DC0017

dirichlet_convolution_positive_source_transport

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

Construct the comparison fold before transporting an actual convolution value across positive-source equality; zero entries are untouched.

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

Exact expanded first-order arithmetic statement

forall N F G H K n z. (exists dst_positive_code_transport_left dst_positive_scale_transport_left dst_negative_code_transport_left dst_negative_scale_transport_left. (((H) = (((((dst_positive_code_transport_left) + (dst_positive_scale_transport_left)) * S ((dst_positive_code_transport_left) + (dst_positive_scale_transport_left)) + ((dst_positive_scale_transport_left) + (dst_positive_scale_transport_left))) + (((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) * S ((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) + ((dst_negative_scale_transport_left) + (dst_negative_scale_transport_left)))) * S ((((dst_positive_code_transport_left) + (dst_positive_scale_transport_left)) * S ((dst_positive_code_transport_left) + (dst_positive_scale_transport_left)) + ((dst_positive_scale_transport_left) + (dst_positive_scale_transport_left))) + (((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) * S ((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) + ((dst_negative_scale_transport_left) + (dst_negative_scale_transport_left)))) + ((((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) * S ((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) + ((dst_negative_scale_transport_left) + (dst_negative_scale_transport_left))) + (((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) * S ((dst_negative_code_transport_left) + (dst_negative_scale_transport_left)) + ((dst_negative_scale_transport_left) + (dst_negative_scale_transport_left)))))) /\ (forall dst_index_transport_left. (exists pvs_le_gap_transport_leftdomain. pvs_le_gap_transport_leftdomain + (dst_index_transport_left) = (N)) -> exists dst_positive_transport_left dst_negative_transport_left dst_value_transport_left. ((((exists ff_h_pvs_transport_leftentrypositive. ff_h_pvs_transport_leftentrypositive + S (dst_positive_transport_left) = S ((S (dst_index_transport_left)) * dst_positive_scale_transport_left)) /\ exists ff_q_pvs_transport_leftentrypositive. dst_positive_code_transport_left = ff_q_pvs_transport_leftentrypositive * S ((S (dst_index_transport_left)) * dst_positive_scale_transport_left) + (dst_positive_transport_left))) /\ (((((exists ff_h_pvs_transport_leftentrynegative. ff_h_pvs_transport_leftentrynegative + S (dst_negative_transport_left) = S ((S (dst_index_transport_left)) * dst_negative_scale_transport_left)) /\ exists ff_q_pvs_transport_leftentrynegative. dst_negative_code_transport_left = ff_q_pvs_transport_leftentrynegative * S ((S (dst_index_transport_left)) * dst_negative_scale_transport_left) + (dst_negative_transport_left))) /\ (exists ge_balance_positive_transport_leftentryvalue ge_balance_negative_transport_leftentryvalue. (((((dst_value_transport_left) = 2 * (ge_balance_positive_transport_leftentryvalue) /\ (ge_balance_negative_transport_leftentryvalue) = 0) \/ exists ge_signed_half_transport_leftentryvaluedecode. (((dst_value_transport_left) = 2 * ge_signed_half_transport_leftentryvaluedecode + 1 /\ (ge_balance_positive_transport_leftentryvalue) = 0) /\ (ge_balance_negative_transport_leftentryvalue) = S ge_signed_half_transport_leftentryvaluedecode))) /\ ((dst_positive_transport_left) + ge_balance_negative_transport_leftentryvalue = (dst_negative_transport_left) + ge_balance_positive_transport_leftentryvalue))))))))) -> (exists dst_positive_code_transport_right dst_positive_scale_transport_right dst_negative_code_transport_right dst_negative_scale_transport_right. (((K) = (((((dst_positive_code_transport_right) + (dst_positive_scale_transport_right)) * S ((dst_positive_code_transport_right) + (dst_positive_scale_transport_right)) + ((dst_positive_scale_transport_right) + (dst_positive_scale_transport_right))) + (((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) * S ((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) + ((dst_negative_scale_transport_right) + (dst_negative_scale_transport_right)))) * S ((((dst_positive_code_transport_right) + (dst_positive_scale_transport_right)) * S ((dst_positive_code_transport_right) + (dst_positive_scale_transport_right)) + ((dst_positive_scale_transport_right) + (dst_positive_scale_transport_right))) + (((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) * S ((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) + ((dst_negative_scale_transport_right) + (dst_negative_scale_transport_right)))) + ((((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) * S ((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) + ((dst_negative_scale_transport_right) + (dst_negative_scale_transport_right))) + (((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) * S ((dst_negative_code_transport_right) + (dst_negative_scale_transport_right)) + ((dst_negative_scale_transport_right) + (dst_negative_scale_transport_right)))))) /\ (forall dst_index_transport_right. (exists pvs_le_gap_transport_rightdomain. pvs_le_gap_transport_rightdomain + (dst_index_transport_right) = (N)) -> exists dst_positive_transport_right dst_negative_transport_right dst_value_transport_right. ((((exists ff_h_pvs_transport_rightentrypositive. ff_h_pvs_transport_rightentrypositive + S (dst_positive_transport_right) = S ((S (dst_index_transport_right)) * dst_positive_scale_transport_right)) /\ exists ff_q_pvs_transport_rightentrypositive. dst_positive_code_transport_right = ff_q_pvs_transport_rightentrypositive * S ((S (dst_index_transport_right)) * dst_positive_scale_transport_right) + (dst_positive_transport_right))) /\ (((((exists ff_h_pvs_transport_rightentrynegative. ff_h_pvs_transport_rightentrynegative + S (dst_negative_transport_right) = S ((S (dst_index_transport_right)) * dst_negative_scale_transport_right)) /\ exists ff_q_pvs_transport_rightentrynegative. dst_negative_code_transport_right = ff_q_pvs_transport_rightentrynegative * S ((S (dst_index_transport_right)) * dst_negative_scale_transport_right) + (dst_negative_transport_right))) /\ (exists ge_balance_positive_transport_rightentryvalue ge_balance_negative_transport_rightentryvalue. (((((dst_value_transport_right) = 2 * (ge_balance_positive_transport_rightentryvalue) /\ (ge_balance_negative_transport_rightentryvalue) = 0) \/ exists ge_signed_half_transport_rightentryvaluedecode. (((dst_value_transport_right) = 2 * ge_signed_half_transport_rightentryvaluedecode + 1 /\ (ge_balance_positive_transport_rightentryvalue) = 0) /\ (ge_balance_negative_transport_rightentryvalue) = S ge_signed_half_transport_rightentryvaluedecode))) /\ ((dst_positive_transport_right) + ge_balance_negative_transport_rightentryvalue = (dst_negative_transport_right) + ge_balance_positive_transport_rightentryvalue))))))))) -> (exists pvs_le_gap_transport_bound. pvs_le_gap_transport_bound + (n) = (N)) -> (forall dm_index_transport_equal_left dm_first_value_transport_equal_left dm_second_value_transport_equal_left. ~(dm_index_transport_equal_left=0) -> (exists pvs_le_gap_transport_equal_leftdomain. pvs_le_gap_transport_equal_leftdomain + (dm_index_transport_equal_left) = (n)) -> (exists dst_positive_code_transport_equal_leftfirst dst_positive_scale_transport_equal_leftfirst dst_negative_code_transport_equal_leftfirst dst_negative_scale_transport_equal_leftfirst dst_positive_transport_equal_leftfirst dst_negative_transport_equal_leftfirst. (((F) = (((((dst_positive_code_transport_equal_leftfirst) + (dst_positive_scale_transport_equal_leftfirst)) * S ((dst_positive_code_transport_equal_leftfirst) + (dst_positive_scale_transport_equal_leftfirst)) + ((dst_positive_scale_transport_equal_leftfirst) + (dst_positive_scale_transport_equal_leftfirst))) + (((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) * S ((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) + ((dst_negative_scale_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)))) * S ((((dst_positive_code_transport_equal_leftfirst) + (dst_positive_scale_transport_equal_leftfirst)) * S ((dst_positive_code_transport_equal_leftfirst) + (dst_positive_scale_transport_equal_leftfirst)) + ((dst_positive_scale_transport_equal_leftfirst) + (dst_positive_scale_transport_equal_leftfirst))) + (((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) * S ((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) + ((dst_negative_scale_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)))) + ((((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) * S ((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) + ((dst_negative_scale_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst))) + (((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) * S ((dst_negative_code_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)) + ((dst_negative_scale_transport_equal_leftfirst) + (dst_negative_scale_transport_equal_leftfirst)))))) /\ (((((exists ff_h_pvs_transport_equal_leftfirstpositive. ff_h_pvs_transport_equal_leftfirstpositive + S (dst_positive_transport_equal_leftfirst) = S ((S (dm_index_transport_equal_left)) * dst_positive_scale_transport_equal_leftfirst)) /\ exists ff_q_pvs_transport_equal_leftfirstpositive. dst_positive_code_transport_equal_leftfirst = ff_q_pvs_transport_equal_leftfirstpositive * S ((S (dm_index_transport_equal_left)) * dst_positive_scale_transport_equal_leftfirst) + (dst_positive_transport_equal_leftfirst))) /\ (((((exists ff_h_pvs_transport_equal_leftfirstnegative. ff_h_pvs_transport_equal_leftfirstnegative + S (dst_negative_transport_equal_leftfirst) = S ((S (dm_index_transport_equal_left)) * dst_negative_scale_transport_equal_leftfirst)) /\ exists ff_q_pvs_transport_equal_leftfirstnegative. dst_negative_code_transport_equal_leftfirst = ff_q_pvs_transport_equal_leftfirstnegative * S ((S (dm_index_transport_equal_left)) * dst_negative_scale_transport_equal_leftfirst) + (dst_negative_transport_equal_leftfirst))) /\ (exists ge_balance_positive_transport_equal_leftfirstvalue ge_balance_negative_transport_equal_leftfirstvalue. (((((dm_first_value_transport_equal_left) = 2 * (ge_balance_positive_transport_equal_leftfirstvalue) /\ (ge_balance_negative_transport_equal_leftfirstvalue) = 0) \/ exists ge_signed_half_transport_equal_leftfirstvaluedecode. (((dm_first_value_transport_equal_left) = 2 * ge_signed_half_transport_equal_leftfirstvaluedecode + 1 /\ (ge_balance_positive_transport_equal_leftfirstvalue) = 0) /\ (ge_balance_negative_transport_equal_leftfirstvalue) = S ge_signed_half_transport_equal_leftfirstvaluedecode))) /\ ((dst_positive_transport_equal_leftfirst) + ge_balance_negative_transport_equal_leftfirstvalue = (dst_negative_transport_equal_leftfirst) + ge_balance_positive_transport_equal_leftfirstvalue))))))))) -> (exists dst_positive_code_transport_equal_leftsecond dst_positive_scale_transport_equal_leftsecond dst_negative_code_transport_equal_leftsecond dst_negative_scale_transport_equal_leftsecond dst_positive_transport_equal_leftsecond dst_negative_transport_equal_leftsecond. (((H) = (((((dst_positive_code_transport_equal_leftsecond) + (dst_positive_scale_transport_equal_leftsecond)) * S ((dst_positive_code_transport_equal_leftsecond) + (dst_positive_scale_transport_equal_leftsecond)) + ((dst_positive_scale_transport_equal_leftsecond) + (dst_positive_scale_transport_equal_leftsecond))) + (((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) * S ((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) + ((dst_negative_scale_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)))) * S ((((dst_positive_code_transport_equal_leftsecond) + (dst_positive_scale_transport_equal_leftsecond)) * S ((dst_positive_code_transport_equal_leftsecond) + (dst_positive_scale_transport_equal_leftsecond)) + ((dst_positive_scale_transport_equal_leftsecond) + (dst_positive_scale_transport_equal_leftsecond))) + (((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) * S ((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) + ((dst_negative_scale_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)))) + ((((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) * S ((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) + ((dst_negative_scale_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond))) + (((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) * S ((dst_negative_code_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)) + ((dst_negative_scale_transport_equal_leftsecond) + (dst_negative_scale_transport_equal_leftsecond)))))) /\ (((((exists ff_h_pvs_transport_equal_leftsecondpositive. ff_h_pvs_transport_equal_leftsecondpositive + S (dst_positive_transport_equal_leftsecond) = S ((S (dm_index_transport_equal_left)) * dst_positive_scale_transport_equal_leftsecond)) /\ exists ff_q_pvs_transport_equal_leftsecondpositive. dst_positive_code_transport_equal_leftsecond = ff_q_pvs_transport_equal_leftsecondpositive * S ((S (dm_index_transport_equal_left)) * dst_positive_scale_transport_equal_leftsecond) + (dst_positive_transport_equal_leftsecond))) /\ (((((exists ff_h_pvs_transport_equal_leftsecondnegative. ff_h_pvs_transport_equal_leftsecondnegative + S (dst_negative_transport_equal_leftsecond) = S ((S (dm_index_transport_equal_left)) * dst_negative_scale_transport_equal_leftsecond)) /\ exists ff_q_pvs_transport_equal_leftsecondnegative. dst_negative_code_transport_equal_leftsecond = ff_q_pvs_transport_equal_leftsecondnegative * S ((S (dm_index_transport_equal_left)) * dst_negative_scale_transport_equal_leftsecond) + (dst_negative_transport_equal_leftsecond))) /\ (exists ge_balance_positive_transport_equal_leftsecondvalue ge_balance_negative_transport_equal_leftsecondvalue. (((((dm_second_value_transport_equal_left) = 2 * (ge_balance_positive_transport_equal_leftsecondvalue) /\ (ge_balance_negative_transport_equal_leftsecondvalue) = 0) \/ exists ge_signed_half_transport_equal_leftsecondvaluedecode. (((dm_second_value_transport_equal_left) = 2 * ge_signed_half_transport_equal_leftsecondvaluedecode + 1 /\ (ge_balance_positive_transport_equal_leftsecondvalue) = 0) /\ (ge_balance_negative_transport_equal_leftsecondvalue) = S ge_signed_half_transport_equal_leftsecondvaluedecode))) /\ ((dst_positive_transport_equal_leftsecond) + ge_balance_negative_transport_equal_leftsecondvalue = (dst_negative_transport_equal_leftsecond) + ge_balance_positive_transport_equal_leftsecondvalue))))))))) -> dm_first_value_transport_equal_left=dm_second_value_transport_equal_left) -> (forall dm_index_transport_equal_right dm_first_value_transport_equal_right dm_second_value_transport_equal_right. ~(dm_index_transport_equal_right=0) -> (exists pvs_le_gap_transport_equal_rightdomain. pvs_le_gap_transport_equal_rightdomain + (dm_index_transport_equal_right) = (n)) -> (exists dst_positive_code_transport_equal_rightfirst dst_positive_scale_transport_equal_rightfirst dst_negative_code_transport_equal_rightfirst dst_negative_scale_transport_equal_rightfirst dst_positive_transport_equal_rightfirst dst_negative_transport_equal_rightfirst. (((G) = (((((dst_positive_code_transport_equal_rightfirst) + (dst_positive_scale_transport_equal_rightfirst)) * S ((dst_positive_code_transport_equal_rightfirst) + (dst_positive_scale_transport_equal_rightfirst)) + ((dst_positive_scale_transport_equal_rightfirst) + (dst_positive_scale_transport_equal_rightfirst))) + (((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) * S ((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) + ((dst_negative_scale_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)))) * S ((((dst_positive_code_transport_equal_rightfirst) + (dst_positive_scale_transport_equal_rightfirst)) * S ((dst_positive_code_transport_equal_rightfirst) + (dst_positive_scale_transport_equal_rightfirst)) + ((dst_positive_scale_transport_equal_rightfirst) + (dst_positive_scale_transport_equal_rightfirst))) + (((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) * S ((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) + ((dst_negative_scale_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)))) + ((((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) * S ((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) + ((dst_negative_scale_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst))) + (((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) * S ((dst_negative_code_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)) + ((dst_negative_scale_transport_equal_rightfirst) + (dst_negative_scale_transport_equal_rightfirst)))))) /\ (((((exists ff_h_pvs_transport_equal_rightfirstpositive. ff_h_pvs_transport_equal_rightfirstpositive + S (dst_positive_transport_equal_rightfirst) = S ((S (dm_index_transport_equal_right)) * dst_positive_scale_transport_equal_rightfirst)) /\ exists ff_q_pvs_transport_equal_rightfirstpositive. dst_positive_code_transport_equal_rightfirst = ff_q_pvs_transport_equal_rightfirstpositive * S ((S (dm_index_transport_equal_right)) * dst_positive_scale_transport_equal_rightfirst) + (dst_positive_transport_equal_rightfirst))) /\ (((((exists ff_h_pvs_transport_equal_rightfirstnegative. ff_h_pvs_transport_equal_rightfirstnegative + S (dst_negative_transport_equal_rightfirst) = S ((S (dm_index_transport_equal_right)) * dst_negative_scale_transport_equal_rightfirst)) /\ exists ff_q_pvs_transport_equal_rightfirstnegative. dst_negative_code_transport_equal_rightfirst = ff_q_pvs_transport_equal_rightfirstnegative * S ((S (dm_index_transport_equal_right)) * dst_negative_scale_transport_equal_rightfirst) + (dst_negative_transport_equal_rightfirst))) /\ (exists ge_balance_positive_transport_equal_rightfirstvalue ge_balance_negative_transport_equal_rightfirstvalue. (((((dm_first_value_transport_equal_right) = 2 * (ge_balance_positive_transport_equal_rightfirstvalue) /\ (ge_balance_negative_transport_equal_rightfirstvalue) = 0) \/ exists ge_signed_half_transport_equal_rightfirstvaluedecode. (((dm_first_value_transport_equal_right) = 2 * ge_signed_half_transport_equal_rightfirstvaluedecode + 1 /\ (ge_balance_positive_transport_equal_rightfirstvalue) = 0) /\ (ge_balance_negative_transport_equal_rightfirstvalue) = S ge_signed_half_transport_equal_rightfirstvaluedecode))) /\ ((dst_positive_transport_equal_rightfirst) + ge_balance_negative_transport_equal_rightfirstvalue = (dst_negative_transport_equal_rightfirst) + ge_balance_positive_transport_equal_rightfirstvalue))))))))) -> (exists dst_positive_code_transport_equal_rightsecond dst_positive_scale_transport_equal_rightsecond dst_negative_code_transport_equal_rightsecond dst_negative_scale_transport_equal_rightsecond dst_positive_transport_equal_rightsecond dst_negative_transport_equal_rightsecond. (((K) = (((((dst_positive_code_transport_equal_rightsecond) + (dst_positive_scale_transport_equal_rightsecond)) * S ((dst_positive_code_transport_equal_rightsecond) + (dst_positive_scale_transport_equal_rightsecond)) + ((dst_positive_scale_transport_equal_rightsecond) + (dst_positive_scale_transport_equal_rightsecond))) + (((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) * S ((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) + ((dst_negative_scale_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)))) * S ((((dst_positive_code_transport_equal_rightsecond) + (dst_positive_scale_transport_equal_rightsecond)) * S ((dst_positive_code_transport_equal_rightsecond) + (dst_positive_scale_transport_equal_rightsecond)) + ((dst_positive_scale_transport_equal_rightsecond) + (dst_positive_scale_transport_equal_rightsecond))) + (((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) * S ((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) + ((dst_negative_scale_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)))) + ((((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) * S ((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) + ((dst_negative_scale_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond))) + (((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) * S ((dst_negative_code_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)) + ((dst_negative_scale_transport_equal_rightsecond) + (dst_negative_scale_transport_equal_rightsecond)))))) /\ (((((exists ff_h_pvs_transport_equal_rightsecondpositive. ff_h_pvs_transport_equal_rightsecondpositive + S (dst_positive_transport_equal_rightsecond) = S ((S (dm_index_transport_equal_right)) * dst_positive_scale_transport_equal_rightsecond)) /\ exists ff_q_pvs_transport_equal_rightsecondpositive. dst_positive_code_transport_equal_rightsecond = ff_q_pvs_transport_equal_rightsecondpositive * S ((S (dm_index_transport_equal_right)) * dst_positive_scale_transport_equal_rightsecond) + (dst_positive_transport_equal_rightsecond))) /\ (((((exists ff_h_pvs_transport_equal_rightsecondnegative. ff_h_pvs_transport_equal_rightsecondnegative + S (dst_negative_transport_equal_rightsecond) = S ((S (dm_index_transport_equal_right)) * dst_negative_scale_transport_equal_rightsecond)) /\ exists ff_q_pvs_transport_equal_rightsecondnegative. dst_negative_code_transport_equal_rightsecond = ff_q_pvs_transport_equal_rightsecondnegative * S ((S (dm_index_transport_equal_right)) * dst_negative_scale_transport_equal_rightsecond) + (dst_negative_transport_equal_rightsecond))) /\ (exists ge_balance_positive_transport_equal_rightsecondvalue ge_balance_negative_transport_equal_rightsecondvalue. (((((dm_second_value_transport_equal_right) = 2 * (ge_balance_positive_transport_equal_rightsecondvalue) /\ (ge_balance_negative_transport_equal_rightsecondvalue) = 0) \/ exists ge_signed_half_transport_equal_rightsecondvaluedecode. (((dm_second_value_transport_equal_right) = 2 * ge_signed_half_transport_equal_rightsecondvaluedecode + 1 /\ (ge_balance_positive_transport_equal_rightsecondvalue) = 0) /\ (ge_balance_negative_transport_equal_rightsecondvalue) = S ge_signed_half_transport_equal_rightsecondvaluedecode))) /\ ((dst_positive_transport_equal_rightsecond) + ge_balance_negative_transport_equal_rightsecondvalue = (dst_negative_transport_equal_rightsecond) + ge_balance_positive_transport_equal_rightsecondvalue))))))))) -> dm_first_value_transport_equal_right=dm_second_value_transport_equal_right) -> (((~((n)=0)) /\ (exists dc_mask_transport_source. ((((exists dst_positive_code_transport_sourcemasktable dst_positive_scale_transport_sourcemasktable dst_negative_code_transport_sourcemasktable dst_negative_scale_transport_sourcemasktable. (((dc_mask_transport_source) = (((((dst_positive_code_transport_sourcemasktable) + (dst_positive_scale_transport_sourcemasktable)) * S ((dst_positive_code_transport_sourcemasktable) + (dst_positive_scale_transport_sourcemasktable)) + ((dst_positive_scale_transport_sourcemasktable) + (dst_positive_scale_transport_sourcemasktable))) + (((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) * S ((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) + ((dst_negative_scale_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)))) * S ((((dst_positive_code_transport_sourcemasktable) + (dst_positive_scale_transport_sourcemasktable)) * S ((dst_positive_code_transport_sourcemasktable) + (dst_positive_scale_transport_sourcemasktable)) + ((dst_positive_scale_transport_sourcemasktable) + (dst_positive_scale_transport_sourcemasktable))) + (((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) * S ((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) + ((dst_negative_scale_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)))) + ((((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) * S ((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) + ((dst_negative_scale_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable))) + (((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) * S ((dst_negative_code_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)) + ((dst_negative_scale_transport_sourcemasktable) + (dst_negative_scale_transport_sourcemasktable)))))) /\ (forall dst_index_transport_sourcemasktable. (exists pvs_le_gap_transport_sourcemasktabledomain. pvs_le_gap_transport_sourcemasktabledomain + (dst_index_transport_sourcemasktable) = (n)) -> exists dst_positive_transport_sourcemasktable dst_negative_transport_sourcemasktable dst_value_transport_sourcemasktable. ((((exists ff_h_pvs_transport_sourcemasktableentrypositive. ff_h_pvs_transport_sourcemasktableentrypositive + S (dst_positive_transport_sourcemasktable) = S ((S (dst_index_transport_sourcemasktable)) * dst_positive_scale_transport_sourcemasktable)) /\ exists ff_q_pvs_transport_sourcemasktableentrypositive. dst_positive_code_transport_sourcemasktable = ff_q_pvs_transport_sourcemasktableentrypositive * S ((S (dst_index_transport_sourcemasktable)) * dst_positive_scale_transport_sourcemasktable) + (dst_positive_transport_sourcemasktable))) /\ (((((exists ff_h_pvs_transport_sourcemasktableentrynegative. ff_h_pvs_transport_sourcemasktableentrynegative + S (dst_negative_transport_sourcemasktable) = S ((S (dst_index_transport_sourcemasktable)) * dst_negative_scale_transport_sourcemasktable)) /\ exists ff_q_pvs_transport_sourcemasktableentrynegative. dst_negative_code_transport_sourcemasktable = ff_q_pvs_transport_sourcemasktableentrynegative * S ((S (dst_index_transport_sourcemasktable)) * dst_negative_scale_transport_sourcemasktable) + (dst_negative_transport_sourcemasktable))) /\ (exists ge_balance_positive_transport_sourcemasktableentryvalue ge_balance_negative_transport_sourcemasktableentryvalue. (((((dst_value_transport_sourcemasktable) = 2 * (ge_balance_positive_transport_sourcemasktableentryvalue) /\ (ge_balance_negative_transport_sourcemasktableentryvalue) = 0) \/ exists ge_signed_half_transport_sourcemasktableentryvaluedecode. (((dst_value_transport_sourcemasktable) = 2 * ge_signed_half_transport_sourcemasktableentryvaluedecode + 1 /\ (ge_balance_positive_transport_sourcemasktableentryvalue) = 0) /\ (ge_balance_negative_transport_sourcemasktableentryvalue) = S ge_signed_half_transport_sourcemasktableentryvaluedecode))) /\ ((dst_positive_transport_sourcemasktable) + ge_balance_negative_transport_sourcemasktableentryvalue = (dst_negative_transport_sourcemasktable) + ge_balance_positive_transport_sourcemasktableentryvalue))))))))) /\ (forall dc_index_transport_sourcemask dc_value_transport_sourcemask. (exists pvs_le_gap_transport_sourcemaskdomain. pvs_le_gap_transport_sourcemaskdomain + (dc_index_transport_sourcemask) = (n)) -> (exists dst_positive_code_transport_sourcemasklookup dst_positive_scale_transport_sourcemasklookup dst_negative_code_transport_sourcemasklookup dst_negative_scale_transport_sourcemasklookup dst_positive_transport_sourcemasklookup dst_negative_transport_sourcemasklookup. (((dc_mask_transport_source) = (((((dst_positive_code_transport_sourcemasklookup) + (dst_positive_scale_transport_sourcemasklookup)) * S ((dst_positive_code_transport_sourcemasklookup) + (dst_positive_scale_transport_sourcemasklookup)) + ((dst_positive_scale_transport_sourcemasklookup) + (dst_positive_scale_transport_sourcemasklookup))) + (((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) * S ((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) + ((dst_negative_scale_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)))) * S ((((dst_positive_code_transport_sourcemasklookup) + (dst_positive_scale_transport_sourcemasklookup)) * S ((dst_positive_code_transport_sourcemasklookup) + (dst_positive_scale_transport_sourcemasklookup)) + ((dst_positive_scale_transport_sourcemasklookup) + (dst_positive_scale_transport_sourcemasklookup))) + (((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) * S ((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) + ((dst_negative_scale_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)))) + ((((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) * S ((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) + ((dst_negative_scale_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup))) + (((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) * S ((dst_negative_code_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)) + ((dst_negative_scale_transport_sourcemasklookup) + (dst_negative_scale_transport_sourcemasklookup)))))) /\ (((((exists ff_h_pvs_transport_sourcemasklookuppositive. ff_h_pvs_transport_sourcemasklookuppositive + S (dst_positive_transport_sourcemasklookup) = S ((S (dc_index_transport_sourcemask)) * dst_positive_scale_transport_sourcemasklookup)) /\ exists ff_q_pvs_transport_sourcemasklookuppositive. dst_positive_code_transport_sourcemasklookup = ff_q_pvs_transport_sourcemasklookuppositive * S ((S (dc_index_transport_sourcemask)) * dst_positive_scale_transport_sourcemasklookup) + (dst_positive_transport_sourcemasklookup))) /\ (((((exists ff_h_pvs_transport_sourcemasklookupnegative. ff_h_pvs_transport_sourcemasklookupnegative + S (dst_negative_transport_sourcemasklookup) = S ((S (dc_index_transport_sourcemask)) * dst_negative_scale_transport_sourcemasklookup)) /\ exists ff_q_pvs_transport_sourcemasklookupnegative. dst_negative_code_transport_sourcemasklookup = ff_q_pvs_transport_sourcemasklookupnegative * S ((S (dc_index_transport_sourcemask)) * dst_negative_scale_transport_sourcemasklookup) + (dst_negative_transport_sourcemasklookup))) /\ (exists ge_balance_positive_transport_sourcemasklookupvalue ge_balance_negative_transport_sourcemasklookupvalue. (((((dc_value_transport_sourcemask) = 2 * (ge_balance_positive_transport_sourcemasklookupvalue) /\ (ge_balance_negative_transport_sourcemasklookupvalue) = 0) \/ exists ge_signed_half_transport_sourcemasklookupvaluedecode. (((dc_value_transport_sourcemask) = 2 * ge_signed_half_transport_sourcemasklookupvaluedecode + 1 /\ (ge_balance_positive_transport_sourcemasklookupvalue) = 0) /\ (ge_balance_negative_transport_sourcemasklookupvalue) = S ge_signed_half_transport_sourcemasklookupvaluedecode))) /\ ((dst_positive_transport_sourcemasklookup) + ge_balance_negative_transport_sourcemasklookupvalue = (dst_negative_transport_sourcemasklookup) + ge_balance_positive_transport_sourcemasklookupvalue))))))))) -> ((((~((dc_index_transport_sourcemask)=0)) /\ (exists dc_quotient_transport_sourcemaskentry dc_left_transport_sourcemaskentry dc_right_transport_sourcemaskentry. (((n)=(dc_index_transport_sourcemask)*dc_quotient_transport_sourcemaskentry) /\ (((exists dst_positive_code_transport_sourcemaskentryleft dst_positive_scale_transport_sourcemaskentryleft dst_negative_code_transport_sourcemaskentryleft dst_negative_scale_transport_sourcemaskentryleft dst_positive_transport_sourcemaskentryleft dst_negative_transport_sourcemaskentryleft. (((F) = (((((dst_positive_code_transport_sourcemaskentryleft) + (dst_positive_scale_transport_sourcemaskentryleft)) * S ((dst_positive_code_transport_sourcemaskentryleft) + (dst_positive_scale_transport_sourcemaskentryleft)) + ((dst_positive_scale_transport_sourcemaskentryleft) + (dst_positive_scale_transport_sourcemaskentryleft))) + (((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) * S ((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) + ((dst_negative_scale_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)))) * S ((((dst_positive_code_transport_sourcemaskentryleft) + (dst_positive_scale_transport_sourcemaskentryleft)) * S ((dst_positive_code_transport_sourcemaskentryleft) + (dst_positive_scale_transport_sourcemaskentryleft)) + ((dst_positive_scale_transport_sourcemaskentryleft) + (dst_positive_scale_transport_sourcemaskentryleft))) + (((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) * S ((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) + ((dst_negative_scale_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)))) + ((((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) * S ((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) + ((dst_negative_scale_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft))) + (((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) * S ((dst_negative_code_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)) + ((dst_negative_scale_transport_sourcemaskentryleft) + (dst_negative_scale_transport_sourcemaskentryleft)))))) /\ (((((exists ff_h_pvs_transport_sourcemaskentryleftpositive. ff_h_pvs_transport_sourcemaskentryleftpositive + S (dst_positive_transport_sourcemaskentryleft) = S ((S (dc_index_transport_sourcemask)) * dst_positive_scale_transport_sourcemaskentryleft)) /\ exists ff_q_pvs_transport_sourcemaskentryleftpositive. dst_positive_code_transport_sourcemaskentryleft = ff_q_pvs_transport_sourcemaskentryleftpositive * S ((S (dc_index_transport_sourcemask)) * dst_positive_scale_transport_sourcemaskentryleft) + (dst_positive_transport_sourcemaskentryleft))) /\ (((((exists ff_h_pvs_transport_sourcemaskentryleftnegative. ff_h_pvs_transport_sourcemaskentryleftnegative + S (dst_negative_transport_sourcemaskentryleft) = S ((S (dc_index_transport_sourcemask)) * dst_negative_scale_transport_sourcemaskentryleft)) /\ exists ff_q_pvs_transport_sourcemaskentryleftnegative. dst_negative_code_transport_sourcemaskentryleft = ff_q_pvs_transport_sourcemaskentryleftnegative * S ((S (dc_index_transport_sourcemask)) * dst_negative_scale_transport_sourcemaskentryleft) + (dst_negative_transport_sourcemaskentryleft))) /\ (exists ge_balance_positive_transport_sourcemaskentryleftvalue ge_balance_negative_transport_sourcemaskentryleftvalue. (((((dc_left_transport_sourcemaskentry) = 2 * (ge_balance_positive_transport_sourcemaskentryleftvalue) /\ (ge_balance_negative_transport_sourcemaskentryleftvalue) = 0) \/ exists ge_signed_half_transport_sourcemaskentryleftvaluedecode. (((dc_left_transport_sourcemaskentry) = 2 * ge_signed_half_transport_sourcemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_transport_sourcemaskentryleftvalue) = 0) /\ (ge_balance_negative_transport_sourcemaskentryleftvalue) = S ge_signed_half_transport_sourcemaskentryleftvaluedecode))) /\ ((dst_positive_transport_sourcemaskentryleft) + ge_balance_negative_transport_sourcemaskentryleftvalue = (dst_negative_transport_sourcemaskentryleft) + ge_balance_positive_transport_sourcemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_transport_sourcemaskentryright dst_positive_scale_transport_sourcemaskentryright dst_negative_code_transport_sourcemaskentryright dst_negative_scale_transport_sourcemaskentryright dst_positive_transport_sourcemaskentryright dst_negative_transport_sourcemaskentryright. (((G) = (((((dst_positive_code_transport_sourcemaskentryright) + (dst_positive_scale_transport_sourcemaskentryright)) * S ((dst_positive_code_transport_sourcemaskentryright) + (dst_positive_scale_transport_sourcemaskentryright)) + ((dst_positive_scale_transport_sourcemaskentryright) + (dst_positive_scale_transport_sourcemaskentryright))) + (((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) * S ((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) + ((dst_negative_scale_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)))) * S ((((dst_positive_code_transport_sourcemaskentryright) + (dst_positive_scale_transport_sourcemaskentryright)) * S ((dst_positive_code_transport_sourcemaskentryright) + (dst_positive_scale_transport_sourcemaskentryright)) + ((dst_positive_scale_transport_sourcemaskentryright) + (dst_positive_scale_transport_sourcemaskentryright))) + (((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) * S ((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) + ((dst_negative_scale_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)))) + ((((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) * S ((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) + ((dst_negative_scale_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright))) + (((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) * S ((dst_negative_code_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)) + ((dst_negative_scale_transport_sourcemaskentryright) + (dst_negative_scale_transport_sourcemaskentryright)))))) /\ (((((exists ff_h_pvs_transport_sourcemaskentryrightpositive. ff_h_pvs_transport_sourcemaskentryrightpositive + S (dst_positive_transport_sourcemaskentryright) = S ((S (dc_quotient_transport_sourcemaskentry)) * dst_positive_scale_transport_sourcemaskentryright)) /\ exists ff_q_pvs_transport_sourcemaskentryrightpositive. dst_positive_code_transport_sourcemaskentryright = ff_q_pvs_transport_sourcemaskentryrightpositive * S ((S (dc_quotient_transport_sourcemaskentry)) * dst_positive_scale_transport_sourcemaskentryright) + (dst_positive_transport_sourcemaskentryright))) /\ (((((exists ff_h_pvs_transport_sourcemaskentryrightnegative. ff_h_pvs_transport_sourcemaskentryrightnegative + S (dst_negative_transport_sourcemaskentryright) = S ((S (dc_quotient_transport_sourcemaskentry)) * dst_negative_scale_transport_sourcemaskentryright)) /\ exists ff_q_pvs_transport_sourcemaskentryrightnegative. dst_negative_code_transport_sourcemaskentryright = ff_q_pvs_transport_sourcemaskentryrightnegative * S ((S (dc_quotient_transport_sourcemaskentry)) * dst_negative_scale_transport_sourcemaskentryright) + (dst_negative_transport_sourcemaskentryright))) /\ (exists ge_balance_positive_transport_sourcemaskentryrightvalue ge_balance_negative_transport_sourcemaskentryrightvalue. (((((dc_right_transport_sourcemaskentry) = 2 * (ge_balance_positive_transport_sourcemaskentryrightvalue) /\ (ge_balance_negative_transport_sourcemaskentryrightvalue) = 0) \/ exists ge_signed_half_transport_sourcemaskentryrightvaluedecode. (((dc_right_transport_sourcemaskentry) = 2 * ge_signed_half_transport_sourcemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_transport_sourcemaskentryrightvalue) = 0) /\ (ge_balance_negative_transport_sourcemaskentryrightvalue) = S ge_signed_half_transport_sourcemaskentryrightvaluedecode))) /\ ((dst_positive_transport_sourcemaskentryright) + ge_balance_negative_transport_sourcemaskentryrightvalue = (dst_negative_transport_sourcemaskentryright) + ge_balance_positive_transport_sourcemaskentryrightvalue))))))))) /\ (exists sto_ap_transport_sourcemaskentryproduct sto_an_transport_sourcemaskentryproduct sto_bp_transport_sourcemaskentryproduct sto_bn_transport_sourcemaskentryproduct sto_cp_transport_sourcemaskentryproduct sto_cn_transport_sourcemaskentryproduct. (((((dc_left_transport_sourcemaskentry) = 2 * (sto_ap_transport_sourcemaskentryproduct) /\ (sto_an_transport_sourcemaskentryproduct) = 0) \/ exists ge_signed_half_transport_sourcemaskentryproductleft. (((dc_left_transport_sourcemaskentry) = 2 * ge_signed_half_transport_sourcemaskentryproductleft + 1 /\ (sto_ap_transport_sourcemaskentryproduct) = 0) /\ (sto_an_transport_sourcemaskentryproduct) = S ge_signed_half_transport_sourcemaskentryproductleft))) /\ ((((((dc_right_transport_sourcemaskentry) = 2 * (sto_bp_transport_sourcemaskentryproduct) /\ (sto_bn_transport_sourcemaskentryproduct) = 0) \/ exists ge_signed_half_transport_sourcemaskentryproductright. (((dc_right_transport_sourcemaskentry) = 2 * ge_signed_half_transport_sourcemaskentryproductright + 1 /\ (sto_bp_transport_sourcemaskentryproduct) = 0) /\ (sto_bn_transport_sourcemaskentryproduct) = S ge_signed_half_transport_sourcemaskentryproductright))) /\ ((((((dc_value_transport_sourcemask) = 2 * (sto_cp_transport_sourcemaskentryproduct) /\ (sto_cn_transport_sourcemaskentryproduct) = 0) \/ exists ge_signed_half_transport_sourcemaskentryproductoutput. (((dc_value_transport_sourcemask) = 2 * ge_signed_half_transport_sourcemaskentryproductoutput + 1 /\ (sto_cp_transport_sourcemaskentryproduct) = 0) /\ (sto_cn_transport_sourcemaskentryproduct) = S ge_signed_half_transport_sourcemaskentryproductoutput))) /\ ((sto_ap_transport_sourcemaskentryproduct * sto_bp_transport_sourcemaskentryproduct + sto_an_transport_sourcemaskentryproduct * sto_bn_transport_sourcemaskentryproduct) + sto_cn_transport_sourcemaskentryproduct = (sto_ap_transport_sourcemaskentryproduct * sto_bn_transport_sourcemaskentryproduct + sto_an_transport_sourcemaskentryproduct * sto_bp_transport_sourcemaskentryproduct) + sto_cp_transport_sourcemaskentryproduct))))))))))))))) \/ ((((dc_index_transport_sourcemask)=0 \/ ~(exists pvs_factor_transport_sourcemaskentrynondivisor. (n) = (dc_index_transport_sourcemask) * pvs_factor_transport_sourcemaskentrynondivisor)) /\ ((dc_value_transport_sourcemask)=0))))))) /\ (exists dst_positive_code_transport_sourcefold dst_positive_scale_transport_sourcefold dst_negative_code_transport_sourcefold dst_negative_scale_transport_sourcefold dst_positive_sum_transport_sourcefold dst_negative_sum_transport_sourcefold. (((dc_mask_transport_source) = (((((dst_positive_code_transport_sourcefold) + (dst_positive_scale_transport_sourcefold)) * S ((dst_positive_code_transport_sourcefold) + (dst_positive_scale_transport_sourcefold)) + ((dst_positive_scale_transport_sourcefold) + (dst_positive_scale_transport_sourcefold))) + (((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) * S ((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) + ((dst_negative_scale_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)))) * S ((((dst_positive_code_transport_sourcefold) + (dst_positive_scale_transport_sourcefold)) * S ((dst_positive_code_transport_sourcefold) + (dst_positive_scale_transport_sourcefold)) + ((dst_positive_scale_transport_sourcefold) + (dst_positive_scale_transport_sourcefold))) + (((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) * S ((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) + ((dst_negative_scale_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)))) + ((((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) * S ((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) + ((dst_negative_scale_transport_sourcefold) + (dst_negative_scale_transport_sourcefold))) + (((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) * S ((dst_negative_code_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)) + ((dst_negative_scale_transport_sourcefold) + (dst_negative_scale_transport_sourcefold)))))) /\ (((exists fs_u_dst_transport_sourcefoldpositive fs_v_dst_transport_sourcefoldpositive. ((((exists fs_h_dst_transport_sourcefoldpositive_body_start. fs_h_dst_transport_sourcefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_transport_sourcefoldpositive)) /\ exists fs_q_dst_transport_sourcefoldpositive_body_start. fs_u_dst_transport_sourcefoldpositive = fs_q_dst_transport_sourcefoldpositive_body_start * S ((S (0)) * fs_v_dst_transport_sourcefoldpositive) + (0))) /\ ((((exists fs_h_dst_transport_sourcefoldpositive_body_terminal. fs_h_dst_transport_sourcefoldpositive_body_terminal + S (dst_positive_sum_transport_sourcefold) = S ((S (S (n))) * fs_v_dst_transport_sourcefoldpositive)) /\ exists fs_q_dst_transport_sourcefoldpositive_body_terminal. fs_u_dst_transport_sourcefoldpositive = fs_q_dst_transport_sourcefoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_transport_sourcefoldpositive) + (dst_positive_sum_transport_sourcefold))) /\ forall fs_i_dst_transport_sourcefoldpositive_body_steps. (exists fs_lt_dst_transport_sourcefoldpositive_body_steps_bound. fs_lt_dst_transport_sourcefoldpositive_body_steps_bound + S fs_i_dst_transport_sourcefoldpositive_body_steps = S (n)) -> exists fs_a_dst_transport_sourcefoldpositive_body_steps fs_r_dst_transport_sourcefoldpositive_body_steps fs_s_dst_transport_sourcefoldpositive_body_steps. ((((exists fs_h_dst_transport_sourcefoldpositive_body_steps_summand. fs_h_dst_transport_sourcefoldpositive_body_steps_summand + S (fs_a_dst_transport_sourcefoldpositive_body_steps) = S ((S (fs_i_dst_transport_sourcefoldpositive_body_steps)) * dst_positive_scale_transport_sourcefold)) /\ exists fs_q_dst_transport_sourcefoldpositive_body_steps_summand. dst_positive_code_transport_sourcefold = fs_q_dst_transport_sourcefoldpositive_body_steps_summand * S ((S (fs_i_dst_transport_sourcefoldpositive_body_steps)) * dst_positive_scale_transport_sourcefold) + (fs_a_dst_transport_sourcefoldpositive_body_steps))) /\ ((((exists fs_h_dst_transport_sourcefoldpositive_body_steps_partial. fs_h_dst_transport_sourcefoldpositive_body_steps_partial + S (fs_r_dst_transport_sourcefoldpositive_body_steps) = S ((S (fs_i_dst_transport_sourcefoldpositive_body_steps)) * fs_v_dst_transport_sourcefoldpositive)) /\ exists fs_q_dst_transport_sourcefoldpositive_body_steps_partial. fs_u_dst_transport_sourcefoldpositive = fs_q_dst_transport_sourcefoldpositive_body_steps_partial * S ((S (fs_i_dst_transport_sourcefoldpositive_body_steps)) * fs_v_dst_transport_sourcefoldpositive) + (fs_r_dst_transport_sourcefoldpositive_body_steps))) /\ ((((exists fs_h_dst_transport_sourcefoldpositive_body_steps_successor. fs_h_dst_transport_sourcefoldpositive_body_steps_successor + S (fs_s_dst_transport_sourcefoldpositive_body_steps) = S ((S (S fs_i_dst_transport_sourcefoldpositive_body_steps)) * fs_v_dst_transport_sourcefoldpositive)) /\ exists fs_q_dst_transport_sourcefoldpositive_body_steps_successor. fs_u_dst_transport_sourcefoldpositive = fs_q_dst_transport_sourcefoldpositive_body_steps_successor * S ((S (S fs_i_dst_transport_sourcefoldpositive_body_steps)) * fs_v_dst_transport_sourcefoldpositive) + (fs_s_dst_transport_sourcefoldpositive_body_steps))) /\ fs_s_dst_transport_sourcefoldpositive_body_steps = fs_r_dst_transport_sourcefoldpositive_body_steps + fs_a_dst_transport_sourcefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_transport_sourcefoldnegative fs_v_dst_transport_sourcefoldnegative. ((((exists fs_h_dst_transport_sourcefoldnegative_body_start. fs_h_dst_transport_sourcefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_transport_sourcefoldnegative)) /\ exists fs_q_dst_transport_sourcefoldnegative_body_start. fs_u_dst_transport_sourcefoldnegative = fs_q_dst_transport_sourcefoldnegative_body_start * S ((S (0)) * fs_v_dst_transport_sourcefoldnegative) + (0))) /\ ((((exists fs_h_dst_transport_sourcefoldnegative_body_terminal. fs_h_dst_transport_sourcefoldnegative_body_terminal + S (dst_negative_sum_transport_sourcefold) = S ((S (S (n))) * fs_v_dst_transport_sourcefoldnegative)) /\ exists fs_q_dst_transport_sourcefoldnegative_body_terminal. fs_u_dst_transport_sourcefoldnegative = fs_q_dst_transport_sourcefoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_transport_sourcefoldnegative) + (dst_negative_sum_transport_sourcefold))) /\ forall fs_i_dst_transport_sourcefoldnegative_body_steps. (exists fs_lt_dst_transport_sourcefoldnegative_body_steps_bound. fs_lt_dst_transport_sourcefoldnegative_body_steps_bound + S fs_i_dst_transport_sourcefoldnegative_body_steps = S (n)) -> exists fs_a_dst_transport_sourcefoldnegative_body_steps fs_r_dst_transport_sourcefoldnegative_body_steps fs_s_dst_transport_sourcefoldnegative_body_steps. ((((exists fs_h_dst_transport_sourcefoldnegative_body_steps_summand. fs_h_dst_transport_sourcefoldnegative_body_steps_summand + S (fs_a_dst_transport_sourcefoldnegative_body_steps) = S ((S (fs_i_dst_transport_sourcefoldnegative_body_steps)) * dst_negative_scale_transport_sourcefold)) /\ exists fs_q_dst_transport_sourcefoldnegative_body_steps_summand. dst_negative_code_transport_sourcefold = fs_q_dst_transport_sourcefoldnegative_body_steps_summand * S ((S (fs_i_dst_transport_sourcefoldnegative_body_steps)) * dst_negative_scale_transport_sourcefold) + (fs_a_dst_transport_sourcefoldnegative_body_steps))) /\ ((((exists fs_h_dst_transport_sourcefoldnegative_body_steps_partial. fs_h_dst_transport_sourcefoldnegative_body_steps_partial + S (fs_r_dst_transport_sourcefoldnegative_body_steps) = S ((S (fs_i_dst_transport_sourcefoldnegative_body_steps)) * fs_v_dst_transport_sourcefoldnegative)) /\ exists fs_q_dst_transport_sourcefoldnegative_body_steps_partial. fs_u_dst_transport_sourcefoldnegative = fs_q_dst_transport_sourcefoldnegative_body_steps_partial * S ((S (fs_i_dst_transport_sourcefoldnegative_body_steps)) * fs_v_dst_transport_sourcefoldnegative) + (fs_r_dst_transport_sourcefoldnegative_body_steps))) /\ ((((exists fs_h_dst_transport_sourcefoldnegative_body_steps_successor. fs_h_dst_transport_sourcefoldnegative_body_steps_successor + S (fs_s_dst_transport_sourcefoldnegative_body_steps) = S ((S (S fs_i_dst_transport_sourcefoldnegative_body_steps)) * fs_v_dst_transport_sourcefoldnegative)) /\ exists fs_q_dst_transport_sourcefoldnegative_body_steps_successor. fs_u_dst_transport_sourcefoldnegative = fs_q_dst_transport_sourcefoldnegative_body_steps_successor * S ((S (S fs_i_dst_transport_sourcefoldnegative_body_steps)) * fs_v_dst_transport_sourcefoldnegative) + (fs_s_dst_transport_sourcefoldnegative_body_steps))) /\ fs_s_dst_transport_sourcefoldnegative_body_steps = fs_r_dst_transport_sourcefoldnegative_body_steps + fs_a_dst_transport_sourcefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_transport_sourcefoldresult ge_balance_negative_transport_sourcefoldresult. (((((z) = 2 * (ge_balance_positive_transport_sourcefoldresult) /\ (ge_balance_negative_transport_sourcefoldresult) = 0) \/ exists ge_signed_half_transport_sourcefoldresultdecode. (((z) = 2 * ge_signed_half_transport_sourcefoldresultdecode + 1 /\ (ge_balance_positive_transport_sourcefoldresult) = 0) /\ (ge_balance_negative_transport_sourcefoldresult) = S ge_signed_half_transport_sourcefoldresultdecode))) /\ ((dst_positive_sum_transport_sourcefold) + ge_balance_negative_transport_sourcefoldresult = (dst_negative_sum_transport_sourcefold) + ge_balance_positive_transport_sourcefoldresult))))))))))))) -> (((~((n)=0)) /\ (exists dc_mask_transport_result. ((((exists dst_positive_code_transport_resultmasktable dst_positive_scale_transport_resultmasktable dst_negative_code_transport_resultmasktable dst_negative_scale_transport_resultmasktable. (((dc_mask_transport_result) = (((((dst_positive_code_transport_resultmasktable) + (dst_positive_scale_transport_resultmasktable)) * S ((dst_positive_code_transport_resultmasktable) + (dst_positive_scale_transport_resultmasktable)) + ((dst_positive_scale_transport_resultmasktable) + (dst_positive_scale_transport_resultmasktable))) + (((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) * S ((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) + ((dst_negative_scale_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)))) * S ((((dst_positive_code_transport_resultmasktable) + (dst_positive_scale_transport_resultmasktable)) * S ((dst_positive_code_transport_resultmasktable) + (dst_positive_scale_transport_resultmasktable)) + ((dst_positive_scale_transport_resultmasktable) + (dst_positive_scale_transport_resultmasktable))) + (((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) * S ((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) + ((dst_negative_scale_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)))) + ((((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) * S ((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) + ((dst_negative_scale_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable))) + (((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) * S ((dst_negative_code_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)) + ((dst_negative_scale_transport_resultmasktable) + (dst_negative_scale_transport_resultmasktable)))))) /\ (forall dst_index_transport_resultmasktable. (exists pvs_le_gap_transport_resultmasktabledomain. pvs_le_gap_transport_resultmasktabledomain + (dst_index_transport_resultmasktable) = (n)) -> exists dst_positive_transport_resultmasktable dst_negative_transport_resultmasktable dst_value_transport_resultmasktable. ((((exists ff_h_pvs_transport_resultmasktableentrypositive. ff_h_pvs_transport_resultmasktableentrypositive + S (dst_positive_transport_resultmasktable) = S ((S (dst_index_transport_resultmasktable)) * dst_positive_scale_transport_resultmasktable)) /\ exists ff_q_pvs_transport_resultmasktableentrypositive. dst_positive_code_transport_resultmasktable = ff_q_pvs_transport_resultmasktableentrypositive * S ((S (dst_index_transport_resultmasktable)) * dst_positive_scale_transport_resultmasktable) + (dst_positive_transport_resultmasktable))) /\ (((((exists ff_h_pvs_transport_resultmasktableentrynegative. ff_h_pvs_transport_resultmasktableentrynegative + S (dst_negative_transport_resultmasktable) = S ((S (dst_index_transport_resultmasktable)) * dst_negative_scale_transport_resultmasktable)) /\ exists ff_q_pvs_transport_resultmasktableentrynegative. dst_negative_code_transport_resultmasktable = ff_q_pvs_transport_resultmasktableentrynegative * S ((S (dst_index_transport_resultmasktable)) * dst_negative_scale_transport_resultmasktable) + (dst_negative_transport_resultmasktable))) /\ (exists ge_balance_positive_transport_resultmasktableentryvalue ge_balance_negative_transport_resultmasktableentryvalue. (((((dst_value_transport_resultmasktable) = 2 * (ge_balance_positive_transport_resultmasktableentryvalue) /\ (ge_balance_negative_transport_resultmasktableentryvalue) = 0) \/ exists ge_signed_half_transport_resultmasktableentryvaluedecode. (((dst_value_transport_resultmasktable) = 2 * ge_signed_half_transport_resultmasktableentryvaluedecode + 1 /\ (ge_balance_positive_transport_resultmasktableentryvalue) = 0) /\ (ge_balance_negative_transport_resultmasktableentryvalue) = S ge_signed_half_transport_resultmasktableentryvaluedecode))) /\ ((dst_positive_transport_resultmasktable) + ge_balance_negative_transport_resultmasktableentryvalue = (dst_negative_transport_resultmasktable) + ge_balance_positive_transport_resultmasktableentryvalue))))))))) /\ (forall dc_index_transport_resultmask dc_value_transport_resultmask. (exists pvs_le_gap_transport_resultmaskdomain. pvs_le_gap_transport_resultmaskdomain + (dc_index_transport_resultmask) = (n)) -> (exists dst_positive_code_transport_resultmasklookup dst_positive_scale_transport_resultmasklookup dst_negative_code_transport_resultmasklookup dst_negative_scale_transport_resultmasklookup dst_positive_transport_resultmasklookup dst_negative_transport_resultmasklookup. (((dc_mask_transport_result) = (((((dst_positive_code_transport_resultmasklookup) + (dst_positive_scale_transport_resultmasklookup)) * S ((dst_positive_code_transport_resultmasklookup) + (dst_positive_scale_transport_resultmasklookup)) + ((dst_positive_scale_transport_resultmasklookup) + (dst_positive_scale_transport_resultmasklookup))) + (((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) * S ((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) + ((dst_negative_scale_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)))) * S ((((dst_positive_code_transport_resultmasklookup) + (dst_positive_scale_transport_resultmasklookup)) * S ((dst_positive_code_transport_resultmasklookup) + (dst_positive_scale_transport_resultmasklookup)) + ((dst_positive_scale_transport_resultmasklookup) + (dst_positive_scale_transport_resultmasklookup))) + (((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) * S ((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) + ((dst_negative_scale_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)))) + ((((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) * S ((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) + ((dst_negative_scale_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup))) + (((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) * S ((dst_negative_code_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)) + ((dst_negative_scale_transport_resultmasklookup) + (dst_negative_scale_transport_resultmasklookup)))))) /\ (((((exists ff_h_pvs_transport_resultmasklookuppositive. ff_h_pvs_transport_resultmasklookuppositive + S (dst_positive_transport_resultmasklookup) = S ((S (dc_index_transport_resultmask)) * dst_positive_scale_transport_resultmasklookup)) /\ exists ff_q_pvs_transport_resultmasklookuppositive. dst_positive_code_transport_resultmasklookup = ff_q_pvs_transport_resultmasklookuppositive * S ((S (dc_index_transport_resultmask)) * dst_positive_scale_transport_resultmasklookup) + (dst_positive_transport_resultmasklookup))) /\ (((((exists ff_h_pvs_transport_resultmasklookupnegative. ff_h_pvs_transport_resultmasklookupnegative + S (dst_negative_transport_resultmasklookup) = S ((S (dc_index_transport_resultmask)) * dst_negative_scale_transport_resultmasklookup)) /\ exists ff_q_pvs_transport_resultmasklookupnegative. dst_negative_code_transport_resultmasklookup = ff_q_pvs_transport_resultmasklookupnegative * S ((S (dc_index_transport_resultmask)) * dst_negative_scale_transport_resultmasklookup) + (dst_negative_transport_resultmasklookup))) /\ (exists ge_balance_positive_transport_resultmasklookupvalue ge_balance_negative_transport_resultmasklookupvalue. (((((dc_value_transport_resultmask) = 2 * (ge_balance_positive_transport_resultmasklookupvalue) /\ (ge_balance_negative_transport_resultmasklookupvalue) = 0) \/ exists ge_signed_half_transport_resultmasklookupvaluedecode. (((dc_value_transport_resultmask) = 2 * ge_signed_half_transport_resultmasklookupvaluedecode + 1 /\ (ge_balance_positive_transport_resultmasklookupvalue) = 0) /\ (ge_balance_negative_transport_resultmasklookupvalue) = S ge_signed_half_transport_resultmasklookupvaluedecode))) /\ ((dst_positive_transport_resultmasklookup) + ge_balance_negative_transport_resultmasklookupvalue = (dst_negative_transport_resultmasklookup) + ge_balance_positive_transport_resultmasklookupvalue))))))))) -> ((((~((dc_index_transport_resultmask)=0)) /\ (exists dc_quotient_transport_resultmaskentry dc_left_transport_resultmaskentry dc_right_transport_resultmaskentry. (((n)=(dc_index_transport_resultmask)*dc_quotient_transport_resultmaskentry) /\ (((exists dst_positive_code_transport_resultmaskentryleft dst_positive_scale_transport_resultmaskentryleft dst_negative_code_transport_resultmaskentryleft dst_negative_scale_transport_resultmaskentryleft dst_positive_transport_resultmaskentryleft dst_negative_transport_resultmaskentryleft. (((H) = (((((dst_positive_code_transport_resultmaskentryleft) + (dst_positive_scale_transport_resultmaskentryleft)) * S ((dst_positive_code_transport_resultmaskentryleft) + (dst_positive_scale_transport_resultmaskentryleft)) + ((dst_positive_scale_transport_resultmaskentryleft) + (dst_positive_scale_transport_resultmaskentryleft))) + (((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) * S ((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) + ((dst_negative_scale_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)))) * S ((((dst_positive_code_transport_resultmaskentryleft) + (dst_positive_scale_transport_resultmaskentryleft)) * S ((dst_positive_code_transport_resultmaskentryleft) + (dst_positive_scale_transport_resultmaskentryleft)) + ((dst_positive_scale_transport_resultmaskentryleft) + (dst_positive_scale_transport_resultmaskentryleft))) + (((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) * S ((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) + ((dst_negative_scale_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)))) + ((((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) * S ((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) + ((dst_negative_scale_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft))) + (((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) * S ((dst_negative_code_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)) + ((dst_negative_scale_transport_resultmaskentryleft) + (dst_negative_scale_transport_resultmaskentryleft)))))) /\ (((((exists ff_h_pvs_transport_resultmaskentryleftpositive. ff_h_pvs_transport_resultmaskentryleftpositive + S (dst_positive_transport_resultmaskentryleft) = S ((S (dc_index_transport_resultmask)) * dst_positive_scale_transport_resultmaskentryleft)) /\ exists ff_q_pvs_transport_resultmaskentryleftpositive. dst_positive_code_transport_resultmaskentryleft = ff_q_pvs_transport_resultmaskentryleftpositive * S ((S (dc_index_transport_resultmask)) * dst_positive_scale_transport_resultmaskentryleft) + (dst_positive_transport_resultmaskentryleft))) /\ (((((exists ff_h_pvs_transport_resultmaskentryleftnegative. ff_h_pvs_transport_resultmaskentryleftnegative + S (dst_negative_transport_resultmaskentryleft) = S ((S (dc_index_transport_resultmask)) * dst_negative_scale_transport_resultmaskentryleft)) /\ exists ff_q_pvs_transport_resultmaskentryleftnegative. dst_negative_code_transport_resultmaskentryleft = ff_q_pvs_transport_resultmaskentryleftnegative * S ((S (dc_index_transport_resultmask)) * dst_negative_scale_transport_resultmaskentryleft) + (dst_negative_transport_resultmaskentryleft))) /\ (exists ge_balance_positive_transport_resultmaskentryleftvalue ge_balance_negative_transport_resultmaskentryleftvalue. (((((dc_left_transport_resultmaskentry) = 2 * (ge_balance_positive_transport_resultmaskentryleftvalue) /\ (ge_balance_negative_transport_resultmaskentryleftvalue) = 0) \/ exists ge_signed_half_transport_resultmaskentryleftvaluedecode. (((dc_left_transport_resultmaskentry) = 2 * ge_signed_half_transport_resultmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_transport_resultmaskentryleftvalue) = 0) /\ (ge_balance_negative_transport_resultmaskentryleftvalue) = S ge_signed_half_transport_resultmaskentryleftvaluedecode))) /\ ((dst_positive_transport_resultmaskentryleft) + ge_balance_negative_transport_resultmaskentryleftvalue = (dst_negative_transport_resultmaskentryleft) + ge_balance_positive_transport_resultmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_transport_resultmaskentryright dst_positive_scale_transport_resultmaskentryright dst_negative_code_transport_resultmaskentryright dst_negative_scale_transport_resultmaskentryright dst_positive_transport_resultmaskentryright dst_negative_transport_resultmaskentryright. (((K) = (((((dst_positive_code_transport_resultmaskentryright) + (dst_positive_scale_transport_resultmaskentryright)) * S ((dst_positive_code_transport_resultmaskentryright) + (dst_positive_scale_transport_resultmaskentryright)) + ((dst_positive_scale_transport_resultmaskentryright) + (dst_positive_scale_transport_resultmaskentryright))) + (((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) * S ((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) + ((dst_negative_scale_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)))) * S ((((dst_positive_code_transport_resultmaskentryright) + (dst_positive_scale_transport_resultmaskentryright)) * S ((dst_positive_code_transport_resultmaskentryright) + (dst_positive_scale_transport_resultmaskentryright)) + ((dst_positive_scale_transport_resultmaskentryright) + (dst_positive_scale_transport_resultmaskentryright))) + (((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) * S ((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) + ((dst_negative_scale_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)))) + ((((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) * S ((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) + ((dst_negative_scale_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright))) + (((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) * S ((dst_negative_code_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)) + ((dst_negative_scale_transport_resultmaskentryright) + (dst_negative_scale_transport_resultmaskentryright)))))) /\ (((((exists ff_h_pvs_transport_resultmaskentryrightpositive. ff_h_pvs_transport_resultmaskentryrightpositive + S (dst_positive_transport_resultmaskentryright) = S ((S (dc_quotient_transport_resultmaskentry)) * dst_positive_scale_transport_resultmaskentryright)) /\ exists ff_q_pvs_transport_resultmaskentryrightpositive. dst_positive_code_transport_resultmaskentryright = ff_q_pvs_transport_resultmaskentryrightpositive * S ((S (dc_quotient_transport_resultmaskentry)) * dst_positive_scale_transport_resultmaskentryright) + (dst_positive_transport_resultmaskentryright))) /\ (((((exists ff_h_pvs_transport_resultmaskentryrightnegative. ff_h_pvs_transport_resultmaskentryrightnegative + S (dst_negative_transport_resultmaskentryright) = S ((S (dc_quotient_transport_resultmaskentry)) * dst_negative_scale_transport_resultmaskentryright)) /\ exists ff_q_pvs_transport_resultmaskentryrightnegative. dst_negative_code_transport_resultmaskentryright = ff_q_pvs_transport_resultmaskentryrightnegative * S ((S (dc_quotient_transport_resultmaskentry)) * dst_negative_scale_transport_resultmaskentryright) + (dst_negative_transport_resultmaskentryright))) /\ (exists ge_balance_positive_transport_resultmaskentryrightvalue ge_balance_negative_transport_resultmaskentryrightvalue. (((((dc_right_transport_resultmaskentry) = 2 * (ge_balance_positive_transport_resultmaskentryrightvalue) /\ (ge_balance_negative_transport_resultmaskentryrightvalue) = 0) \/ exists ge_signed_half_transport_resultmaskentryrightvaluedecode. (((dc_right_transport_resultmaskentry) = 2 * ge_signed_half_transport_resultmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_transport_resultmaskentryrightvalue) = 0) /\ (ge_balance_negative_transport_resultmaskentryrightvalue) = S ge_signed_half_transport_resultmaskentryrightvaluedecode))) /\ ((dst_positive_transport_resultmaskentryright) + ge_balance_negative_transport_resultmaskentryrightvalue = (dst_negative_transport_resultmaskentryright) + ge_balance_positive_transport_resultmaskentryrightvalue))))))))) /\ (exists sto_ap_transport_resultmaskentryproduct sto_an_transport_resultmaskentryproduct sto_bp_transport_resultmaskentryproduct sto_bn_transport_resultmaskentryproduct sto_cp_transport_resultmaskentryproduct sto_cn_transport_resultmaskentryproduct. (((((dc_left_transport_resultmaskentry) = 2 * (sto_ap_transport_resultmaskentryproduct) /\ (sto_an_transport_resultmaskentryproduct) = 0) \/ exists ge_signed_half_transport_resultmaskentryproductleft. (((dc_left_transport_resultmaskentry) = 2 * ge_signed_half_transport_resultmaskentryproductleft + 1 /\ (sto_ap_transport_resultmaskentryproduct) = 0) /\ (sto_an_transport_resultmaskentryproduct) = S ge_signed_half_transport_resultmaskentryproductleft))) /\ ((((((dc_right_transport_resultmaskentry) = 2 * (sto_bp_transport_resultmaskentryproduct) /\ (sto_bn_transport_resultmaskentryproduct) = 0) \/ exists ge_signed_half_transport_resultmaskentryproductright. (((dc_right_transport_resultmaskentry) = 2 * ge_signed_half_transport_resultmaskentryproductright + 1 /\ (sto_bp_transport_resultmaskentryproduct) = 0) /\ (sto_bn_transport_resultmaskentryproduct) = S ge_signed_half_transport_resultmaskentryproductright))) /\ ((((((dc_value_transport_resultmask) = 2 * (sto_cp_transport_resultmaskentryproduct) /\ (sto_cn_transport_resultmaskentryproduct) = 0) \/ exists ge_signed_half_transport_resultmaskentryproductoutput. (((dc_value_transport_resultmask) = 2 * ge_signed_half_transport_resultmaskentryproductoutput + 1 /\ (sto_cp_transport_resultmaskentryproduct) = 0) /\ (sto_cn_transport_resultmaskentryproduct) = S ge_signed_half_transport_resultmaskentryproductoutput))) /\ ((sto_ap_transport_resultmaskentryproduct * sto_bp_transport_resultmaskentryproduct + sto_an_transport_resultmaskentryproduct * sto_bn_transport_resultmaskentryproduct) + sto_cn_transport_resultmaskentryproduct = (sto_ap_transport_resultmaskentryproduct * sto_bn_transport_resultmaskentryproduct + sto_an_transport_resultmaskentryproduct * sto_bp_transport_resultmaskentryproduct) + sto_cp_transport_resultmaskentryproduct))))))))))))))) \/ ((((dc_index_transport_resultmask)=0 \/ ~(exists pvs_factor_transport_resultmaskentrynondivisor. (n) = (dc_index_transport_resultmask) * pvs_factor_transport_resultmaskentrynondivisor)) /\ ((dc_value_transport_resultmask)=0))))))) /\ (exists dst_positive_code_transport_resultfold dst_positive_scale_transport_resultfold dst_negative_code_transport_resultfold dst_negative_scale_transport_resultfold dst_positive_sum_transport_resultfold dst_negative_sum_transport_resultfold. (((dc_mask_transport_result) = (((((dst_positive_code_transport_resultfold) + (dst_positive_scale_transport_resultfold)) * S ((dst_positive_code_transport_resultfold) + (dst_positive_scale_transport_resultfold)) + ((dst_positive_scale_transport_resultfold) + (dst_positive_scale_transport_resultfold))) + (((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) * S ((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) + ((dst_negative_scale_transport_resultfold) + (dst_negative_scale_transport_resultfold)))) * S ((((dst_positive_code_transport_resultfold) + (dst_positive_scale_transport_resultfold)) * S ((dst_positive_code_transport_resultfold) + (dst_positive_scale_transport_resultfold)) + ((dst_positive_scale_transport_resultfold) + (dst_positive_scale_transport_resultfold))) + (((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) * S ((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) + ((dst_negative_scale_transport_resultfold) + (dst_negative_scale_transport_resultfold)))) + ((((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) * S ((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) + ((dst_negative_scale_transport_resultfold) + (dst_negative_scale_transport_resultfold))) + (((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) * S ((dst_negative_code_transport_resultfold) + (dst_negative_scale_transport_resultfold)) + ((dst_negative_scale_transport_resultfold) + (dst_negative_scale_transport_resultfold)))))) /\ (((exists fs_u_dst_transport_resultfoldpositive fs_v_dst_transport_resultfoldpositive. ((((exists fs_h_dst_transport_resultfoldpositive_body_start. fs_h_dst_transport_resultfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_transport_resultfoldpositive)) /\ exists fs_q_dst_transport_resultfoldpositive_body_start. fs_u_dst_transport_resultfoldpositive = fs_q_dst_transport_resultfoldpositive_body_start * S ((S (0)) * fs_v_dst_transport_resultfoldpositive) + (0))) /\ ((((exists fs_h_dst_transport_resultfoldpositive_body_terminal. fs_h_dst_transport_resultfoldpositive_body_terminal + S (dst_positive_sum_transport_resultfold) = S ((S (S (n))) * fs_v_dst_transport_resultfoldpositive)) /\ exists fs_q_dst_transport_resultfoldpositive_body_terminal. fs_u_dst_transport_resultfoldpositive = fs_q_dst_transport_resultfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_transport_resultfoldpositive) + (dst_positive_sum_transport_resultfold))) /\ forall fs_i_dst_transport_resultfoldpositive_body_steps. (exists fs_lt_dst_transport_resultfoldpositive_body_steps_bound. fs_lt_dst_transport_resultfoldpositive_body_steps_bound + S fs_i_dst_transport_resultfoldpositive_body_steps = S (n)) -> exists fs_a_dst_transport_resultfoldpositive_body_steps fs_r_dst_transport_resultfoldpositive_body_steps fs_s_dst_transport_resultfoldpositive_body_steps. ((((exists fs_h_dst_transport_resultfoldpositive_body_steps_summand. fs_h_dst_transport_resultfoldpositive_body_steps_summand + S (fs_a_dst_transport_resultfoldpositive_body_steps) = S ((S (fs_i_dst_transport_resultfoldpositive_body_steps)) * dst_positive_scale_transport_resultfold)) /\ exists fs_q_dst_transport_resultfoldpositive_body_steps_summand. dst_positive_code_transport_resultfold = fs_q_dst_transport_resultfoldpositive_body_steps_summand * S ((S (fs_i_dst_transport_resultfoldpositive_body_steps)) * dst_positive_scale_transport_resultfold) + (fs_a_dst_transport_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_transport_resultfoldpositive_body_steps_partial. fs_h_dst_transport_resultfoldpositive_body_steps_partial + S (fs_r_dst_transport_resultfoldpositive_body_steps) = S ((S (fs_i_dst_transport_resultfoldpositive_body_steps)) * fs_v_dst_transport_resultfoldpositive)) /\ exists fs_q_dst_transport_resultfoldpositive_body_steps_partial. fs_u_dst_transport_resultfoldpositive = fs_q_dst_transport_resultfoldpositive_body_steps_partial * S ((S (fs_i_dst_transport_resultfoldpositive_body_steps)) * fs_v_dst_transport_resultfoldpositive) + (fs_r_dst_transport_resultfoldpositive_body_steps))) /\ ((((exists fs_h_dst_transport_resultfoldpositive_body_steps_successor. fs_h_dst_transport_resultfoldpositive_body_steps_successor + S (fs_s_dst_transport_resultfoldpositive_body_steps) = S ((S (S fs_i_dst_transport_resultfoldpositive_body_steps)) * fs_v_dst_transport_resultfoldpositive)) /\ exists fs_q_dst_transport_resultfoldpositive_body_steps_successor. fs_u_dst_transport_resultfoldpositive = fs_q_dst_transport_resultfoldpositive_body_steps_successor * S ((S (S fs_i_dst_transport_resultfoldpositive_body_steps)) * fs_v_dst_transport_resultfoldpositive) + (fs_s_dst_transport_resultfoldpositive_body_steps))) /\ fs_s_dst_transport_resultfoldpositive_body_steps = fs_r_dst_transport_resultfoldpositive_body_steps + fs_a_dst_transport_resultfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_transport_resultfoldnegative fs_v_dst_transport_resultfoldnegative. ((((exists fs_h_dst_transport_resultfoldnegative_body_start. fs_h_dst_transport_resultfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_transport_resultfoldnegative)) /\ exists fs_q_dst_transport_resultfoldnegative_body_start. fs_u_dst_transport_resultfoldnegative = fs_q_dst_transport_resultfoldnegative_body_start * S ((S (0)) * fs_v_dst_transport_resultfoldnegative) + (0))) /\ ((((exists fs_h_dst_transport_resultfoldnegative_body_terminal. fs_h_dst_transport_resultfoldnegative_body_terminal + S (dst_negative_sum_transport_resultfold) = S ((S (S (n))) * fs_v_dst_transport_resultfoldnegative)) /\ exists fs_q_dst_transport_resultfoldnegative_body_terminal. fs_u_dst_transport_resultfoldnegative = fs_q_dst_transport_resultfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_transport_resultfoldnegative) + (dst_negative_sum_transport_resultfold))) /\ forall fs_i_dst_transport_resultfoldnegative_body_steps. (exists fs_lt_dst_transport_resultfoldnegative_body_steps_bound. fs_lt_dst_transport_resultfoldnegative_body_steps_bound + S fs_i_dst_transport_resultfoldnegative_body_steps = S (n)) -> exists fs_a_dst_transport_resultfoldnegative_body_steps fs_r_dst_transport_resultfoldnegative_body_steps fs_s_dst_transport_resultfoldnegative_body_steps. ((((exists fs_h_dst_transport_resultfoldnegative_body_steps_summand. fs_h_dst_transport_resultfoldnegative_body_steps_summand + S (fs_a_dst_transport_resultfoldnegative_body_steps) = S ((S (fs_i_dst_transport_resultfoldnegative_body_steps)) * dst_negative_scale_transport_resultfold)) /\ exists fs_q_dst_transport_resultfoldnegative_body_steps_summand. dst_negative_code_transport_resultfold = fs_q_dst_transport_resultfoldnegative_body_steps_summand * S ((S (fs_i_dst_transport_resultfoldnegative_body_steps)) * dst_negative_scale_transport_resultfold) + (fs_a_dst_transport_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_transport_resultfoldnegative_body_steps_partial. fs_h_dst_transport_resultfoldnegative_body_steps_partial + S (fs_r_dst_transport_resultfoldnegative_body_steps) = S ((S (fs_i_dst_transport_resultfoldnegative_body_steps)) * fs_v_dst_transport_resultfoldnegative)) /\ exists fs_q_dst_transport_resultfoldnegative_body_steps_partial. fs_u_dst_transport_resultfoldnegative = fs_q_dst_transport_resultfoldnegative_body_steps_partial * S ((S (fs_i_dst_transport_resultfoldnegative_body_steps)) * fs_v_dst_transport_resultfoldnegative) + (fs_r_dst_transport_resultfoldnegative_body_steps))) /\ ((((exists fs_h_dst_transport_resultfoldnegative_body_steps_successor. fs_h_dst_transport_resultfoldnegative_body_steps_successor + S (fs_s_dst_transport_resultfoldnegative_body_steps) = S ((S (S fs_i_dst_transport_resultfoldnegative_body_steps)) * fs_v_dst_transport_resultfoldnegative)) /\ exists fs_q_dst_transport_resultfoldnegative_body_steps_successor. fs_u_dst_transport_resultfoldnegative = fs_q_dst_transport_resultfoldnegative_body_steps_successor * S ((S (S fs_i_dst_transport_resultfoldnegative_body_steps)) * fs_v_dst_transport_resultfoldnegative) + (fs_s_dst_transport_resultfoldnegative_body_steps))) /\ fs_s_dst_transport_resultfoldnegative_body_steps = fs_r_dst_transport_resultfoldnegative_body_steps + fs_a_dst_transport_resultfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_transport_resultfoldresult ge_balance_negative_transport_resultfoldresult. (((((z) = 2 * (ge_balance_positive_transport_resultfoldresult) /\ (ge_balance_negative_transport_resultfoldresult) = 0) \/ exists ge_signed_half_transport_resultfoldresultdecode. (((z) = 2 * ge_signed_half_transport_resultfoldresultdecode + 1 /\ (ge_balance_positive_transport_resultfoldresult) = 0) /\ (ge_balance_negative_transport_resultfoldresult) = S ge_signed_half_transport_resultfoldresultdecode))) /\ ((dst_positive_sum_transport_resultfold) + ge_balance_negative_transport_resultfoldresult = (dst_negative_sum_transport_resultfold) + ge_balance_positive_transport_resultfoldresult)))))))))))))

Constructive proof overview

Generated structural guide

Construct the comparison fold before transporting an actual convolution value across positive-source equality; zero entries are untouched.

The unchanged tactic script uses 2 declared prerequisites and contains 41 exact native proof lines.

Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

Direct dependents

none

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.

Read the argument

Proof checkpoints

41 script commands · 9 reading checkpoints · 2 local claims

This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.

Named ingredients (2)

Long local formulas use this family’s existing definitions. Each new abbreviation was expanded back to the identical native formula, including its free-variable context. The original edition is preserved below.

01Fix variables and assumptionsL1–10

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro N
  2. L2
    intro F
  3. L3
    intro G
  4. L4
    intro H
  5. L5
    intro K
  6. L6
    intro n
  7. L7
    intro z
  8. L8
    intro hH
  9. L9
    intro hK
  10. L10
    intro hbound
02Fix variables and assumptionsL11–13

Work with arbitrary variables or the premises of the current implication.

  1. L11
    intro hF
  2. L12
    intro hG
  3. L13
    intro hz
03Separate the logical casesL14–14

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L14
    cases hz
04Establish huL15–24

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution sum exists.

  1. L15
    have hu : ∃ u. DirichletSum(H,K,n,u)Definitions: DirichletSum
  2. L16
    specialize dirichlet_convolution_sum_exists (N)
  3. L17
    specialize dirichlet_convolution_sum_exists (H)
  4. L18
    specialize dirichlet_convolution_sum_exists (K)
  5. L19
    specialize dirichlet_convolution_sum_exists (n)
  6. L20
    apply dirichlet_convolution_sum_exists
  7. L21
    exact hH
  8. L22
    exact hK
  9. L23
    exact hz_left
  10. L24
    exact hbound
05Separate the logical casesL25–25

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L25
    cases hu
06Establish heqL26–35

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply dirichlet convolution positive source extensional.

  1. L26
    have heq : z=x
  2. L27
    specialize dirichlet_convolution_positive_source_extensional (F)
  3. L28
    specialize dirichlet_convolution_positive_source_extensional (G)
  4. L29
    specialize dirichlet_convolution_positive_source_extensional (H)
  5. L30
    specialize dirichlet_convolution_positive_source_extensional (K)
  6. L31
    specialize dirichlet_convolution_positive_source_extensional (n)
  7. L32
    specialize dirichlet_convolution_positive_source_extensional (z)
  8. L33
    specialize dirichlet_convolution_positive_source_extensional (x)
  9. L34
    apply dirichlet_convolution_positive_source_extensional
  10. L35
    exact hF
07Use earlier factsL36–38

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L36
    exact hG
  2. L37
    exact hz
  3. L38
    exact hu_witness
08Calculate and transport equalitiesL39–40

Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.

  1. L39
    rewrite heq
  2. L40
    rewrite heq
09Use earlier factsL41–41

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L41
    exact hu_witness

Library-wide reading audit

Original exact command ledger · 41 lines
  1. 0001intro N
  2. 0002intro F
  3. 0003intro G
  4. 0004intro H
  5. 0005intro K
  6. 0006intro n
  7. 0007intro z
  8. 0008intro hH
  9. 0009intro hK
  10. 0010intro hbound
  11. 0011intro hF
  12. 0012intro hG
  13. 0013intro hz
  14. 0014cases hz
  15. 0015have hu : exists u. (((~((n)=0)) /\ (exists dc_mask_source_transport_actual. ((((exists dst_positive_code_source_transport_actualmasktable dst_positive_scale_source_transport_actualmasktable dst_negative_code_source_transport_actualmasktable dst_negative_scale_source_transport_actualmasktable. (((dc_mask_source_transport_actual) = (((((dst_positive_code_source_transport_actualmasktable) + (dst_positive_scale_source_transport_actualmasktable)) * S ((dst_positive_code_source_transport_actualmasktable) + (dst_positive_scale_source_transport_actualmasktable)) + ((dst_positive_scale_source_transport_actualmasktable) + (dst_positive_scale_source_transport_actualmasktable))) + (((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) * S ((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) + ((dst_negative_scale_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)))) * S ((((dst_positive_code_source_transport_actualmasktable) + (dst_positive_scale_source_transport_actualmasktable)) * S ((dst_positive_code_source_transport_actualmasktable) + (dst_positive_scale_source_transport_actualmasktable)) + ((dst_positive_scale_source_transport_actualmasktable) + (dst_positive_scale_source_transport_actualmasktable))) + (((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) * S ((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) + ((dst_negative_scale_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)))) + ((((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) * S ((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) + ((dst_negative_scale_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable))) + (((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) * S ((dst_negative_code_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)) + ((dst_negative_scale_source_transport_actualmasktable) + (dst_negative_scale_source_transport_actualmasktable)))))) /\ (forall dst_index_source_transport_actualmasktable. (exists pvs_le_gap_source_transport_actualmasktabledomain. pvs_le_gap_source_transport_actualmasktabledomain + (dst_index_source_transport_actualmasktable) = (n)) -> exists dst_positive_source_transport_actualmasktable dst_negative_source_transport_actualmasktable dst_value_source_transport_actualmasktable. ((((exists ff_h_pvs_source_transport_actualmasktableentrypositive. ff_h_pvs_source_transport_actualmasktableentrypositive + S (dst_positive_source_transport_actualmasktable) = S ((S (dst_index_source_transport_actualmasktable)) * dst_positive_scale_source_transport_actualmasktable)) /\ exists ff_q_pvs_source_transport_actualmasktableentrypositive. dst_positive_code_source_transport_actualmasktable = ff_q_pvs_source_transport_actualmasktableentrypositive * S ((S (dst_index_source_transport_actualmasktable)) * dst_positive_scale_source_transport_actualmasktable) + (dst_positive_source_transport_actualmasktable))) /\ (((((exists ff_h_pvs_source_transport_actualmasktableentrynegative. ff_h_pvs_source_transport_actualmasktableentrynegative + S (dst_negative_source_transport_actualmasktable) = S ((S (dst_index_source_transport_actualmasktable)) * dst_negative_scale_source_transport_actualmasktable)) /\ exists ff_q_pvs_source_transport_actualmasktableentrynegative. dst_negative_code_source_transport_actualmasktable = ff_q_pvs_source_transport_actualmasktableentrynegative * S ((S (dst_index_source_transport_actualmasktable)) * dst_negative_scale_source_transport_actualmasktable) + (dst_negative_source_transport_actualmasktable))) /\ (exists ge_balance_positive_source_transport_actualmasktableentryvalue ge_balance_negative_source_transport_actualmasktableentryvalue. (((((dst_value_source_transport_actualmasktable) = 2 * (ge_balance_positive_source_transport_actualmasktableentryvalue) /\ (ge_balance_negative_source_transport_actualmasktableentryvalue) = 0) \/ exists ge_signed_half_source_transport_actualmasktableentryvaluedecode. (((dst_value_source_transport_actualmasktable) = 2 * ge_signed_half_source_transport_actualmasktableentryvaluedecode + 1 /\ (ge_balance_positive_source_transport_actualmasktableentryvalue) = 0) /\ (ge_balance_negative_source_transport_actualmasktableentryvalue) = S ge_signed_half_source_transport_actualmasktableentryvaluedecode))) /\ ((dst_positive_source_transport_actualmasktable) + ge_balance_negative_source_transport_actualmasktableentryvalue = (dst_negative_source_transport_actualmasktable) + ge_balance_positive_source_transport_actualmasktableentryvalue))))))))) /\ (forall dc_index_source_transport_actualmask dc_value_source_transport_actualmask. (exists pvs_le_gap_source_transport_actualmaskdomain. pvs_le_gap_source_transport_actualmaskdomain + (dc_index_source_transport_actualmask) = (n)) -> (exists dst_positive_code_source_transport_actualmasklookup dst_positive_scale_source_transport_actualmasklookup dst_negative_code_source_transport_actualmasklookup dst_negative_scale_source_transport_actualmasklookup dst_positive_source_transport_actualmasklookup dst_negative_source_transport_actualmasklookup. (((dc_mask_source_transport_actual) = (((((dst_positive_code_source_transport_actualmasklookup) + (dst_positive_scale_source_transport_actualmasklookup)) * S ((dst_positive_code_source_transport_actualmasklookup) + (dst_positive_scale_source_transport_actualmasklookup)) + ((dst_positive_scale_source_transport_actualmasklookup) + (dst_positive_scale_source_transport_actualmasklookup))) + (((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) * S ((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) + ((dst_negative_scale_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)))) * S ((((dst_positive_code_source_transport_actualmasklookup) + (dst_positive_scale_source_transport_actualmasklookup)) * S ((dst_positive_code_source_transport_actualmasklookup) + (dst_positive_scale_source_transport_actualmasklookup)) + ((dst_positive_scale_source_transport_actualmasklookup) + (dst_positive_scale_source_transport_actualmasklookup))) + (((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) * S ((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) + ((dst_negative_scale_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)))) + ((((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) * S ((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) + ((dst_negative_scale_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup))) + (((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) * S ((dst_negative_code_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)) + ((dst_negative_scale_source_transport_actualmasklookup) + (dst_negative_scale_source_transport_actualmasklookup)))))) /\ (((((exists ff_h_pvs_source_transport_actualmasklookuppositive. ff_h_pvs_source_transport_actualmasklookuppositive + S (dst_positive_source_transport_actualmasklookup) = S ((S (dc_index_source_transport_actualmask)) * dst_positive_scale_source_transport_actualmasklookup)) /\ exists ff_q_pvs_source_transport_actualmasklookuppositive. dst_positive_code_source_transport_actualmasklookup = ff_q_pvs_source_transport_actualmasklookuppositive * S ((S (dc_index_source_transport_actualmask)) * dst_positive_scale_source_transport_actualmasklookup) + (dst_positive_source_transport_actualmasklookup))) /\ (((((exists ff_h_pvs_source_transport_actualmasklookupnegative. ff_h_pvs_source_transport_actualmasklookupnegative + S (dst_negative_source_transport_actualmasklookup) = S ((S (dc_index_source_transport_actualmask)) * dst_negative_scale_source_transport_actualmasklookup)) /\ exists ff_q_pvs_source_transport_actualmasklookupnegative. dst_negative_code_source_transport_actualmasklookup = ff_q_pvs_source_transport_actualmasklookupnegative * S ((S (dc_index_source_transport_actualmask)) * dst_negative_scale_source_transport_actualmasklookup) + (dst_negative_source_transport_actualmasklookup))) /\ (exists ge_balance_positive_source_transport_actualmasklookupvalue ge_balance_negative_source_transport_actualmasklookupvalue. (((((dc_value_source_transport_actualmask) = 2 * (ge_balance_positive_source_transport_actualmasklookupvalue) /\ (ge_balance_negative_source_transport_actualmasklookupvalue) = 0) \/ exists ge_signed_half_source_transport_actualmasklookupvaluedecode. (((dc_value_source_transport_actualmask) = 2 * ge_signed_half_source_transport_actualmasklookupvaluedecode + 1 /\ (ge_balance_positive_source_transport_actualmasklookupvalue) = 0) /\ (ge_balance_negative_source_transport_actualmasklookupvalue) = S ge_signed_half_source_transport_actualmasklookupvaluedecode))) /\ ((dst_positive_source_transport_actualmasklookup) + ge_balance_negative_source_transport_actualmasklookupvalue = (dst_negative_source_transport_actualmasklookup) + ge_balance_positive_source_transport_actualmasklookupvalue))))))))) -> ((((~((dc_index_source_transport_actualmask)=0)) /\ (exists dc_quotient_source_transport_actualmaskentry dc_left_source_transport_actualmaskentry dc_right_source_transport_actualmaskentry. (((n)=(dc_index_source_transport_actualmask)*dc_quotient_source_transport_actualmaskentry) /\ (((exists dst_positive_code_source_transport_actualmaskentryleft dst_positive_scale_source_transport_actualmaskentryleft dst_negative_code_source_transport_actualmaskentryleft dst_negative_scale_source_transport_actualmaskentryleft dst_positive_source_transport_actualmaskentryleft dst_negative_source_transport_actualmaskentryleft. (((H) = (((((dst_positive_code_source_transport_actualmaskentryleft) + (dst_positive_scale_source_transport_actualmaskentryleft)) * S ((dst_positive_code_source_transport_actualmaskentryleft) + (dst_positive_scale_source_transport_actualmaskentryleft)) + ((dst_positive_scale_source_transport_actualmaskentryleft) + (dst_positive_scale_source_transport_actualmaskentryleft))) + (((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) * S ((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) + ((dst_negative_scale_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)))) * S ((((dst_positive_code_source_transport_actualmaskentryleft) + (dst_positive_scale_source_transport_actualmaskentryleft)) * S ((dst_positive_code_source_transport_actualmaskentryleft) + (dst_positive_scale_source_transport_actualmaskentryleft)) + ((dst_positive_scale_source_transport_actualmaskentryleft) + (dst_positive_scale_source_transport_actualmaskentryleft))) + (((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) * S ((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) + ((dst_negative_scale_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)))) + ((((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) * S ((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) + ((dst_negative_scale_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft))) + (((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) * S ((dst_negative_code_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)) + ((dst_negative_scale_source_transport_actualmaskentryleft) + (dst_negative_scale_source_transport_actualmaskentryleft)))))) /\ (((((exists ff_h_pvs_source_transport_actualmaskentryleftpositive. ff_h_pvs_source_transport_actualmaskentryleftpositive + S (dst_positive_source_transport_actualmaskentryleft) = S ((S (dc_index_source_transport_actualmask)) * dst_positive_scale_source_transport_actualmaskentryleft)) /\ exists ff_q_pvs_source_transport_actualmaskentryleftpositive. dst_positive_code_source_transport_actualmaskentryleft = ff_q_pvs_source_transport_actualmaskentryleftpositive * S ((S (dc_index_source_transport_actualmask)) * dst_positive_scale_source_transport_actualmaskentryleft) + (dst_positive_source_transport_actualmaskentryleft))) /\ (((((exists ff_h_pvs_source_transport_actualmaskentryleftnegative. ff_h_pvs_source_transport_actualmaskentryleftnegative + S (dst_negative_source_transport_actualmaskentryleft) = S ((S (dc_index_source_transport_actualmask)) * dst_negative_scale_source_transport_actualmaskentryleft)) /\ exists ff_q_pvs_source_transport_actualmaskentryleftnegative. dst_negative_code_source_transport_actualmaskentryleft = ff_q_pvs_source_transport_actualmaskentryleftnegative * S ((S (dc_index_source_transport_actualmask)) * dst_negative_scale_source_transport_actualmaskentryleft) + (dst_negative_source_transport_actualmaskentryleft))) /\ (exists ge_balance_positive_source_transport_actualmaskentryleftvalue ge_balance_negative_source_transport_actualmaskentryleftvalue. (((((dc_left_source_transport_actualmaskentry) = 2 * (ge_balance_positive_source_transport_actualmaskentryleftvalue) /\ (ge_balance_negative_source_transport_actualmaskentryleftvalue) = 0) \/ exists ge_signed_half_source_transport_actualmaskentryleftvaluedecode. (((dc_left_source_transport_actualmaskentry) = 2 * ge_signed_half_source_transport_actualmaskentryleftvaluedecode + 1 /\ (ge_balance_positive_source_transport_actualmaskentryleftvalue) = 0) /\ (ge_balance_negative_source_transport_actualmaskentryleftvalue) = S ge_signed_half_source_transport_actualmaskentryleftvaluedecode))) /\ ((dst_positive_source_transport_actualmaskentryleft) + ge_balance_negative_source_transport_actualmaskentryleftvalue = (dst_negative_source_transport_actualmaskentryleft) + ge_balance_positive_source_transport_actualmaskentryleftvalue))))))))) /\ (((exists dst_positive_code_source_transport_actualmaskentryright dst_positive_scale_source_transport_actualmaskentryright dst_negative_code_source_transport_actualmaskentryright dst_negative_scale_source_transport_actualmaskentryright dst_positive_source_transport_actualmaskentryright dst_negative_source_transport_actualmaskentryright. (((K) = (((((dst_positive_code_source_transport_actualmaskentryright) + (dst_positive_scale_source_transport_actualmaskentryright)) * S ((dst_positive_code_source_transport_actualmaskentryright) + (dst_positive_scale_source_transport_actualmaskentryright)) + ((dst_positive_scale_source_transport_actualmaskentryright) + (dst_positive_scale_source_transport_actualmaskentryright))) + (((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) * S ((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) + ((dst_negative_scale_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)))) * S ((((dst_positive_code_source_transport_actualmaskentryright) + (dst_positive_scale_source_transport_actualmaskentryright)) * S ((dst_positive_code_source_transport_actualmaskentryright) + (dst_positive_scale_source_transport_actualmaskentryright)) + ((dst_positive_scale_source_transport_actualmaskentryright) + (dst_positive_scale_source_transport_actualmaskentryright))) + (((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) * S ((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) + ((dst_negative_scale_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)))) + ((((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) * S ((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) + ((dst_negative_scale_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright))) + (((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) * S ((dst_negative_code_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)) + ((dst_negative_scale_source_transport_actualmaskentryright) + (dst_negative_scale_source_transport_actualmaskentryright)))))) /\ (((((exists ff_h_pvs_source_transport_actualmaskentryrightpositive. ff_h_pvs_source_transport_actualmaskentryrightpositive + S (dst_positive_source_transport_actualmaskentryright) = S ((S (dc_quotient_source_transport_actualmaskentry)) * dst_positive_scale_source_transport_actualmaskentryright)) /\ exists ff_q_pvs_source_transport_actualmaskentryrightpositive. dst_positive_code_source_transport_actualmaskentryright = ff_q_pvs_source_transport_actualmaskentryrightpositive * S ((S (dc_quotient_source_transport_actualmaskentry)) * dst_positive_scale_source_transport_actualmaskentryright) + (dst_positive_source_transport_actualmaskentryright))) /\ (((((exists ff_h_pvs_source_transport_actualmaskentryrightnegative. ff_h_pvs_source_transport_actualmaskentryrightnegative + S (dst_negative_source_transport_actualmaskentryright) = S ((S (dc_quotient_source_transport_actualmaskentry)) * dst_negative_scale_source_transport_actualmaskentryright)) /\ exists ff_q_pvs_source_transport_actualmaskentryrightnegative. dst_negative_code_source_transport_actualmaskentryright = ff_q_pvs_source_transport_actualmaskentryrightnegative * S ((S (dc_quotient_source_transport_actualmaskentry)) * dst_negative_scale_source_transport_actualmaskentryright) + (dst_negative_source_transport_actualmaskentryright))) /\ (exists ge_balance_positive_source_transport_actualmaskentryrightvalue ge_balance_negative_source_transport_actualmaskentryrightvalue. (((((dc_right_source_transport_actualmaskentry) = 2 * (ge_balance_positive_source_transport_actualmaskentryrightvalue) /\ (ge_balance_negative_source_transport_actualmaskentryrightvalue) = 0) \/ exists ge_signed_half_source_transport_actualmaskentryrightvaluedecode. (((dc_right_source_transport_actualmaskentry) = 2 * ge_signed_half_source_transport_actualmaskentryrightvaluedecode + 1 /\ (ge_balance_positive_source_transport_actualmaskentryrightvalue) = 0) /\ (ge_balance_negative_source_transport_actualmaskentryrightvalue) = S ge_signed_half_source_transport_actualmaskentryrightvaluedecode))) /\ ((dst_positive_source_transport_actualmaskentryright) + ge_balance_negative_source_transport_actualmaskentryrightvalue = (dst_negative_source_transport_actualmaskentryright) + ge_balance_positive_source_transport_actualmaskentryrightvalue))))))))) /\ (exists sto_ap_source_transport_actualmaskentryproduct sto_an_source_transport_actualmaskentryproduct sto_bp_source_transport_actualmaskentryproduct sto_bn_source_transport_actualmaskentryproduct sto_cp_source_transport_actualmaskentryproduct sto_cn_source_transport_actualmaskentryproduct. (((((dc_left_source_transport_actualmaskentry) = 2 * (sto_ap_source_transport_actualmaskentryproduct) /\ (sto_an_source_transport_actualmaskentryproduct) = 0) \/ exists ge_signed_half_source_transport_actualmaskentryproductleft. (((dc_left_source_transport_actualmaskentry) = 2 * ge_signed_half_source_transport_actualmaskentryproductleft + 1 /\ (sto_ap_source_transport_actualmaskentryproduct) = 0) /\ (sto_an_source_transport_actualmaskentryproduct) = S ge_signed_half_source_transport_actualmaskentryproductleft))) /\ ((((((dc_right_source_transport_actualmaskentry) = 2 * (sto_bp_source_transport_actualmaskentryproduct) /\ (sto_bn_source_transport_actualmaskentryproduct) = 0) \/ exists ge_signed_half_source_transport_actualmaskentryproductright. (((dc_right_source_transport_actualmaskentry) = 2 * ge_signed_half_source_transport_actualmaskentryproductright + 1 /\ (sto_bp_source_transport_actualmaskentryproduct) = 0) /\ (sto_bn_source_transport_actualmaskentryproduct) = S ge_signed_half_source_transport_actualmaskentryproductright))) /\ ((((((dc_value_source_transport_actualmask) = 2 * (sto_cp_source_transport_actualmaskentryproduct) /\ (sto_cn_source_transport_actualmaskentryproduct) = 0) \/ exists ge_signed_half_source_transport_actualmaskentryproductoutput. (((dc_value_source_transport_actualmask) = 2 * ge_signed_half_source_transport_actualmaskentryproductoutput + 1 /\ (sto_cp_source_transport_actualmaskentryproduct) = 0) /\ (sto_cn_source_transport_actualmaskentryproduct) = S ge_signed_half_source_transport_actualmaskentryproductoutput))) /\ ((sto_ap_source_transport_actualmaskentryproduct * sto_bp_source_transport_actualmaskentryproduct + sto_an_source_transport_actualmaskentryproduct * sto_bn_source_transport_actualmaskentryproduct) + sto_cn_source_transport_actualmaskentryproduct = (sto_ap_source_transport_actualmaskentryproduct * sto_bn_source_transport_actualmaskentryproduct + sto_an_source_transport_actualmaskentryproduct * sto_bp_source_transport_actualmaskentryproduct) + sto_cp_source_transport_actualmaskentryproduct))))))))))))))) \/ ((((dc_index_source_transport_actualmask)=0 \/ ~(exists pvs_factor_source_transport_actualmaskentrynondivisor. (n) = (dc_index_source_transport_actualmask) * pvs_factor_source_transport_actualmaskentrynondivisor)) /\ ((dc_value_source_transport_actualmask)=0))))))) /\ (exists dst_positive_code_source_transport_actualfold dst_positive_scale_source_transport_actualfold dst_negative_code_source_transport_actualfold dst_negative_scale_source_transport_actualfold dst_positive_sum_source_transport_actualfold dst_negative_sum_source_transport_actualfold. (((dc_mask_source_transport_actual) = (((((dst_positive_code_source_transport_actualfold) + (dst_positive_scale_source_transport_actualfold)) * S ((dst_positive_code_source_transport_actualfold) + (dst_positive_scale_source_transport_actualfold)) + ((dst_positive_scale_source_transport_actualfold) + (dst_positive_scale_source_transport_actualfold))) + (((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) * S ((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) + ((dst_negative_scale_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)))) * S ((((dst_positive_code_source_transport_actualfold) + (dst_positive_scale_source_transport_actualfold)) * S ((dst_positive_code_source_transport_actualfold) + (dst_positive_scale_source_transport_actualfold)) + ((dst_positive_scale_source_transport_actualfold) + (dst_positive_scale_source_transport_actualfold))) + (((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) * S ((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) + ((dst_negative_scale_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)))) + ((((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) * S ((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) + ((dst_negative_scale_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold))) + (((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) * S ((dst_negative_code_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)) + ((dst_negative_scale_source_transport_actualfold) + (dst_negative_scale_source_transport_actualfold)))))) /\ (((exists fs_u_dst_source_transport_actualfoldpositive fs_v_dst_source_transport_actualfoldpositive. ((((exists fs_h_dst_source_transport_actualfoldpositive_body_start. fs_h_dst_source_transport_actualfoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_source_transport_actualfoldpositive)) /\ exists fs_q_dst_source_transport_actualfoldpositive_body_start. fs_u_dst_source_transport_actualfoldpositive = fs_q_dst_source_transport_actualfoldpositive_body_start * S ((S (0)) * fs_v_dst_source_transport_actualfoldpositive) + (0))) /\ ((((exists fs_h_dst_source_transport_actualfoldpositive_body_terminal. fs_h_dst_source_transport_actualfoldpositive_body_terminal + S (dst_positive_sum_source_transport_actualfold) = S ((S (S (n))) * fs_v_dst_source_transport_actualfoldpositive)) /\ exists fs_q_dst_source_transport_actualfoldpositive_body_terminal. fs_u_dst_source_transport_actualfoldpositive = fs_q_dst_source_transport_actualfoldpositive_body_terminal * S ((S (S (n))) * fs_v_dst_source_transport_actualfoldpositive) + (dst_positive_sum_source_transport_actualfold))) /\ forall fs_i_dst_source_transport_actualfoldpositive_body_steps. (exists fs_lt_dst_source_transport_actualfoldpositive_body_steps_bound. fs_lt_dst_source_transport_actualfoldpositive_body_steps_bound + S fs_i_dst_source_transport_actualfoldpositive_body_steps = S (n)) -> exists fs_a_dst_source_transport_actualfoldpositive_body_steps fs_r_dst_source_transport_actualfoldpositive_body_steps fs_s_dst_source_transport_actualfoldpositive_body_steps. ((((exists fs_h_dst_source_transport_actualfoldpositive_body_steps_summand. fs_h_dst_source_transport_actualfoldpositive_body_steps_summand + S (fs_a_dst_source_transport_actualfoldpositive_body_steps) = S ((S (fs_i_dst_source_transport_actualfoldpositive_body_steps)) * dst_positive_scale_source_transport_actualfold)) /\ exists fs_q_dst_source_transport_actualfoldpositive_body_steps_summand. dst_positive_code_source_transport_actualfold = fs_q_dst_source_transport_actualfoldpositive_body_steps_summand * S ((S (fs_i_dst_source_transport_actualfoldpositive_body_steps)) * dst_positive_scale_source_transport_actualfold) + (fs_a_dst_source_transport_actualfoldpositive_body_steps))) /\ ((((exists fs_h_dst_source_transport_actualfoldpositive_body_steps_partial. fs_h_dst_source_transport_actualfoldpositive_body_steps_partial + S (fs_r_dst_source_transport_actualfoldpositive_body_steps) = S ((S (fs_i_dst_source_transport_actualfoldpositive_body_steps)) * fs_v_dst_source_transport_actualfoldpositive)) /\ exists fs_q_dst_source_transport_actualfoldpositive_body_steps_partial. fs_u_dst_source_transport_actualfoldpositive = fs_q_dst_source_transport_actualfoldpositive_body_steps_partial * S ((S (fs_i_dst_source_transport_actualfoldpositive_body_steps)) * fs_v_dst_source_transport_actualfoldpositive) + (fs_r_dst_source_transport_actualfoldpositive_body_steps))) /\ ((((exists fs_h_dst_source_transport_actualfoldpositive_body_steps_successor. fs_h_dst_source_transport_actualfoldpositive_body_steps_successor + S (fs_s_dst_source_transport_actualfoldpositive_body_steps) = S ((S (S fs_i_dst_source_transport_actualfoldpositive_body_steps)) * fs_v_dst_source_transport_actualfoldpositive)) /\ exists fs_q_dst_source_transport_actualfoldpositive_body_steps_successor. fs_u_dst_source_transport_actualfoldpositive = fs_q_dst_source_transport_actualfoldpositive_body_steps_successor * S ((S (S fs_i_dst_source_transport_actualfoldpositive_body_steps)) * fs_v_dst_source_transport_actualfoldpositive) + (fs_s_dst_source_transport_actualfoldpositive_body_steps))) /\ fs_s_dst_source_transport_actualfoldpositive_body_steps = fs_r_dst_source_transport_actualfoldpositive_body_steps + fs_a_dst_source_transport_actualfoldpositive_body_steps)))))) /\ (((exists fs_u_dst_source_transport_actualfoldnegative fs_v_dst_source_transport_actualfoldnegative. ((((exists fs_h_dst_source_transport_actualfoldnegative_body_start. fs_h_dst_source_transport_actualfoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_source_transport_actualfoldnegative)) /\ exists fs_q_dst_source_transport_actualfoldnegative_body_start. fs_u_dst_source_transport_actualfoldnegative = fs_q_dst_source_transport_actualfoldnegative_body_start * S ((S (0)) * fs_v_dst_source_transport_actualfoldnegative) + (0))) /\ ((((exists fs_h_dst_source_transport_actualfoldnegative_body_terminal. fs_h_dst_source_transport_actualfoldnegative_body_terminal + S (dst_negative_sum_source_transport_actualfold) = S ((S (S (n))) * fs_v_dst_source_transport_actualfoldnegative)) /\ exists fs_q_dst_source_transport_actualfoldnegative_body_terminal. fs_u_dst_source_transport_actualfoldnegative = fs_q_dst_source_transport_actualfoldnegative_body_terminal * S ((S (S (n))) * fs_v_dst_source_transport_actualfoldnegative) + (dst_negative_sum_source_transport_actualfold))) /\ forall fs_i_dst_source_transport_actualfoldnegative_body_steps. (exists fs_lt_dst_source_transport_actualfoldnegative_body_steps_bound. fs_lt_dst_source_transport_actualfoldnegative_body_steps_bound + S fs_i_dst_source_transport_actualfoldnegative_body_steps = S (n)) -> exists fs_a_dst_source_transport_actualfoldnegative_body_steps fs_r_dst_source_transport_actualfoldnegative_body_steps fs_s_dst_source_transport_actualfoldnegative_body_steps. ((((exists fs_h_dst_source_transport_actualfoldnegative_body_steps_summand. fs_h_dst_source_transport_actualfoldnegative_body_steps_summand + S (fs_a_dst_source_transport_actualfoldnegative_body_steps) = S ((S (fs_i_dst_source_transport_actualfoldnegative_body_steps)) * dst_negative_scale_source_transport_actualfold)) /\ exists fs_q_dst_source_transport_actualfoldnegative_body_steps_summand. dst_negative_code_source_transport_actualfold = fs_q_dst_source_transport_actualfoldnegative_body_steps_summand * S ((S (fs_i_dst_source_transport_actualfoldnegative_body_steps)) * dst_negative_scale_source_transport_actualfold) + (fs_a_dst_source_transport_actualfoldnegative_body_steps))) /\ ((((exists fs_h_dst_source_transport_actualfoldnegative_body_steps_partial. fs_h_dst_source_transport_actualfoldnegative_body_steps_partial + S (fs_r_dst_source_transport_actualfoldnegative_body_steps) = S ((S (fs_i_dst_source_transport_actualfoldnegative_body_steps)) * fs_v_dst_source_transport_actualfoldnegative)) /\ exists fs_q_dst_source_transport_actualfoldnegative_body_steps_partial. fs_u_dst_source_transport_actualfoldnegative = fs_q_dst_source_transport_actualfoldnegative_body_steps_partial * S ((S (fs_i_dst_source_transport_actualfoldnegative_body_steps)) * fs_v_dst_source_transport_actualfoldnegative) + (fs_r_dst_source_transport_actualfoldnegative_body_steps))) /\ ((((exists fs_h_dst_source_transport_actualfoldnegative_body_steps_successor. fs_h_dst_source_transport_actualfoldnegative_body_steps_successor + S (fs_s_dst_source_transport_actualfoldnegative_body_steps) = S ((S (S fs_i_dst_source_transport_actualfoldnegative_body_steps)) * fs_v_dst_source_transport_actualfoldnegative)) /\ exists fs_q_dst_source_transport_actualfoldnegative_body_steps_successor. fs_u_dst_source_transport_actualfoldnegative = fs_q_dst_source_transport_actualfoldnegative_body_steps_successor * S ((S (S fs_i_dst_source_transport_actualfoldnegative_body_steps)) * fs_v_dst_source_transport_actualfoldnegative) + (fs_s_dst_source_transport_actualfoldnegative_body_steps))) /\ fs_s_dst_source_transport_actualfoldnegative_body_steps = fs_r_dst_source_transport_actualfoldnegative_body_steps + fs_a_dst_source_transport_actualfoldnegative_body_steps)))))) /\ (exists ge_balance_positive_source_transport_actualfoldresult ge_balance_negative_source_transport_actualfoldresult. (((((u) = 2 * (ge_balance_positive_source_transport_actualfoldresult) /\ (ge_balance_negative_source_transport_actualfoldresult) = 0) \/ exists ge_signed_half_source_transport_actualfoldresultdecode. (((u) = 2 * ge_signed_half_source_transport_actualfoldresultdecode + 1 /\ (ge_balance_positive_source_transport_actualfoldresult) = 0) /\ (ge_balance_negative_source_transport_actualfoldresult) = S ge_signed_half_source_transport_actualfoldresultdecode))) /\ ((dst_positive_sum_source_transport_actualfold) + ge_balance_negative_source_transport_actualfoldresult = (dst_negative_sum_source_transport_actualfold) + ge_balance_positive_source_transport_actualfoldresult)))))))))))))
  16. 0016specialize dirichlet_convolution_sum_exists (N)
  17. 0017specialize dirichlet_convolution_sum_exists (H)
  18. 0018specialize dirichlet_convolution_sum_exists (K)
  19. 0019specialize dirichlet_convolution_sum_exists (n)
  20. 0020apply dirichlet_convolution_sum_exists
  21. 0021exact hH
  22. 0022exact hK
  23. 0023exact hz_left
  24. 0024exact hbound
  25. 0025cases hu
  26. 0026have heq : z=x
  27. 0027specialize dirichlet_convolution_positive_source_extensional (F)
  28. 0028specialize dirichlet_convolution_positive_source_extensional (G)
  29. 0029specialize dirichlet_convolution_positive_source_extensional (H)
  30. 0030specialize dirichlet_convolution_positive_source_extensional (K)
  31. 0031specialize dirichlet_convolution_positive_source_extensional (n)
  32. 0032specialize dirichlet_convolution_positive_source_extensional (z)
  33. 0033specialize dirichlet_convolution_positive_source_extensional (x)
  34. 0034apply dirichlet_convolution_positive_source_extensional
  35. 0035exact hF
  36. 0036exact hG
  37. 0037exact hz
  38. 0038exact hu_witness
  39. 0039rewrite heq
  40. 0040rewrite heq
  41. 0041exact hu_witness