. ff_h_pvs_sum_source_equalfirstpositive + S (dst_positive_sum_source_equalfirst) = S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalfirst)) /\ exists ff_q_pvs_sum_source_equalfirstpositive. dst_positive_code_sum_source_equalfirst = ff_q_pvs_sum_source_equalfirstpositive * S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalfirst) + (dst_positive_sum_source_equalfirst))) /\ (((((exists ff_h_pvs_sum_source_equalfirstnegative. ff_h_pvs_sum_source_equalfirstnegative + S (dst_negative_sum_source_equalfirst) = S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalfirst)) /\ exists ff_q_pvs_sum_source_equalfirstnegative. dst_negative_code_sum_source_equalfirst = ff_q_pvs_sum_source_equalfirstnegative * S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalfirst) + (dst_negative_sum_source_equalfirst))) /\ (exists ge_balance_positive_sum_source_equalfirstvalue ge_balance_negative_sum_source_equalfirstvalue. (((((dm_first_value_sum_source_equal) = 2 * (ge_balance_positive_sum_source_equalfirstvalue) /\ (ge_balance_negative_sum_source_equalfirstvalue) = 0) \/ exists ge_signed_half_sum_source_equalfirstvaluedecode. (((dm_first_value_sum_source_equal) = 2 * ge_signed_half_sum_source_equalfirstvaluedecode + 1 /\ (ge_balance_positive_sum_source_equalfirstvalue) = 0) /\ (ge_balance_negative_sum_source_equalfirstvalue) = S ge_signed_half_sum_source_equalfirstvaluedecode))) /\ ((dst_positive_sum_source_equalfirst) + ge_balance_negative_sum_source_equalfirstvalue = (dst_negative_sum_source_equalfirst) + ge_balance_positive_sum_source_equalfirstvalue))))))))) -> (exists dst_positive_code_sum_source_equalsecond dst_positive_scale_sum_source_equalsecond dst_negative_code_sum_source_equalsecond dst_negative_scale_sum_source_equalsecond dst_positive_sum_source_equalsecond dst_negative_sum_source_equalsecond. (((G) = (((((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) * S ((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) + ((dst_positive_scale_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond))) + (((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)))) * S ((((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) * S ((dst_positive_code_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond)) + ((dst_positive_scale_sum_source_equalsecond) + (dst_positive_scale_sum_source_equalsecond))) + (((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)))) + ((((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond))) + (((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) * S ((dst_negative_code_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)) + ((dst_negative_scale_sum_source_equalsecond) + (dst_negative_scale_sum_source_equalsecond)))))) /\ (((((exists ff_h_pvs_sum_source_equalsecondpositive. ff_h_pvs_sum_source_equalsecondpositive + S (dst_positive_sum_source_equalsecond) = S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalsecond)) /\ exists ff_q_pvs_sum_source_equalsecondpositive. dst_positive_code_sum_source_equalsecond = ff_q_pvs_sum_source_equalsecondpositive * S ((S (dm_index_sum_source_equal)) * dst_positive_scale_sum_source_equalsecond) + (dst_positive_sum_source_equalsecond))) /\ (((((exists ff_h_pvs_sum_source_equalsecondnegative. ff_h_pvs_sum_source_equalsecondnegative + S (dst_negative_sum_source_equalsecond) = S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalsecond)) /\ exists ff_q_pvs_sum_source_equalsecondnegative. dst_negative_code_sum_source_equalsecond = ff_q_pvs_sum_source_equalsecondnegative * S ((S (dm_index_sum_source_equal)) * dst_negative_scale_sum_source_equalsecond) + (dst_negative_sum_source_equalsecond))) /\ (exists ge_balance_positive_sum_source_equalsecondvalue ge_balance_negative_sum_source_equalsecondvalue. (((((dm_second_value_sum_source_equal) = 2 * (ge_balance_positive_sum_source_equalsecondvalue) /\ (ge_balance_negative_sum_source_equalsecondvalue) = 0) \/ exists ge_signed_half_sum_source_equalsecondvaluedecode. (((dm_second_value_sum_source_equal) = 2 * ge_signed_half_sum_source_equalsecondvaluedecode + 1 /\ (ge_balance_positive_sum_source_equalsecondvalue) = 0) /\ (ge_balance_negative_sum_source_equalsecondvalue) = S ge_signed_half_sum_source_equalsecondvaluedecode))) /\ ((dst_positive_sum_source_equalsecond) + ge_balance_negative_sum_source_equalsecondvalue = (dst_negative_sum_source_equalsecond) + ge_balance_positive_sum_source_equalsecondvalue))))))))) -> dm_first_value_sum_source_equal=dm_second_value_sum_source_equal) -> (((~((n)=0)) /\ (exists dm_mask_table_sum_source_first. ((((exists dst_positive_code_sum_source_firstmasktable dst_positive_scale_sum_source_firstmasktable dst_negative_code_sum_source_firstmasktable dst_negative_scale_sum_source_firstmasktable. (((dm_mask_table_sum_source_first) = (((((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) * S ((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) + ((dst_positive_scale_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable))) + (((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)))) * S ((((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) * S ((dst_positive_code_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable)) + ((dst_positive_scale_sum_source_firstmasktable) + (dst_positive_scale_sum_source_firstmasktable))) + (((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)))) + ((((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable))) + (((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) * S ((dst_negative_code_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)) + ((dst_negative_scale_sum_source_firstmasktable) + (dst_negative_scale_sum_source_firstmasktable)))))) /\ (forall dst_index_sum_source_firstmasktable. (exists pvs_le_gap_sum_source_firstmasktabledomain. pvs_le_gap_sum_source_firstmasktabledomain + (dst_index_sum_source_firstmasktable) = (n)) -> exists dst_positive_sum_source_firstmasktable dst_negative_sum_source_firstmasktable dst_value_sum_source_firstmasktable. ((((exists ff_h_pvs_sum_source_firstmasktableentrypositive. ff_h_pvs_sum_source_firstmasktableentrypositive + S (dst_positive_sum_source_firstmasktable) = S ((S (dst_index_sum_source_firstmasktable)) * dst_positive_scale_sum_source_firstmasktable)) /\ exists ff_q_pvs_sum_source_firstmasktableentrypositive. dst_positive_code_sum_source_firstmasktable = ff_q_pvs_sum_source_firstmasktableentrypositive * S ((S (dst_index_sum_source_firstmasktable)) * dst_positive_scale_sum_source_firstmasktable) + (dst_positive_sum_source_firstmasktable))) /\ (((((exists ff_h_pvs_sum_source_firstmasktableentrynegative. ff_h_pvs_sum_source_firstmasktableentrynegative + S (dst_negative_sum_source_firstmasktable) = S ((S (dst_index_sum_source_firstmasktable)) * dst_negative_scale_sum_source_firstmasktable)) /\ exists ff_q_pvs_sum_source_firstmasktableentrynegative. dst_negative_code_sum_source_firstmasktable = ff_q_pvs_sum_source_firstmasktableentrynegative * S ((S (dst_index_sum_source_firstmasktable)) * dst_negative_scale_sum_source_firstmasktable) + (dst_negative_sum_source_firstmasktable))) /\ (exists ge_balance_positive_sum_source_firstmasktableentryvalue ge_balance_negative_sum_source_firstmasktableentryvalue. (((((dst_value_sum_source_firstmasktable) = 2 * (ge_balance_positive_sum_source_firstmasktableentryvalue) /\ (ge_balance_negative_sum_source_firstmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_source_firstmasktableentryvaluedecode. (((dst_value_sum_source_firstmasktable) = 2 * ge_signed_half_sum_source_firstmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_source_firstmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_source_firstmasktableentryvalue) = S ge_signed_half_sum_source_firstmasktableentryvaluedecode))) /\ ((dst_positive_sum_source_firstmasktable) + ge_balance_negative_sum_source_firstmasktableentryvalue = (dst_negative_sum_source_firstmasktable) + ge_balance_positive_sum_source_firstmasktableentryvalue))))))))) /\ (forall dm_index_sum_source_firstmask dm_value_sum_source_firstmask. (exists pvs_le_gap_sum_source_firstmaskdomain. pvs_le_gap_sum_source_firstmaskdomain + (dm_index_sum_source_firstmask) = (n)) -> (exists dst_positive_code_sum_source_firstmasklookup dst_positive_scale_sum_source_firstmasklookup dst_negative_code_sum_source_firstmasklookup dst_negative_scale_sum_source_firstmasklookup dst_positive_sum_source_firstmasklookup dst_negative_sum_source_firstmasklookup. (((dm_mask_table_sum_source_first) = (((((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) * S ((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) + ((dst_positive_scale_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup))) + (((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)))) * S ((((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) * S ((dst_positive_code_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup)) + ((dst_positive_scale_sum_source_firstmasklookup) + (dst_positive_scale_sum_source_firstmasklookup))) + (((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)))) + ((((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup))) + (((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) * S ((dst_negative_code_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)) + ((dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_scale_sum_source_firstmasklookup)))))) /\ (((((exists ff_h_pvs_sum_source_firstmasklookuppositive. ff_h_pvs_sum_source_firstmasklookuppositive + S (dst_positive_sum_source_firstmasklookup) = S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmasklookup)) /\ exists ff_q_pvs_sum_source_firstmasklookuppositive. dst_positive_code_sum_source_firstmasklookup = ff_q_pvs_sum_source_firstmasklookuppositive * S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmasklookup) + (dst_positive_sum_source_firstmasklookup))) /\ (((((exists ff_h_pvs_sum_source_firstmasklookupnegative. ff_h_pvs_sum_source_firstmasklookupnegative + S (dst_negative_sum_source_firstmasklookup) = S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmasklookup)) /\ exists ff_q_pvs_sum_source_firstmasklookupnegative. dst_negative_code_sum_source_firstmasklookup = ff_q_pvs_sum_source_firstmasklookupnegative * S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmasklookup) + (dst_negative_sum_source_firstmasklookup))) /\ (exists ge_balance_positive_sum_source_firstmasklookupvalue ge_balance_negative_sum_source_firstmasklookupvalue. (((((dm_value_sum_source_firstmask) = 2 * (ge_balance_positive_sum_source_firstmasklookupvalue) /\ (ge_balance_negative_sum_source_firstmasklookupvalue) = 0) \/ exists ge_signed_half_sum_source_firstmasklookupvaluedecode. (((dm_value_sum_source_firstmask) = 2 * ge_signed_half_sum_source_firstmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_source_firstmasklookupvalue) = 0) /\ (ge_balance_negative_sum_source_firstmasklookupvalue) = S ge_signed_half_sum_source_firstmasklookupvaluedecode))) /\ ((dst_positive_sum_source_firstmasklookup) + ge_balance_negative_sum_source_firstmasklookupvalue = (dst_negative_sum_source_firstmasklookup) + ge_balance_positive_sum_source_firstmasklookupvalue))))))))) -> ((((~((dm_index_sum_source_firstmask)=0)) /\ (exists dm_quotient_sum_source_firstmaskentry. (((n)=(dm_index_sum_source_firstmask)*dm_quotient_sum_source_firstmaskentry) /\ (exists dst_positive_code_sum_source_firstmaskentryinput dst_positive_scale_sum_source_firstmaskentryinput dst_negative_code_sum_source_firstmaskentryinput dst_negative_scale_sum_source_firstmaskentryinput dst_positive_sum_source_firstmaskentryinput dst_negative_sum_source_firstmaskentryinput. (((F) = (((((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) * S ((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) + ((dst_positive_scale_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput))) + (((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)))) * S ((((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) * S ((dst_positive_code_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput)) + ((dst_positive_scale_sum_source_firstmaskentryinput) + (dst_positive_scale_sum_source_firstmaskentryinput))) + (((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)))) + ((((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput))) + (((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) * S ((dst_negative_code_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)) + ((dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_scale_sum_source_firstmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_source_firstmaskentryinputpositive. ff_h_pvs_sum_source_firstmaskentryinputpositive + S (dst_positive_sum_source_firstmaskentryinput) = S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmaskentryinput)) /\ exists ff_q_pvs_sum_source_firstmaskentryinputpositive. dst_positive_code_sum_source_firstmaskentryinput = ff_q_pvs_sum_source_firstmaskentryinputpositive * S ((S (dm_index_sum_source_firstmask)) * dst_positive_scale_sum_source_firstmaskentryinput) + (dst_positive_sum_source_firstmaskentryinput))) /\ (((((exists ff_h_pvs_sum_source_firstmaskentryinputnegative. ff_h_pvs_sum_source_firstmaskentryinputnegative + S (dst_negative_sum_source_firstmaskentryinput) = S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmaskentryinput)) /\ exists ff_q_pvs_sum_source_firstmaskentryinputnegative. dst_negative_code_sum_source_firstmaskentryinput = ff_q_pvs_sum_source_firstmaskentryinputnegative * S ((S (dm_index_sum_source_firstmask)) * dst_negative_scale_sum_source_firstmaskentryinput) + (dst_negative_sum_source_firstmaskentryinput))) /\ (exists ge_balance_positive_sum_source_firstmaskentryinputvalue ge_balance_negative_sum_source_firstmaskentryinputvalue. (((((dm_value_sum_source_firstmask) = 2 * (ge_balance_positive_sum_source_firstmaskentryinputvalue) /\ (ge_balance_negative_sum_source_firstmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_source_firstmaskentryinputvaluedecode. (((dm_value_sum_source_firstmask) = 2 * ge_signed_half_sum_source_firstmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_source_firstmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_source_firstmaskentryinputvalue) = S ge_signed_half_sum_source_firstmaskentryinputvaluedecode))) /\ ((dst_positive_sum_source_firstmaskentryinput) + ge_balance_negative_sum_source_firstmaskentryinputvalue = (dst_negative_sum_source_firstmaskentryinput) + ge_balance_positive_sum_source_firstmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_source_firstmask)=0 \/ ~(exists pvs_factor_sum_source_firstmaskentrynondivisor. (n) = (dm_index_sum_source_firstmask) * pvs_factor_sum_source_firstmaskentrynondivisor)) /\ ((dm_value_sum_source_firstmask)=0))))))) /\ (exists dst_positive_code_sum_source_firstfold dst_positive_scale_sum_source_firstfold dst_negative_code_sum_source_firstfold dst_negative_scale_sum_source_firstfold dst_positive_sum_sum_source_firstfold dst_negative_sum_sum_source_firstfold. (((dm_mask_table_sum_source_first) = (((((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) * S ((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) + ((dst_positive_scale_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold))) + (((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)))) * S ((((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) * S ((dst_positive_code_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold)) + ((dst_positive_scale_sum_source_firstfold) + (dst_positive_scale_sum_source_firstfold))) + (((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)))) + ((((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold))) + (((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) * S ((dst_negative_code_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)) + ((dst_negative_scale_sum_source_firstfold) + (dst_negative_scale_sum_source_firstfold)))))) /\ (((exists fs_u_dst_sum_source_firstfoldpositive fs_v_dst_sum_source_firstfoldpositive. ((((exists fs_h_dst_sum_source_firstfoldpositive_body_start. fs_h_dst_sum_source_firstfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_start. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_source_firstfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_source_firstfoldpositive_body_terminal. fs_h_dst_sum_source_firstfoldpositive_body_terminal + S (dst_positive_sum_sum_source_firstfold) = S ((S (S (n))) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_terminal. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_firstfoldpositive) + (dst_positive_sum_sum_source_firstfold))) /\ forall fs_i_dst_sum_source_firstfoldpositive_body_steps. (exists fs_lt_dst_sum_source_firstfoldpositive_body_steps_bound. fs_lt_dst_sum_source_firstfoldpositive_body_steps_bound + S fs_i_dst_sum_source_firstfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_source_firstfoldpositive_body_steps fs_r_dst_sum_source_firstfoldpositive_body_steps fs_s_dst_sum_source_firstfoldpositive_body_steps. ((((exists fs_h_dst_sum_source_firstfoldpositive_body_steps_summand. fs_h_dst_sum_source_firstfoldpositive_body_steps_summand + S (fs_a_dst_sum_source_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * dst_positive_scale_sum_source_firstfold)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_steps_summand. dst_positive_code_sum_source_firstfold = fs_q_dst_sum_source_firstfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * dst_positive_scale_sum_source_firstfold) + (fs_a_dst_sum_source_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldpositive_body_steps_partial. fs_h_dst_sum_source_firstfoldpositive_body_steps_partial + S (fs_r_dst_sum_source_firstfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_steps_partial. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive) + (fs_r_dst_sum_source_firstfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldpositive_body_steps_successor. fs_h_dst_sum_source_firstfoldpositive_body_steps_successor + S (fs_s_dst_sum_source_firstfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive)) /\ exists fs_q_dst_sum_source_firstfoldpositive_body_steps_successor. fs_u_dst_sum_source_firstfoldpositive = fs_q_dst_sum_source_firstfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_source_firstfoldpositive_body_steps)) * fs_v_dst_sum_source_firstfoldpositive) + (fs_s_dst_sum_source_firstfoldpositive_body_steps))) /\ fs_s_dst_sum_source_firstfoldpositive_body_steps = fs_r_dst_sum_source_firstfoldpositive_body_steps + fs_a_dst_sum_source_firstfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_source_firstfoldnegative fs_v_dst_sum_source_firstfoldnegative. ((((exists fs_h_dst_sum_source_firstfoldnegative_body_start. fs_h_dst_sum_source_firstfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_start. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_source_firstfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_source_firstfoldnegative_body_terminal. fs_h_dst_sum_source_firstfoldnegative_body_terminal + S (dst_negative_sum_sum_source_firstfold) = S ((S (S (n))) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_terminal. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_firstfoldnegative) + (dst_negative_sum_sum_source_firstfold))) /\ forall fs_i_dst_sum_source_firstfoldnegative_body_steps. (exists fs_lt_dst_sum_source_firstfoldnegative_body_steps_bound. fs_lt_dst_sum_source_firstfoldnegative_body_steps_bound + S fs_i_dst_sum_source_firstfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_source_firstfoldnegative_body_steps fs_r_dst_sum_source_firstfoldnegative_body_steps fs_s_dst_sum_source_firstfoldnegative_body_steps. ((((exists fs_h_dst_sum_source_firstfoldnegative_body_steps_summand. fs_h_dst_sum_source_firstfoldnegative_body_steps_summand + S (fs_a_dst_sum_source_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * dst_negative_scale_sum_source_firstfold)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_steps_summand. dst_negative_code_sum_source_firstfold = fs_q_dst_sum_source_firstfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * dst_negative_scale_sum_source_firstfold) + (fs_a_dst_sum_source_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldnegative_body_steps_partial. fs_h_dst_sum_source_firstfoldnegative_body_steps_partial + S (fs_r_dst_sum_source_firstfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_steps_partial. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative) + (fs_r_dst_sum_source_firstfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_firstfoldnegative_body_steps_successor. fs_h_dst_sum_source_firstfoldnegative_body_steps_successor + S (fs_s_dst_sum_source_firstfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative)) /\ exists fs_q_dst_sum_source_firstfoldnegative_body_steps_successor. fs_u_dst_sum_source_firstfoldnegative = fs_q_dst_sum_source_firstfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_source_firstfoldnegative_body_steps)) * fs_v_dst_sum_source_firstfoldnegative) + (fs_s_dst_sum_source_firstfoldnegative_body_steps))) /\ fs_s_dst_sum_source_firstfoldnegative_body_steps = fs_r_dst_sum_source_firstfoldnegative_body_steps + fs_a_dst_sum_source_firstfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_source_firstfoldresult ge_balance_negative_sum_source_firstfoldresult. (((((a) = 2 * (ge_balance_positive_sum_source_firstfoldresult) /\ (ge_balance_negative_sum_source_firstfoldresult) = 0) \/ exists ge_signed_half_sum_source_firstfoldresultdecode. (((a) = 2 * ge_signed_half_sum_source_firstfoldresultdecode + 1 /\ (ge_balance_positive_sum_source_firstfoldresult) = 0) /\ (ge_balance_negative_sum_source_firstfoldresult) = S ge_signed_half_sum_source_firstfoldresultdecode))) /\ ((dst_positive_sum_sum_source_firstfold) + ge_balance_negative_sum_source_firstfoldresult = (dst_negative_sum_sum_source_firstfold) + ge_balance_positive_sum_source_firstfoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dm_mask_table_sum_source_second. ((((exists dst_positive_code_sum_source_secondmasktable dst_positive_scale_sum_source_secondmasktable dst_negative_code_sum_source_secondmasktable dst_negative_scale_sum_source_secondmasktable. (((dm_mask_table_sum_source_second) = (((((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) * S ((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) + ((dst_positive_scale_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable))) + (((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)))) * S ((((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) * S ((dst_positive_code_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable)) + ((dst_positive_scale_sum_source_secondmasktable) + (dst_positive_scale_sum_source_secondmasktable))) + (((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)))) + ((((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable))) + (((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) * S ((dst_negative_code_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)) + ((dst_negative_scale_sum_source_secondmasktable) + (dst_negative_scale_sum_source_secondmasktable)))))) /\ (forall dst_index_sum_source_secondmasktable. (exists pvs_le_gap_sum_source_secondmasktabledomain. pvs_le_gap_sum_source_secondmasktabledomain + (dst_index_sum_source_secondmasktable) = (n)) -> exists dst_positive_sum_source_secondmasktable dst_negative_sum_source_secondmasktable dst_value_sum_source_secondmasktable. ((((exists ff_h_pvs_sum_source_secondmasktableentrypositive. ff_h_pvs_sum_source_secondmasktableentrypositive + S (dst_positive_sum_source_secondmasktable) = S ((S (dst_index_sum_source_secondmasktable)) * dst_positive_scale_sum_source_secondmasktable)) /\ exists ff_q_pvs_sum_source_secondmasktableentrypositive. dst_positive_code_sum_source_secondmasktable = ff_q_pvs_sum_source_secondmasktableentrypositive * S ((S (dst_index_sum_source_secondmasktable)) * dst_positive_scale_sum_source_secondmasktable) + (dst_positive_sum_source_secondmasktable))) /\ (((((exists ff_h_pvs_sum_source_secondmasktableentrynegative. ff_h_pvs_sum_source_secondmasktableentrynegative + S (dst_negative_sum_source_secondmasktable) = S ((S (dst_index_sum_source_secondmasktable)) * dst_negative_scale_sum_source_secondmasktable)) /\ exists ff_q_pvs_sum_source_secondmasktableentrynegative. dst_negative_code_sum_source_secondmasktable = ff_q_pvs_sum_source_secondmasktableentrynegative * S ((S (dst_index_sum_source_secondmasktable)) * dst_negative_scale_sum_source_secondmasktable) + (dst_negative_sum_source_secondmasktable))) /\ (exists ge_balance_positive_sum_source_secondmasktableentryvalue ge_balance_negative_sum_source_secondmasktableentryvalue. (((((dst_value_sum_source_secondmasktable) = 2 * (ge_balance_positive_sum_source_secondmasktableentryvalue) /\ (ge_balance_negative_sum_source_secondmasktableentryvalue) = 0) \/ exists ge_signed_half_sum_source_secondmasktableentryvaluedecode. (((dst_value_sum_source_secondmasktable) = 2 * ge_signed_half_sum_source_secondmasktableentryvaluedecode + 1 /\ (ge_balance_positive_sum_source_secondmasktableentryvalue) = 0) /\ (ge_balance_negative_sum_source_secondmasktableentryvalue) = S ge_signed_half_sum_source_secondmasktableentryvaluedecode))) /\ ((dst_positive_sum_source_secondmasktable) + ge_balance_negative_sum_source_secondmasktableentryvalue = (dst_negative_sum_source_secondmasktable) + ge_balance_positive_sum_source_secondmasktableentryvalue))))))))) /\ (forall dm_index_sum_source_secondmask dm_value_sum_source_secondmask. (exists pvs_le_gap_sum_source_secondmaskdomain. pvs_le_gap_sum_source_secondmaskdomain + (dm_index_sum_source_secondmask) = (n)) -> (exists dst_positive_code_sum_source_secondmasklookup dst_positive_scale_sum_source_secondmasklookup dst_negative_code_sum_source_secondmasklookup dst_negative_scale_sum_source_secondmasklookup dst_positive_sum_source_secondmasklookup dst_negative_sum_source_secondmasklookup. (((dm_mask_table_sum_source_second) = (((((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) * S ((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) + ((dst_positive_scale_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup))) + (((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)))) * S ((((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) * S ((dst_positive_code_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup)) + ((dst_positive_scale_sum_source_secondmasklookup) + (dst_positive_scale_sum_source_secondmasklookup))) + (((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)))) + ((((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup))) + (((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) * S ((dst_negative_code_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)) + ((dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_scale_sum_source_secondmasklookup)))))) /\ (((((exists ff_h_pvs_sum_source_secondmasklookuppositive. ff_h_pvs_sum_source_secondmasklookuppositive + S (dst_positive_sum_source_secondmasklookup) = S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmasklookup)) /\ exists ff_q_pvs_sum_source_secondmasklookuppositive. dst_positive_code_sum_source_secondmasklookup = ff_q_pvs_sum_source_secondmasklookuppositive * S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmasklookup) + (dst_positive_sum_source_secondmasklookup))) /\ (((((exists ff_h_pvs_sum_source_secondmasklookupnegative. ff_h_pvs_sum_source_secondmasklookupnegative + S (dst_negative_sum_source_secondmasklookup) = S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmasklookup)) /\ exists ff_q_pvs_sum_source_secondmasklookupnegative. dst_negative_code_sum_source_secondmasklookup = ff_q_pvs_sum_source_secondmasklookupnegative * S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmasklookup) + (dst_negative_sum_source_secondmasklookup))) /\ (exists ge_balance_positive_sum_source_secondmasklookupvalue ge_balance_negative_sum_source_secondmasklookupvalue. (((((dm_value_sum_source_secondmask) = 2 * (ge_balance_positive_sum_source_secondmasklookupvalue) /\ (ge_balance_negative_sum_source_secondmasklookupvalue) = 0) \/ exists ge_signed_half_sum_source_secondmasklookupvaluedecode. (((dm_value_sum_source_secondmask) = 2 * ge_signed_half_sum_source_secondmasklookupvaluedecode + 1 /\ (ge_balance_positive_sum_source_secondmasklookupvalue) = 0) /\ (ge_balance_negative_sum_source_secondmasklookupvalue) = S ge_signed_half_sum_source_secondmasklookupvaluedecode))) /\ ((dst_positive_sum_source_secondmasklookup) + ge_balance_negative_sum_source_secondmasklookupvalue = (dst_negative_sum_source_secondmasklookup) + ge_balance_positive_sum_source_secondmasklookupvalue))))))))) -> ((((~((dm_index_sum_source_secondmask)=0)) /\ (exists dm_quotient_sum_source_secondmaskentry. (((n)=(dm_index_sum_source_secondmask)*dm_quotient_sum_source_secondmaskentry) /\ (exists dst_positive_code_sum_source_secondmaskentryinput dst_positive_scale_sum_source_secondmaskentryinput dst_negative_code_sum_source_secondmaskentryinput dst_negative_scale_sum_source_secondmaskentryinput dst_positive_sum_source_secondmaskentryinput dst_negative_sum_source_secondmaskentryinput. (((G) = (((((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) * S ((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) + ((dst_positive_scale_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput))) + (((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)))) * S ((((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) * S ((dst_positive_code_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput)) + ((dst_positive_scale_sum_source_secondmaskentryinput) + (dst_positive_scale_sum_source_secondmaskentryinput))) + (((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)))) + ((((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput))) + (((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) * S ((dst_negative_code_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)) + ((dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_scale_sum_source_secondmaskentryinput)))))) /\ (((((exists ff_h_pvs_sum_source_secondmaskentryinputpositive. ff_h_pvs_sum_source_secondmaskentryinputpositive + S (dst_positive_sum_source_secondmaskentryinput) = S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmaskentryinput)) /\ exists ff_q_pvs_sum_source_secondmaskentryinputpositive. dst_positive_code_sum_source_secondmaskentryinput = ff_q_pvs_sum_source_secondmaskentryinputpositive * S ((S (dm_index_sum_source_secondmask)) * dst_positive_scale_sum_source_secondmaskentryinput) + (dst_positive_sum_source_secondmaskentryinput))) /\ (((((exists ff_h_pvs_sum_source_secondmaskentryinputnegative. ff_h_pvs_sum_source_secondmaskentryinputnegative + S (dst_negative_sum_source_secondmaskentryinput) = S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmaskentryinput)) /\ exists ff_q_pvs_sum_source_secondmaskentryinputnegative. dst_negative_code_sum_source_secondmaskentryinput = ff_q_pvs_sum_source_secondmaskentryinputnegative * S ((S (dm_index_sum_source_secondmask)) * dst_negative_scale_sum_source_secondmaskentryinput) + (dst_negative_sum_source_secondmaskentryinput))) /\ (exists ge_balance_positive_sum_source_secondmaskentryinputvalue ge_balance_negative_sum_source_secondmaskentryinputvalue. (((((dm_value_sum_source_secondmask) = 2 * (ge_balance_positive_sum_source_secondmaskentryinputvalue) /\ (ge_balance_negative_sum_source_secondmaskentryinputvalue) = 0) \/ exists ge_signed_half_sum_source_secondmaskentryinputvaluedecode. (((dm_value_sum_source_secondmask) = 2 * ge_signed_half_sum_source_secondmaskentryinputvaluedecode + 1 /\ (ge_balance_positive_sum_source_secondmaskentryinputvalue) = 0) /\ (ge_balance_negative_sum_source_secondmaskentryinputvalue) = S ge_signed_half_sum_source_secondmaskentryinputvaluedecode))) /\ ((dst_positive_sum_source_secondmaskentryinput) + ge_balance_negative_sum_source_secondmaskentryinputvalue = (dst_negative_sum_source_secondmaskentryinput) + ge_balance_positive_sum_source_secondmaskentryinputvalue))))))))))))) \/ ((((dm_index_sum_source_secondmask)=0 \/ ~(exists pvs_factor_sum_source_secondmaskentrynondivisor. (n) = (dm_index_sum_source_secondmask) * pvs_factor_sum_source_secondmaskentrynondivisor)) /\ ((dm_value_sum_source_secondmask)=0))))))) /\ (exists dst_positive_code_sum_source_secondfold dst_positive_scale_sum_source_secondfold dst_negative_code_sum_source_secondfold dst_negative_scale_sum_source_secondfold dst_positive_sum_sum_source_secondfold dst_negative_sum_sum_source_secondfold. (((dm_mask_table_sum_source_second) = (((((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) * S ((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) + ((dst_positive_scale_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold))) + (((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)))) * S ((((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) * S ((dst_positive_code_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold)) + ((dst_positive_scale_sum_source_secondfold) + (dst_positive_scale_sum_source_secondfold))) + (((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)))) + ((((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold))) + (((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) * S ((dst_negative_code_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)) + ((dst_negative_scale_sum_source_secondfold) + (dst_negative_scale_sum_source_secondfold)))))) /\ (((exists fs_u_dst_sum_source_secondfoldpositive fs_v_dst_sum_source_secondfoldpositive. ((((exists fs_h_dst_sum_source_secondfoldpositive_body_start. fs_h_dst_sum_source_secondfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_start. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_start * S ((S (0)) * fs_v_dst_sum_source_secondfoldpositive) + (0))) /\ ((((exists fs_h_dst_sum_source_secondfoldpositive_body_terminal. fs_h_dst_sum_source_secondfoldpositive_body_terminal + S (dst_positive_sum_sum_source_secondfold) = S ((S (S (n))) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_terminal. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_secondfoldpositive) + (dst_positive_sum_sum_source_secondfold))) /\ forall fs_i_dst_sum_source_secondfoldpositive_body_steps. (exists fs_lt_dst_sum_source_secondfoldpositive_body_steps_bound. fs_lt_dst_sum_source_secondfoldpositive_body_steps_bound + S fs_i_dst_sum_source_secondfoldpositive_body_steps = S (n)) -> exists fs_a_dst_sum_source_secondfoldpositive_body_steps fs_r_dst_sum_source_secondfoldpositive_body_steps fs_s_dst_sum_source_secondfoldpositive_body_steps. ((((exists fs_h_dst_sum_source_secondfoldpositive_body_steps_summand. fs_h_dst_sum_source_secondfoldpositive_body_steps_summand + S (fs_a_dst_sum_source_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * dst_positive_scale_sum_source_secondfold)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_steps_summand. dst_positive_code_sum_source_secondfold = fs_q_dst_sum_source_secondfoldpositive_body_steps_summand * S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * dst_positive_scale_sum_source_secondfold) + (fs_a_dst_sum_source_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldpositive_body_steps_partial. fs_h_dst_sum_source_secondfoldpositive_body_steps_partial + S (fs_r_dst_sum_source_secondfoldpositive_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_steps_partial. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_steps_partial * S ((S (fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive) + (fs_r_dst_sum_source_secondfoldpositive_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldpositive_body_steps_successor. fs_h_dst_sum_source_secondfoldpositive_body_steps_successor + S (fs_s_dst_sum_source_secondfoldpositive_body_steps) = S ((S (S fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive)) /\ exists fs_q_dst_sum_source_secondfoldpositive_body_steps_successor. fs_u_dst_sum_source_secondfoldpositive = fs_q_dst_sum_source_secondfoldpositive_body_steps_successor * S ((S (S fs_i_dst_sum_source_secondfoldpositive_body_steps)) * fs_v_dst_sum_source_secondfoldpositive) + (fs_s_dst_sum_source_secondfoldpositive_body_steps))) /\ fs_s_dst_sum_source_secondfoldpositive_body_steps = fs_r_dst_sum_source_secondfoldpositive_body_steps + fs_a_dst_sum_source_secondfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_sum_source_secondfoldnegative fs_v_dst_sum_source_secondfoldnegative. ((((exists fs_h_dst_sum_source_secondfoldnegative_body_start. fs_h_dst_sum_source_secondfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_start. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_start * S ((S (0)) * fs_v_dst_sum_source_secondfoldnegative) + (0))) /\ ((((exists fs_h_dst_sum_source_secondfoldnegative_body_terminal. fs_h_dst_sum_source_secondfoldnegative_body_terminal + S (dst_negative_sum_sum_source_secondfold) = S ((S (S (n))) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_terminal. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_sum_source_secondfoldnegative) + (dst_negative_sum_sum_source_secondfold))) /\ forall fs_i_dst_sum_source_secondfoldnegative_body_steps. (exists fs_lt_dst_sum_source_secondfoldnegative_body_steps_bound. fs_lt_dst_sum_source_secondfoldnegative_body_steps_bound + S fs_i_dst_sum_source_secondfoldnegative_body_steps = S (n)) -> exists fs_a_dst_sum_source_secondfoldnegative_body_steps fs_r_dst_sum_source_secondfoldnegative_body_steps fs_s_dst_sum_source_secondfoldnegative_body_steps. ((((exists fs_h_dst_sum_source_secondfoldnegative_body_steps_summand. fs_h_dst_sum_source_secondfoldnegative_body_steps_summand + S (fs_a_dst_sum_source_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * dst_negative_scale_sum_source_secondfold)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_steps_summand. dst_negative_code_sum_source_secondfold = fs_q_dst_sum_source_secondfoldnegative_body_steps_summand * S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * dst_negative_scale_sum_source_secondfold) + (fs_a_dst_sum_source_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldnegative_body_steps_partial. fs_h_dst_sum_source_secondfoldnegative_body_steps_partial + S (fs_r_dst_sum_source_secondfoldnegative_body_steps) = S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_steps_partial. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_steps_partial * S ((S (fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative) + (fs_r_dst_sum_source_secondfoldnegative_body_steps))) /\ ((((exists fs_h_dst_sum_source_secondfoldnegative_body_steps_successor. fs_h_dst_sum_source_secondfoldnegative_body_steps_successor + S (fs_s_dst_sum_source_secondfoldnegative_body_steps) = S ((S (S fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative)) /\ exists fs_q_dst_sum_source_secondfoldnegative_body_steps_successor. fs_u_dst_sum_source_secondfoldnegative = fs_q_dst_sum_source_secondfoldnegative_body_steps_successor * S ((S (S fs_i_dst_sum_source_secondfoldnegative_body_steps)) * fs_v_dst_sum_source_secondfoldnegative) + (fs_s_dst_sum_source_secondfoldnegative_body_steps))) /\ fs_s_dst_sum_source_secondfoldnegative_body_steps = fs_r_dst_sum_source_secondfoldnegative_body_steps + fs_a_dst_sum_source_secondfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_sum_source_secondfoldresult ge_balance_negative_sum_source_secondfoldresult. (((((b) = 2 * (ge_balance_positive_sum_source_secondfoldresult) /\ (ge_balance_negative_sum_source_secondfoldresult) = 0) \/ exists ge_signed_half_sum_source_secondfoldresultdecode. (((b) = 2 * ge_signed_half_sum_source_secondfoldresultdecode + 1 /\ (ge_balance_positive_sum_source_secondfoldresult) = 0) /\ (ge_balance_negative_sum_source_secondfoldresult) = S ge_signed_half_sum_source_secondfoldresultdecode))) /\ ((dst_positive_sum_sum_source_secondfold) + ge_balance_negative_sum_source_secondfoldresult = (dst_negative_sum_sum_source_secondfold) + ge_balance_positive_sum_source_secondfoldresult))))))))))))) -> a=b

• signed_negate_functional · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall input output1 output2. (exists sn_pos_functional_left sn_neg_functional_left. (((input = 2 * sn_pos_functional_left /\ sn_neg_functional_left = 0) \/ exists sd_half_functional_left_input. ((input = 2 * sd_half_functional_left_input + 1 /\ sn_pos_functional_left = 0) /\ sn_neg_functional_left = S sd_half_functional_left_input)) /\ ((output1 = 2 * sn_neg_functional_left /\ sn_pos_functional_left = 0) \/ exists sd_half_functional_left_output. ((output1 = 2 * sd_half_functional_left_output + 1 /\ sn_neg_functional_left = 0) /\ sn_pos_functional_left = S sd_half_functional_left_output)))) -> (exists sn_pos_functional_right sn_neg_functional_right. (((input = 2 * sn_pos_functional_right /\ sn_neg_functional_right = 0) \/ exists sd_half_functional_right_input. ((input = 2 * sd_half_functional_right_input + 1 /\ sn_pos_functional_right = 0) /\ sn_neg_functional_right = S sd_half_functional_right_input)) /\ ((output2 = 2 * sn_neg_functional_right /\ sn_pos_functional_right = 0) \/ exists sd_half_functional_right_output. ((output2 = 2 * sd_half_functional_right_output + 1 /\ sn_neg_functional_right = 0) /\ sn_pos_functional_right = S sd_half_functional_right_output)))) -> output1 = output2

• signed_negate_symmetric · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall input output. (exists sn_pos_symmetric_forward sn_neg_symmetric_forward. (((input = 2 * sn_pos_symmetric_forward /\ sn_neg_symmetric_forward = 0) \/ exists sd_half_symmetric_forward_input. ((input = 2 * sd_half_symmetric_forward_input + 1 /\ sn_pos_symmetric_forward = 0) /\ sn_neg_symmetric_forward = S sd_half_symmetric_forward_input)) /\ ((output = 2 * sn_neg_symmetric_forward /\ sn_pos_symmetric_forward = 0) \/ exists sd_half_symmetric_forward_output. ((output = 2 * sd_half_symmetric_forward_output + 1 /\ sn_neg_symmetric_forward = 0) /\ sn_pos_symmetric_forward = S sd_half_symmetric_forward_output)))) -> (exists sn_pos_symmetric_reverse sn_neg_symmetric_reverse. (((output = 2 * sn_pos_symmetric_reverse /\ sn_neg_symmetric_reverse = 0) \/ exists sd_half_symmetric_reverse_input. ((output = 2 * sd_half_symmetric_reverse_input + 1 /\ sn_pos_symmetric_reverse = 0) /\ sn_neg_symmetric_reverse = S sd_half_symmetric_reverse_input)) /\ ((input = 2 * sn_neg_symmetric_reverse /\ sn_pos_symmetric_reverse = 0) \/ exists sd_half_symmetric_reverse_output. ((input = 2 * sd_half_symmetric_reverse_output + 1 /\ sn_neg_symmetric_reverse = 0) /\ sn_pos_symmetric_reverse = S sd_half_symmetric_reverse_output))))

• signed_negate_total · checked inherited prerequisite
  Exact statement in the checked dependency cone

  forall input. exists output. (exists sn_pos_total sn_neg_total. (((input = 2 * sn_pos_total /\ sn_neg_total = 0) \/ exists sd_half_total_input. ((input = 2 * sd_half_total_input + 1 /\ sn_pos_total = 0) /\ sn_neg_total = S sd_half_total_input)) /\ ((output = 2 * sn_neg_total /\ sn_pos_total = 0) \/ exists sd_half_total_output. ((output = 2 * sd_half_total_output + 1 /\ sn_neg_total = 0) /\ sn_pos_total = S sd_half_total_output))))

• signed_negate_zero · checked inherited prerequisite
  Exact statement in the checked dependency cone

  exists sn_pos_zero sn_neg_zero. (((0 = 2 * sn_pos_zero /\ sn_neg_zero = 0) \/ exists sd_half_zero_input. ((0 = 2 * sd_half_zero_input + 1 /\ sn_pos_zero = 0) /\ sn_neg_zero = S sd_half_zero_input)) /\ ((0 = 2 * sn_neg_zero /\ sn_pos_zero = 0) \/ exists sd_half_zero_output. ((0 = 2 * sd_half_zero_output + 1 /\ sn_neg_zero = 0) /\ sn_pos_zero = S sd_half_zero_output)))

• 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