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. (exists di_delta_inverse_tables_source. ((((exists dst_positive_code_inverse_tables_sourcedeltatable dst_positive_scale_inverse_tables_sourcedeltatable dst_negative_code_inverse_tables_sourcedeltatable dst_negative_scale_inverse_tables_sourcedeltatable. (((di_delta_inverse_tables_source) = (((((dst_positive_code_inverse_tables_sourcedeltatable) + (dst_positive_scale_inverse_tables_sourcedeltatable)) * S ((dst_positive_code_inverse_tables_sourcedeltatable) + (dst_positive_scale_inverse_tables_sourcedeltatable)) + ((dst_positive_scale_inverse_tables_sourcedeltatable) + (dst_positive_scale_inverse_tables_sourcedeltatable))) + (((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) * S ((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) + ((dst_negative_scale_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)))) * S ((((dst_positive_code_inverse_tables_sourcedeltatable) + (dst_positive_scale_inverse_tables_sourcedeltatable)) * S ((dst_positive_code_inverse_tables_sourcedeltatable) + (dst_positive_scale_inverse_tables_sourcedeltatable)) + ((dst_positive_scale_inverse_tables_sourcedeltatable) + (dst_positive_scale_inverse_tables_sourcedeltatable))) + (((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) * S ((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) + ((dst_negative_scale_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)))) + ((((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) * S ((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) + ((dst_negative_scale_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable))) + (((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) * S ((dst_negative_code_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)) + ((dst_negative_scale_inverse_tables_sourcedeltatable) + (dst_negative_scale_inverse_tables_sourcedeltatable)))))) /\ (forall dst_index_inverse_tables_sourcedeltatable. (exists pvs_le_gap_inverse_tables_sourcedeltatabledomain. pvs_le_gap_inverse_tables_sourcedeltatabledomain + (dst_index_inverse_tables_sourcedeltatable) = (N)) -> exists dst_positive_inverse_tables_sourcedeltatable dst_negative_inverse_tables_sourcedeltatable dst_value_inverse_tables_sourcedeltatable. ((((exists ff_h_pvs_inverse_tables_sourcedeltatableentrypositive. ff_h_pvs_inverse_tables_sourcedeltatableentrypositive + S (dst_positive_inverse_tables_sourcedeltatable) = S ((S (dst_index_inverse_tables_sourcedeltatable)) * dst_positive_scale_inverse_tables_sourcedeltatable)) /\ exists ff_q_pvs_inverse_tables_sourcedeltatableentrypositive. dst_positive_code_inverse_tables_sourcedeltatable = ff_q_pvs_inverse_tables_sourcedeltatableentrypositive * S ((S (dst_index_inverse_tables_sourcedeltatable)) * dst_positive_scale_inverse_tables_sourcedeltatable) + (dst_positive_inverse_tables_sourcedeltatable))) /\ (((((exists ff_h_pvs_inverse_tables_sourcedeltatableentrynegative. ff_h_pvs_inverse_tables_sourcedeltatableentrynegative + S (dst_negative_inverse_tables_sourcedeltatable) = S ((S (dst_index_inverse_tables_sourcedeltatable)) * dst_negative_scale_inverse_tables_sourcedeltatable)) /\ exists ff_q_pvs_inverse_tables_sourcedeltatableentrynegative. dst_negative_code_inverse_tables_sourcedeltatable = ff_q_pvs_inverse_tables_sourcedeltatableentrynegative * S ((S (dst_index_inverse_tables_sourcedeltatable)) * dst_negative_scale_inverse_tables_sourcedeltatable) + (dst_negative_inverse_tables_sourcedeltatable))) /\ (exists ge_balance_positive_inverse_tables_sourcedeltatableentryvalue ge_balance_negative_inverse_tables_sourcedeltatableentryvalue. (((((dst_value_inverse_tables_sourcedeltatable) = 2 * (ge_balance_positive_inverse_tables_sourcedeltatableentryvalue) /\ (ge_balance_negative_inverse_tables_sourcedeltatableentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcedeltatableentryvaluedecode. (((dst_value_inverse_tables_sourcedeltatable) = 2 * ge_signed_half_inverse_tables_sourcedeltatableentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcedeltatableentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcedeltatableentryvalue) = S ge_signed_half_inverse_tables_sourcedeltatableentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourcedeltatable) + ge_balance_negative_inverse_tables_sourcedeltatableentryvalue = (dst_negative_inverse_tables_sourcedeltatable) + ge_balance_positive_inverse_tables_sourcedeltatableentryvalue))))))))) /\ (forall du_index_inverse_tables_sourcedelta du_value_inverse_tables_sourcedelta. ~(du_index_inverse_tables_sourcedelta=0) -> (exists pvs_le_gap_inverse_tables_sourcedeltabound. pvs_le_gap_inverse_tables_sourcedeltabound + (du_index_inverse_tables_sourcedelta) = (N)) -> (exists dst_positive_code_inverse_tables_sourcedeltaentry dst_positive_scale_inverse_tables_sourcedeltaentry dst_negative_code_inverse_tables_sourcedeltaentry dst_negative_scale_inverse_tables_sourcedeltaentry dst_positive_inverse_tables_sourcedeltaentry dst_negative_inverse_tables_sourcedeltaentry. (((di_delta_inverse_tables_source) = (((((dst_positive_code_inverse_tables_sourcedeltaentry) + (dst_positive_scale_inverse_tables_sourcedeltaentry)) * S ((dst_positive_code_inverse_tables_sourcedeltaentry) + (dst_positive_scale_inverse_tables_sourcedeltaentry)) + ((dst_positive_scale_inverse_tables_sourcedeltaentry) + (dst_positive_scale_inverse_tables_sourcedeltaentry))) + (((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) * S ((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) + ((dst_negative_scale_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)))) * S ((((dst_positive_code_inverse_tables_sourcedeltaentry) + (dst_positive_scale_inverse_tables_sourcedeltaentry)) * S ((dst_positive_code_inverse_tables_sourcedeltaentry) + (dst_positive_scale_inverse_tables_sourcedeltaentry)) + ((dst_positive_scale_inverse_tables_sourcedeltaentry) + (dst_positive_scale_inverse_tables_sourcedeltaentry))) + (((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) * S ((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) + ((dst_negative_scale_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)))) + ((((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) * S ((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) + ((dst_negative_scale_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry))) + (((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) * S ((dst_negative_code_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)) + ((dst_negative_scale_inverse_tables_sourcedeltaentry) + (dst_negative_scale_inverse_tables_sourcedeltaentry)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourcedeltaentrypositive. ff_h_pvs_inverse_tables_sourcedeltaentrypositive + S (dst_positive_inverse_tables_sourcedeltaentry) = S ((S (du_index_inverse_tables_sourcedelta)) * dst_positive_scale_inverse_tables_sourcedeltaentry)) /\ exists ff_q_pvs_inverse_tables_sourcedeltaentrypositive. dst_positive_code_inverse_tables_sourcedeltaentry = ff_q_pvs_inverse_tables_sourcedeltaentrypositive * S ((S (du_index_inverse_tables_sourcedelta)) * dst_positive_scale_inverse_tables_sourcedeltaentry) + (dst_positive_inverse_tables_sourcedeltaentry))) /\ (((((exists ff_h_pvs_inverse_tables_sourcedeltaentrynegative. ff_h_pvs_inverse_tables_sourcedeltaentrynegative + S (dst_negative_inverse_tables_sourcedeltaentry) = S ((S (du_index_inverse_tables_sourcedelta)) * dst_negative_scale_inverse_tables_sourcedeltaentry)) /\ exists ff_q_pvs_inverse_tables_sourcedeltaentrynegative. dst_negative_code_inverse_tables_sourcedeltaentry = ff_q_pvs_inverse_tables_sourcedeltaentrynegative * S ((S (du_index_inverse_tables_sourcedelta)) * dst_negative_scale_inverse_tables_sourcedeltaentry) + (dst_negative_inverse_tables_sourcedeltaentry))) /\ (exists ge_balance_positive_inverse_tables_sourcedeltaentryvalue ge_balance_negative_inverse_tables_sourcedeltaentryvalue. (((((du_value_inverse_tables_sourcedelta) = 2 * (ge_balance_positive_inverse_tables_sourcedeltaentryvalue) /\ (ge_balance_negative_inverse_tables_sourcedeltaentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcedeltaentryvaluedecode. (((du_value_inverse_tables_sourcedelta) = 2 * ge_signed_half_inverse_tables_sourcedeltaentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcedeltaentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcedeltaentryvalue) = S ge_signed_half_inverse_tables_sourcedeltaentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourcedeltaentry) + ge_balance_negative_inverse_tables_sourcedeltaentryvalue = (dst_negative_inverse_tables_sourcedeltaentry) + ge_balance_positive_inverse_tables_sourcedeltaentryvalue))))))))) -> ((((du_index_inverse_tables_sourcedelta)=1 -> (du_value_inverse_tables_sourcedelta)=2) /\ (~((du_index_inverse_tables_sourcedelta)=1) -> (du_value_inverse_tables_sourcedelta)=0)))))) /\ (((((exists dst_positive_code_inverse_tables_sourceleftleft dst_positive_scale_inverse_tables_sourceleftleft dst_negative_code_inverse_tables_sourceleftleft dst_negative_scale_inverse_tables_sourceleftleft. (((F) = (((((dst_positive_code_inverse_tables_sourceleftleft) + (dst_positive_scale_inverse_tables_sourceleftleft)) * S ((dst_positive_code_inverse_tables_sourceleftleft) + (dst_positive_scale_inverse_tables_sourceleftleft)) + ((dst_positive_scale_inverse_tables_sourceleftleft) + (dst_positive_scale_inverse_tables_sourceleftleft))) + (((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) * S ((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) + ((dst_negative_scale_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)))) * S ((((dst_positive_code_inverse_tables_sourceleftleft) + (dst_positive_scale_inverse_tables_sourceleftleft)) * S ((dst_positive_code_inverse_tables_sourceleftleft) + (dst_positive_scale_inverse_tables_sourceleftleft)) + ((dst_positive_scale_inverse_tables_sourceleftleft) + (dst_positive_scale_inverse_tables_sourceleftleft))) + (((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) * S ((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) + ((dst_negative_scale_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)))) + ((((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) * S ((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) + ((dst_negative_scale_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft))) + (((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) * S ((dst_negative_code_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)) + ((dst_negative_scale_inverse_tables_sourceleftleft) + (dst_negative_scale_inverse_tables_sourceleftleft)))))) /\ (forall dst_index_inverse_tables_sourceleftleft. (exists pvs_le_gap_inverse_tables_sourceleftleftdomain. pvs_le_gap_inverse_tables_sourceleftleftdomain + (dst_index_inverse_tables_sourceleftleft) = (N)) -> exists dst_positive_inverse_tables_sourceleftleft dst_negative_inverse_tables_sourceleftleft dst_value_inverse_tables_sourceleftleft. ((((exists ff_h_pvs_inverse_tables_sourceleftleftentrypositive. ff_h_pvs_inverse_tables_sourceleftleftentrypositive + S (dst_positive_inverse_tables_sourceleftleft) = S ((S (dst_index_inverse_tables_sourceleftleft)) * dst_positive_scale_inverse_tables_sourceleftleft)) /\ exists ff_q_pvs_inverse_tables_sourceleftleftentrypositive. dst_positive_code_inverse_tables_sourceleftleft = ff_q_pvs_inverse_tables_sourceleftleftentrypositive * S ((S (dst_index_inverse_tables_sourceleftleft)) * dst_positive_scale_inverse_tables_sourceleftleft) + (dst_positive_inverse_tables_sourceleftleft))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftleftentrynegative. ff_h_pvs_inverse_tables_sourceleftleftentrynegative + S (dst_negative_inverse_tables_sourceleftleft) = S ((S (dst_index_inverse_tables_sourceleftleft)) * dst_negative_scale_inverse_tables_sourceleftleft)) /\ exists ff_q_pvs_inverse_tables_sourceleftleftentrynegative. dst_negative_code_inverse_tables_sourceleftleft = ff_q_pvs_inverse_tables_sourceleftleftentrynegative * S ((S (dst_index_inverse_tables_sourceleftleft)) * dst_negative_scale_inverse_tables_sourceleftleft) + (dst_negative_inverse_tables_sourceleftleft))) /\ (exists ge_balance_positive_inverse_tables_sourceleftleftentryvalue ge_balance_negative_inverse_tables_sourceleftleftentryvalue. (((((dst_value_inverse_tables_sourceleftleft) = 2 * (ge_balance_positive_inverse_tables_sourceleftleftentryvalue) /\ (ge_balance_negative_inverse_tables_sourceleftleftentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftleftentryvaluedecode. (((dst_value_inverse_tables_sourceleftleft) = 2 * ge_signed_half_inverse_tables_sourceleftleftentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftleftentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftleftentryvalue) = S ge_signed_half_inverse_tables_sourceleftleftentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourceleftleft) + ge_balance_negative_inverse_tables_sourceleftleftentryvalue = (dst_negative_inverse_tables_sourceleftleft) + ge_balance_positive_inverse_tables_sourceleftleftentryvalue))))))))) /\ (((exists dst_positive_code_inverse_tables_sourceleftright dst_positive_scale_inverse_tables_sourceleftright dst_negative_code_inverse_tables_sourceleftright dst_negative_scale_inverse_tables_sourceleftright. (((G) = (((((dst_positive_code_inverse_tables_sourceleftright) + (dst_positive_scale_inverse_tables_sourceleftright)) * S ((dst_positive_code_inverse_tables_sourceleftright) + (dst_positive_scale_inverse_tables_sourceleftright)) + ((dst_positive_scale_inverse_tables_sourceleftright) + (dst_positive_scale_inverse_tables_sourceleftright))) + (((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) * S ((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) + ((dst_negative_scale_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)))) * S ((((dst_positive_code_inverse_tables_sourceleftright) + (dst_positive_scale_inverse_tables_sourceleftright)) * S ((dst_positive_code_inverse_tables_sourceleftright) + (dst_positive_scale_inverse_tables_sourceleftright)) + ((dst_positive_scale_inverse_tables_sourceleftright) + (dst_positive_scale_inverse_tables_sourceleftright))) + (((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) * S ((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) + ((dst_negative_scale_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)))) + ((((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) * S ((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) + ((dst_negative_scale_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright))) + (((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) * S ((dst_negative_code_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)) + ((dst_negative_scale_inverse_tables_sourceleftright) + (dst_negative_scale_inverse_tables_sourceleftright)))))) /\ (forall dst_index_inverse_tables_sourceleftright. (exists pvs_le_gap_inverse_tables_sourceleftrightdomain. pvs_le_gap_inverse_tables_sourceleftrightdomain + (dst_index_inverse_tables_sourceleftright) = (N)) -> exists dst_positive_inverse_tables_sourceleftright dst_negative_inverse_tables_sourceleftright dst_value_inverse_tables_sourceleftright. ((((exists ff_h_pvs_inverse_tables_sourceleftrightentrypositive. ff_h_pvs_inverse_tables_sourceleftrightentrypositive + S (dst_positive_inverse_tables_sourceleftright) = S ((S (dst_index_inverse_tables_sourceleftright)) * dst_positive_scale_inverse_tables_sourceleftright)) /\ exists ff_q_pvs_inverse_tables_sourceleftrightentrypositive. dst_positive_code_inverse_tables_sourceleftright = ff_q_pvs_inverse_tables_sourceleftrightentrypositive * S ((S (dst_index_inverse_tables_sourceleftright)) * dst_positive_scale_inverse_tables_sourceleftright) + (dst_positive_inverse_tables_sourceleftright))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftrightentrynegative. ff_h_pvs_inverse_tables_sourceleftrightentrynegative + S (dst_negative_inverse_tables_sourceleftright) = S ((S (dst_index_inverse_tables_sourceleftright)) * dst_negative_scale_inverse_tables_sourceleftright)) /\ exists ff_q_pvs_inverse_tables_sourceleftrightentrynegative. dst_negative_code_inverse_tables_sourceleftright = ff_q_pvs_inverse_tables_sourceleftrightentrynegative * S ((S (dst_index_inverse_tables_sourceleftright)) * dst_negative_scale_inverse_tables_sourceleftright) + (dst_negative_inverse_tables_sourceleftright))) /\ (exists ge_balance_positive_inverse_tables_sourceleftrightentryvalue ge_balance_negative_inverse_tables_sourceleftrightentryvalue. (((((dst_value_inverse_tables_sourceleftright) = 2 * (ge_balance_positive_inverse_tables_sourceleftrightentryvalue) /\ (ge_balance_negative_inverse_tables_sourceleftrightentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftrightentryvaluedecode. (((dst_value_inverse_tables_sourceleftright) = 2 * ge_signed_half_inverse_tables_sourceleftrightentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftrightentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftrightentryvalue) = S ge_signed_half_inverse_tables_sourceleftrightentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourceleftright) + ge_balance_negative_inverse_tables_sourceleftrightentryvalue = (dst_negative_inverse_tables_sourceleftright) + ge_balance_positive_inverse_tables_sourceleftrightentryvalue))))))))) /\ (((exists dst_positive_code_inverse_tables_sourcelefttable dst_positive_scale_inverse_tables_sourcelefttable dst_negative_code_inverse_tables_sourcelefttable dst_negative_scale_inverse_tables_sourcelefttable. (((di_delta_inverse_tables_source) = (((((dst_positive_code_inverse_tables_sourcelefttable) + (dst_positive_scale_inverse_tables_sourcelefttable)) * S ((dst_positive_code_inverse_tables_sourcelefttable) + (dst_positive_scale_inverse_tables_sourcelefttable)) + ((dst_positive_scale_inverse_tables_sourcelefttable) + (dst_positive_scale_inverse_tables_sourcelefttable))) + (((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) * S ((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) + ((dst_negative_scale_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)))) * S ((((dst_positive_code_inverse_tables_sourcelefttable) + (dst_positive_scale_inverse_tables_sourcelefttable)) * S ((dst_positive_code_inverse_tables_sourcelefttable) + (dst_positive_scale_inverse_tables_sourcelefttable)) + ((dst_positive_scale_inverse_tables_sourcelefttable) + (dst_positive_scale_inverse_tables_sourcelefttable))) + (((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) * S ((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) + ((dst_negative_scale_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)))) + ((((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) * S ((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) + ((dst_negative_scale_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable))) + (((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) * S ((dst_negative_code_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)) + ((dst_negative_scale_inverse_tables_sourcelefttable) + (dst_negative_scale_inverse_tables_sourcelefttable)))))) /\ (forall dst_index_inverse_tables_sourcelefttable. (exists pvs_le_gap_inverse_tables_sourcelefttabledomain. pvs_le_gap_inverse_tables_sourcelefttabledomain + (dst_index_inverse_tables_sourcelefttable) = (N)) -> exists dst_positive_inverse_tables_sourcelefttable dst_negative_inverse_tables_sourcelefttable dst_value_inverse_tables_sourcelefttable. ((((exists ff_h_pvs_inverse_tables_sourcelefttableentrypositive. ff_h_pvs_inverse_tables_sourcelefttableentrypositive + S (dst_positive_inverse_tables_sourcelefttable) = S ((S (dst_index_inverse_tables_sourcelefttable)) * dst_positive_scale_inverse_tables_sourcelefttable)) /\ exists ff_q_pvs_inverse_tables_sourcelefttableentrypositive. dst_positive_code_inverse_tables_sourcelefttable = ff_q_pvs_inverse_tables_sourcelefttableentrypositive * S ((S (dst_index_inverse_tables_sourcelefttable)) * dst_positive_scale_inverse_tables_sourcelefttable) + (dst_positive_inverse_tables_sourcelefttable))) /\ (((((exists ff_h_pvs_inverse_tables_sourcelefttableentrynegative. ff_h_pvs_inverse_tables_sourcelefttableentrynegative + S (dst_negative_inverse_tables_sourcelefttable) = S ((S (dst_index_inverse_tables_sourcelefttable)) * dst_negative_scale_inverse_tables_sourcelefttable)) /\ exists ff_q_pvs_inverse_tables_sourcelefttableentrynegative. dst_negative_code_inverse_tables_sourcelefttable = ff_q_pvs_inverse_tables_sourcelefttableentrynegative * S ((S (dst_index_inverse_tables_sourcelefttable)) * dst_negative_scale_inverse_tables_sourcelefttable) + (dst_negative_inverse_tables_sourcelefttable))) /\ (exists ge_balance_positive_inverse_tables_sourcelefttableentryvalue ge_balance_negative_inverse_tables_sourcelefttableentryvalue. (((((dst_value_inverse_tables_sourcelefttable) = 2 * (ge_balance_positive_inverse_tables_sourcelefttableentryvalue) /\ (ge_balance_negative_inverse_tables_sourcelefttableentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcelefttableentryvaluedecode. (((dst_value_inverse_tables_sourcelefttable) = 2 * ge_signed_half_inverse_tables_sourcelefttableentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcelefttableentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcelefttableentryvalue) = S ge_signed_half_inverse_tables_sourcelefttableentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourcelefttable) + ge_balance_negative_inverse_tables_sourcelefttableentryvalue = (dst_negative_inverse_tables_sourcelefttable) + ge_balance_positive_inverse_tables_sourcelefttableentryvalue))))))))) /\ (forall dc_input_inverse_tables_sourceleft dc_output_inverse_tables_sourceleft. ~(dc_input_inverse_tables_sourceleft=0) -> (exists pvs_le_gap_inverse_tables_sourceleftdomain. pvs_le_gap_inverse_tables_sourceleftdomain + (dc_input_inverse_tables_sourceleft) = (N)) -> (exists dst_positive_code_inverse_tables_sourceleftlookup dst_positive_scale_inverse_tables_sourceleftlookup dst_negative_code_inverse_tables_sourceleftlookup dst_negative_scale_inverse_tables_sourceleftlookup dst_positive_inverse_tables_sourceleftlookup dst_negative_inverse_tables_sourceleftlookup. (((di_delta_inverse_tables_source) = (((((dst_positive_code_inverse_tables_sourceleftlookup) + (dst_positive_scale_inverse_tables_sourceleftlookup)) * S ((dst_positive_code_inverse_tables_sourceleftlookup) + (dst_positive_scale_inverse_tables_sourceleftlookup)) + ((dst_positive_scale_inverse_tables_sourceleftlookup) + (dst_positive_scale_inverse_tables_sourceleftlookup))) + (((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) * S ((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) + ((dst_negative_scale_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)))) * S ((((dst_positive_code_inverse_tables_sourceleftlookup) + (dst_positive_scale_inverse_tables_sourceleftlookup)) * S ((dst_positive_code_inverse_tables_sourceleftlookup) + (dst_positive_scale_inverse_tables_sourceleftlookup)) + ((dst_positive_scale_inverse_tables_sourceleftlookup) + (dst_positive_scale_inverse_tables_sourceleftlookup))) + (((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) * S ((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) + ((dst_negative_scale_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)))) + ((((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) * S ((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) + ((dst_negative_scale_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup))) + (((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) * S ((dst_negative_code_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)) + ((dst_negative_scale_inverse_tables_sourceleftlookup) + (dst_negative_scale_inverse_tables_sourceleftlookup)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftlookuppositive. ff_h_pvs_inverse_tables_sourceleftlookuppositive + S (dst_positive_inverse_tables_sourceleftlookup) = S ((S (dc_input_inverse_tables_sourceleft)) * dst_positive_scale_inverse_tables_sourceleftlookup)) /\ exists ff_q_pvs_inverse_tables_sourceleftlookuppositive. dst_positive_code_inverse_tables_sourceleftlookup = ff_q_pvs_inverse_tables_sourceleftlookuppositive * S ((S (dc_input_inverse_tables_sourceleft)) * dst_positive_scale_inverse_tables_sourceleftlookup) + (dst_positive_inverse_tables_sourceleftlookup))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftlookupnegative. ff_h_pvs_inverse_tables_sourceleftlookupnegative + S (dst_negative_inverse_tables_sourceleftlookup) = S ((S (dc_input_inverse_tables_sourceleft)) * dst_negative_scale_inverse_tables_sourceleftlookup)) /\ exists ff_q_pvs_inverse_tables_sourceleftlookupnegative. dst_negative_code_inverse_tables_sourceleftlookup = ff_q_pvs_inverse_tables_sourceleftlookupnegative * S ((S (dc_input_inverse_tables_sourceleft)) * dst_negative_scale_inverse_tables_sourceleftlookup) + (dst_negative_inverse_tables_sourceleftlookup))) /\ (exists ge_balance_positive_inverse_tables_sourceleftlookupvalue ge_balance_negative_inverse_tables_sourceleftlookupvalue. (((((dc_output_inverse_tables_sourceleft) = 2 * (ge_balance_positive_inverse_tables_sourceleftlookupvalue) /\ (ge_balance_negative_inverse_tables_sourceleftlookupvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftlookupvaluedecode. (((dc_output_inverse_tables_sourceleft) = 2 * ge_signed_half_inverse_tables_sourceleftlookupvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftlookupvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftlookupvalue) = S ge_signed_half_inverse_tables_sourceleftlookupvaluedecode))) /\ ((dst_positive_inverse_tables_sourceleftlookup) + ge_balance_negative_inverse_tables_sourceleftlookupvalue = (dst_negative_inverse_tables_sourceleftlookup) + ge_balance_positive_inverse_tables_sourceleftlookupvalue))))))))) -> (((~((dc_input_inverse_tables_sourceleft)=0)) /\ (exists dc_mask_inverse_tables_sourceleftvalue. ((((exists dst_positive_code_inverse_tables_sourceleftvaluemasktable dst_positive_scale_inverse_tables_sourceleftvaluemasktable dst_negative_code_inverse_tables_sourceleftvaluemasktable dst_negative_scale_inverse_tables_sourceleftvaluemasktable. (((dc_mask_inverse_tables_sourceleftvalue) = (((((dst_positive_code_inverse_tables_sourceleftvaluemasktable) + (dst_positive_scale_inverse_tables_sourceleftvaluemasktable)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemasktable) + (dst_positive_scale_inverse_tables_sourceleftvaluemasktable)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemasktable) + (dst_positive_scale_inverse_tables_sourceleftvaluemasktable))) + (((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)))) * S ((((dst_positive_code_inverse_tables_sourceleftvaluemasktable) + (dst_positive_scale_inverse_tables_sourceleftvaluemasktable)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemasktable) + (dst_positive_scale_inverse_tables_sourceleftvaluemasktable)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemasktable) + (dst_positive_scale_inverse_tables_sourceleftvaluemasktable))) + (((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)))) + ((((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable))) + (((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasktable) + (dst_negative_scale_inverse_tables_sourceleftvaluemasktable)))))) /\ (forall dst_index_inverse_tables_sourceleftvaluemasktable. (exists pvs_le_gap_inverse_tables_sourceleftvaluemasktabledomain. pvs_le_gap_inverse_tables_sourceleftvaluemasktabledomain + (dst_index_inverse_tables_sourceleftvaluemasktable) = (dc_input_inverse_tables_sourceleft)) -> exists dst_positive_inverse_tables_sourceleftvaluemasktable dst_negative_inverse_tables_sourceleftvaluemasktable dst_value_inverse_tables_sourceleftvaluemasktable. ((((exists ff_h_pvs_inverse_tables_sourceleftvaluemasktableentrypositive. ff_h_pvs_inverse_tables_sourceleftvaluemasktableentrypositive + S (dst_positive_inverse_tables_sourceleftvaluemasktable) = S ((S (dst_index_inverse_tables_sourceleftvaluemasktable)) * dst_positive_scale_inverse_tables_sourceleftvaluemasktable)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemasktableentrypositive. dst_positive_code_inverse_tables_sourceleftvaluemasktable = ff_q_pvs_inverse_tables_sourceleftvaluemasktableentrypositive * S ((S (dst_index_inverse_tables_sourceleftvaluemasktable)) * dst_positive_scale_inverse_tables_sourceleftvaluemasktable) + (dst_positive_inverse_tables_sourceleftvaluemasktable))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftvaluemasktableentrynegative. ff_h_pvs_inverse_tables_sourceleftvaluemasktableentrynegative + S (dst_negative_inverse_tables_sourceleftvaluemasktable) = S ((S (dst_index_inverse_tables_sourceleftvaluemasktable)) * dst_negative_scale_inverse_tables_sourceleftvaluemasktable)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemasktableentrynegative. dst_negative_code_inverse_tables_sourceleftvaluemasktable = ff_q_pvs_inverse_tables_sourceleftvaluemasktableentrynegative * S ((S (dst_index_inverse_tables_sourceleftvaluemasktable)) * dst_negative_scale_inverse_tables_sourceleftvaluemasktable) + (dst_negative_inverse_tables_sourceleftvaluemasktable))) /\ (exists ge_balance_positive_inverse_tables_sourceleftvaluemasktableentryvalue ge_balance_negative_inverse_tables_sourceleftvaluemasktableentryvalue. (((((dst_value_inverse_tables_sourceleftvaluemasktable) = 2 * (ge_balance_positive_inverse_tables_sourceleftvaluemasktableentryvalue) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemasktableentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluemasktableentryvaluedecode. (((dst_value_inverse_tables_sourceleftvaluemasktable) = 2 * ge_signed_half_inverse_tables_sourceleftvaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftvaluemasktableentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemasktableentryvalue) = S ge_signed_half_inverse_tables_sourceleftvaluemasktableentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourceleftvaluemasktable) + ge_balance_negative_inverse_tables_sourceleftvaluemasktableentryvalue = (dst_negative_inverse_tables_sourceleftvaluemasktable) + ge_balance_positive_inverse_tables_sourceleftvaluemasktableentryvalue))))))))) /\ (forall dc_index_inverse_tables_sourceleftvaluemask dc_value_inverse_tables_sourceleftvaluemask. (exists pvs_le_gap_inverse_tables_sourceleftvaluemaskdomain. pvs_le_gap_inverse_tables_sourceleftvaluemaskdomain + (dc_index_inverse_tables_sourceleftvaluemask) = (dc_input_inverse_tables_sourceleft)) -> (exists dst_positive_code_inverse_tables_sourceleftvaluemasklookup dst_positive_scale_inverse_tables_sourceleftvaluemasklookup dst_negative_code_inverse_tables_sourceleftvaluemasklookup dst_negative_scale_inverse_tables_sourceleftvaluemasklookup dst_positive_inverse_tables_sourceleftvaluemasklookup dst_negative_inverse_tables_sourceleftvaluemasklookup. (((dc_mask_inverse_tables_sourceleftvalue) = (((((dst_positive_code_inverse_tables_sourceleftvaluemasklookup) + (dst_positive_scale_inverse_tables_sourceleftvaluemasklookup)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemasklookup) + (dst_positive_scale_inverse_tables_sourceleftvaluemasklookup)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_positive_scale_inverse_tables_sourceleftvaluemasklookup))) + (((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)))) * S ((((dst_positive_code_inverse_tables_sourceleftvaluemasklookup) + (dst_positive_scale_inverse_tables_sourceleftvaluemasklookup)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemasklookup) + (dst_positive_scale_inverse_tables_sourceleftvaluemasklookup)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_positive_scale_inverse_tables_sourceleftvaluemasklookup))) + (((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)))) + ((((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup))) + (((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftvaluemasklookuppositive. ff_h_pvs_inverse_tables_sourceleftvaluemasklookuppositive + S (dst_positive_inverse_tables_sourceleftvaluemasklookup) = S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_positive_scale_inverse_tables_sourceleftvaluemasklookup)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemasklookuppositive. dst_positive_code_inverse_tables_sourceleftvaluemasklookup = ff_q_pvs_inverse_tables_sourceleftvaluemasklookuppositive * S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_positive_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_positive_inverse_tables_sourceleftvaluemasklookup))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftvaluemasklookupnegative. ff_h_pvs_inverse_tables_sourceleftvaluemasklookupnegative + S (dst_negative_inverse_tables_sourceleftvaluemasklookup) = S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_negative_scale_inverse_tables_sourceleftvaluemasklookup)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemasklookupnegative. dst_negative_code_inverse_tables_sourceleftvaluemasklookup = ff_q_pvs_inverse_tables_sourceleftvaluemasklookupnegative * S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_negative_scale_inverse_tables_sourceleftvaluemasklookup) + (dst_negative_inverse_tables_sourceleftvaluemasklookup))) /\ (exists ge_balance_positive_inverse_tables_sourceleftvaluemasklookupvalue ge_balance_negative_inverse_tables_sourceleftvaluemasklookupvalue. (((((dc_value_inverse_tables_sourceleftvaluemask) = 2 * (ge_balance_positive_inverse_tables_sourceleftvaluemasklookupvalue) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemasklookupvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluemasklookupvaluedecode. (((dc_value_inverse_tables_sourceleftvaluemask) = 2 * ge_signed_half_inverse_tables_sourceleftvaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftvaluemasklookupvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemasklookupvalue) = S ge_signed_half_inverse_tables_sourceleftvaluemasklookupvaluedecode))) /\ ((dst_positive_inverse_tables_sourceleftvaluemasklookup) + ge_balance_negative_inverse_tables_sourceleftvaluemasklookupvalue = (dst_negative_inverse_tables_sourceleftvaluemasklookup) + ge_balance_positive_inverse_tables_sourceleftvaluemasklookupvalue))))))))) -> ((((~((dc_index_inverse_tables_sourceleftvaluemask)=0)) /\ (exists dc_quotient_inverse_tables_sourceleftvaluemaskentry dc_left_inverse_tables_sourceleftvaluemaskentry dc_right_inverse_tables_sourceleftvaluemaskentry. (((dc_input_inverse_tables_sourceleft)=(dc_index_inverse_tables_sourceleftvaluemask)*dc_quotient_inverse_tables_sourceleftvaluemaskentry) /\ (((exists dst_positive_code_inverse_tables_sourceleftvaluemaskentryleft dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft dst_positive_inverse_tables_sourceleftvaluemaskentryleft dst_negative_inverse_tables_sourceleftvaluemaskentryleft. (((F) = (((((dst_positive_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft))) + (((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)))) * S ((((dst_positive_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft))) + (((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)))) + ((((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft))) + (((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftvaluemaskentryleftpositive. ff_h_pvs_inverse_tables_sourceleftvaluemaskentryleftpositive + S (dst_positive_inverse_tables_sourceleftvaluemaskentryleft) = S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemaskentryleftpositive. dst_positive_code_inverse_tables_sourceleftvaluemaskentryleft = ff_q_pvs_inverse_tables_sourceleftvaluemaskentryleftpositive * S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_positive_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_positive_inverse_tables_sourceleftvaluemaskentryleft))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftvaluemaskentryleftnegative. ff_h_pvs_inverse_tables_sourceleftvaluemaskentryleftnegative + S (dst_negative_inverse_tables_sourceleftvaluemaskentryleft) = S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemaskentryleftnegative. dst_negative_code_inverse_tables_sourceleftvaluemaskentryleft = ff_q_pvs_inverse_tables_sourceleftvaluemaskentryleftnegative * S ((S (dc_index_inverse_tables_sourceleftvaluemask)) * dst_negative_scale_inverse_tables_sourceleftvaluemaskentryleft) + (dst_negative_inverse_tables_sourceleftvaluemaskentryleft))) /\ (exists ge_balance_positive_inverse_tables_sourceleftvaluemaskentryleftvalue ge_balance_negative_inverse_tables_sourceleftvaluemaskentryleftvalue. (((((dc_left_inverse_tables_sourceleftvaluemaskentry) = 2 * (ge_balance_positive_inverse_tables_sourceleftvaluemaskentryleftvalue) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluemaskentryleftvaluedecode. (((dc_left_inverse_tables_sourceleftvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourceleftvaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftvaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemaskentryleftvalue) = S ge_signed_half_inverse_tables_sourceleftvaluemaskentryleftvaluedecode))) /\ ((dst_positive_inverse_tables_sourceleftvaluemaskentryleft) + ge_balance_negative_inverse_tables_sourceleftvaluemaskentryleftvalue = (dst_negative_inverse_tables_sourceleftvaluemaskentryleft) + ge_balance_positive_inverse_tables_sourceleftvaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_inverse_tables_sourceleftvaluemaskentryright dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright dst_negative_code_inverse_tables_sourceleftvaluemaskentryright dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright dst_positive_inverse_tables_sourceleftvaluemaskentryright dst_negative_inverse_tables_sourceleftvaluemaskentryright. (((G) = (((((dst_positive_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright))) + (((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)))) * S ((((dst_positive_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright)) * S ((dst_positive_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright)) + ((dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright))) + (((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)))) + ((((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright))) + (((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftvaluemaskentryrightpositive. ff_h_pvs_inverse_tables_sourceleftvaluemaskentryrightpositive + S (dst_positive_inverse_tables_sourceleftvaluemaskentryright) = S ((S (dc_quotient_inverse_tables_sourceleftvaluemaskentry)) * dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemaskentryrightpositive. dst_positive_code_inverse_tables_sourceleftvaluemaskentryright = ff_q_pvs_inverse_tables_sourceleftvaluemaskentryrightpositive * S ((S (dc_quotient_inverse_tables_sourceleftvaluemaskentry)) * dst_positive_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_positive_inverse_tables_sourceleftvaluemaskentryright))) /\ (((((exists ff_h_pvs_inverse_tables_sourceleftvaluemaskentryrightnegative. ff_h_pvs_inverse_tables_sourceleftvaluemaskentryrightnegative + S (dst_negative_inverse_tables_sourceleftvaluemaskentryright) = S ((S (dc_quotient_inverse_tables_sourceleftvaluemaskentry)) * dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright)) /\ exists ff_q_pvs_inverse_tables_sourceleftvaluemaskentryrightnegative. dst_negative_code_inverse_tables_sourceleftvaluemaskentryright = ff_q_pvs_inverse_tables_sourceleftvaluemaskentryrightnegative * S ((S (dc_quotient_inverse_tables_sourceleftvaluemaskentry)) * dst_negative_scale_inverse_tables_sourceleftvaluemaskentryright) + (dst_negative_inverse_tables_sourceleftvaluemaskentryright))) /\ (exists ge_balance_positive_inverse_tables_sourceleftvaluemaskentryrightvalue ge_balance_negative_inverse_tables_sourceleftvaluemaskentryrightvalue. (((((dc_right_inverse_tables_sourceleftvaluemaskentry) = 2 * (ge_balance_positive_inverse_tables_sourceleftvaluemaskentryrightvalue) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluemaskentryrightvaluedecode. (((dc_right_inverse_tables_sourceleftvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourceleftvaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftvaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftvaluemaskentryrightvalue) = S ge_signed_half_inverse_tables_sourceleftvaluemaskentryrightvaluedecode))) /\ ((dst_positive_inverse_tables_sourceleftvaluemaskentryright) + ge_balance_negative_inverse_tables_sourceleftvaluemaskentryrightvalue = (dst_negative_inverse_tables_sourceleftvaluemaskentryright) + ge_balance_positive_inverse_tables_sourceleftvaluemaskentryrightvalue))))))))) /\ (exists sto_ap_inverse_tables_sourceleftvaluemaskentryproduct sto_an_inverse_tables_sourceleftvaluemaskentryproduct sto_bp_inverse_tables_sourceleftvaluemaskentryproduct sto_bn_inverse_tables_sourceleftvaluemaskentryproduct sto_cp_inverse_tables_sourceleftvaluemaskentryproduct sto_cn_inverse_tables_sourceleftvaluemaskentryproduct. (((((dc_left_inverse_tables_sourceleftvaluemaskentry) = 2 * (sto_ap_inverse_tables_sourceleftvaluemaskentryproduct) /\ (sto_an_inverse_tables_sourceleftvaluemaskentryproduct) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductleft. (((dc_left_inverse_tables_sourceleftvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductleft + 1 /\ (sto_ap_inverse_tables_sourceleftvaluemaskentryproduct) = 0) /\ (sto_an_inverse_tables_sourceleftvaluemaskentryproduct) = S ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductleft))) /\ ((((((dc_right_inverse_tables_sourceleftvaluemaskentry) = 2 * (sto_bp_inverse_tables_sourceleftvaluemaskentryproduct) /\ (sto_bn_inverse_tables_sourceleftvaluemaskentryproduct) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductright. (((dc_right_inverse_tables_sourceleftvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductright + 1 /\ (sto_bp_inverse_tables_sourceleftvaluemaskentryproduct) = 0) /\ (sto_bn_inverse_tables_sourceleftvaluemaskentryproduct) = S ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductright))) /\ ((((((dc_value_inverse_tables_sourceleftvaluemask) = 2 * (sto_cp_inverse_tables_sourceleftvaluemaskentryproduct) /\ (sto_cn_inverse_tables_sourceleftvaluemaskentryproduct) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductoutput. (((dc_value_inverse_tables_sourceleftvaluemask) = 2 * ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductoutput + 1 /\ (sto_cp_inverse_tables_sourceleftvaluemaskentryproduct) = 0) /\ (sto_cn_inverse_tables_sourceleftvaluemaskentryproduct) = S ge_signed_half_inverse_tables_sourceleftvaluemaskentryproductoutput))) /\ ((sto_ap_inverse_tables_sourceleftvaluemaskentryproduct * sto_bp_inverse_tables_sourceleftvaluemaskentryproduct + sto_an_inverse_tables_sourceleftvaluemaskentryproduct * sto_bn_inverse_tables_sourceleftvaluemaskentryproduct) + sto_cn_inverse_tables_sourceleftvaluemaskentryproduct = (sto_ap_inverse_tables_sourceleftvaluemaskentryproduct * sto_bn_inverse_tables_sourceleftvaluemaskentryproduct + sto_an_inverse_tables_sourceleftvaluemaskentryproduct * sto_bp_inverse_tables_sourceleftvaluemaskentryproduct) + sto_cp_inverse_tables_sourceleftvaluemaskentryproduct))))))))))))))) \/ ((((dc_index_inverse_tables_sourceleftvaluemask)=0 \/ ~(exists pvs_factor_inverse_tables_sourceleftvaluemaskentrynondivisor. (dc_input_inverse_tables_sourceleft) = (dc_index_inverse_tables_sourceleftvaluemask) * pvs_factor_inverse_tables_sourceleftvaluemaskentrynondivisor)) /\ ((dc_value_inverse_tables_sourceleftvaluemask)=0))))))) /\ (exists dst_positive_code_inverse_tables_sourceleftvaluefold dst_positive_scale_inverse_tables_sourceleftvaluefold dst_negative_code_inverse_tables_sourceleftvaluefold dst_negative_scale_inverse_tables_sourceleftvaluefold dst_positive_sum_inverse_tables_sourceleftvaluefold dst_negative_sum_inverse_tables_sourceleftvaluefold. (((dc_mask_inverse_tables_sourceleftvalue) = (((((dst_positive_code_inverse_tables_sourceleftvaluefold) + (dst_positive_scale_inverse_tables_sourceleftvaluefold)) * S ((dst_positive_code_inverse_tables_sourceleftvaluefold) + (dst_positive_scale_inverse_tables_sourceleftvaluefold)) + ((dst_positive_scale_inverse_tables_sourceleftvaluefold) + (dst_positive_scale_inverse_tables_sourceleftvaluefold))) + (((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) * S ((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) + ((dst_negative_scale_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)))) * S ((((dst_positive_code_inverse_tables_sourceleftvaluefold) + (dst_positive_scale_inverse_tables_sourceleftvaluefold)) * S ((dst_positive_code_inverse_tables_sourceleftvaluefold) + (dst_positive_scale_inverse_tables_sourceleftvaluefold)) + ((dst_positive_scale_inverse_tables_sourceleftvaluefold) + (dst_positive_scale_inverse_tables_sourceleftvaluefold))) + (((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) * S ((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) + ((dst_negative_scale_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)))) + ((((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) * S ((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) + ((dst_negative_scale_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold))) + (((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) * S ((dst_negative_code_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)) + ((dst_negative_scale_inverse_tables_sourceleftvaluefold) + (dst_negative_scale_inverse_tables_sourceleftvaluefold)))))) /\ (((exists fs_u_dst_inverse_tables_sourceleftvaluefoldpositive fs_v_dst_inverse_tables_sourceleftvaluefoldpositive. ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_start. fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_start. fs_u_dst_inverse_tables_sourceleftvaluefoldpositive = fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_terminal. fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_terminal + S (dst_positive_sum_inverse_tables_sourceleftvaluefold) = S ((S (S (dc_input_inverse_tables_sourceleft))) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_terminal. fs_u_dst_inverse_tables_sourceleftvaluefoldpositive = fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_terminal * S ((S (S (dc_input_inverse_tables_sourceleft))) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive) + (dst_positive_sum_inverse_tables_sourceleftvaluefold))) /\ forall fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps. (exists fs_lt_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_bound. fs_lt_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_bound + S fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps = S (dc_input_inverse_tables_sourceleft)) -> exists fs_a_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps fs_r_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps fs_s_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps. ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_summand. fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_summand + S (fs_a_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps) = S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps)) * dst_positive_scale_inverse_tables_sourceleftvaluefold)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_summand. dst_positive_code_inverse_tables_sourceleftvaluefold = fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps)) * dst_positive_scale_inverse_tables_sourceleftvaluefold) + (fs_a_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_partial. fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_partial + S (fs_r_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps) = S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_partial. fs_u_dst_inverse_tables_sourceleftvaluefoldpositive = fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive) + (fs_r_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_successor. fs_h_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_successor + S (fs_s_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps) = S ((S (S fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_successor. fs_u_dst_inverse_tables_sourceleftvaluefoldpositive = fs_q_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldpositive) + (fs_s_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps))) /\ fs_s_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps = fs_r_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps + fs_a_dst_inverse_tables_sourceleftvaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_inverse_tables_sourceleftvaluefoldnegative fs_v_dst_inverse_tables_sourceleftvaluefoldnegative. ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_start. fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_start. fs_u_dst_inverse_tables_sourceleftvaluefoldnegative = fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_terminal. fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_terminal + S (dst_negative_sum_inverse_tables_sourceleftvaluefold) = S ((S (S (dc_input_inverse_tables_sourceleft))) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_terminal. fs_u_dst_inverse_tables_sourceleftvaluefoldnegative = fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_terminal * S ((S (S (dc_input_inverse_tables_sourceleft))) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative) + (dst_negative_sum_inverse_tables_sourceleftvaluefold))) /\ forall fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps. (exists fs_lt_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_bound. fs_lt_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_bound + S fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps = S (dc_input_inverse_tables_sourceleft)) -> exists fs_a_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps fs_r_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps fs_s_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps. ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_summand. fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_summand + S (fs_a_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps) = S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps)) * dst_negative_scale_inverse_tables_sourceleftvaluefold)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_summand. dst_negative_code_inverse_tables_sourceleftvaluefold = fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps)) * dst_negative_scale_inverse_tables_sourceleftvaluefold) + (fs_a_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_partial. fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_partial + S (fs_r_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps) = S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_partial. fs_u_dst_inverse_tables_sourceleftvaluefoldnegative = fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative) + (fs_r_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_successor. fs_h_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_successor + S (fs_s_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps) = S ((S (S fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_successor. fs_u_dst_inverse_tables_sourceleftvaluefoldnegative = fs_q_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourceleftvaluefoldnegative) + (fs_s_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps))) /\ fs_s_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps = fs_r_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps + fs_a_dst_inverse_tables_sourceleftvaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_inverse_tables_sourceleftvaluefoldresult ge_balance_negative_inverse_tables_sourceleftvaluefoldresult. (((((dc_output_inverse_tables_sourceleft) = 2 * (ge_balance_positive_inverse_tables_sourceleftvaluefoldresult) /\ (ge_balance_negative_inverse_tables_sourceleftvaluefoldresult) = 0) \/ exists ge_signed_half_inverse_tables_sourceleftvaluefoldresultdecode. (((dc_output_inverse_tables_sourceleft) = 2 * ge_signed_half_inverse_tables_sourceleftvaluefoldresultdecode + 1 /\ (ge_balance_positive_inverse_tables_sourceleftvaluefoldresult) = 0) /\ (ge_balance_negative_inverse_tables_sourceleftvaluefoldresult) = S ge_signed_half_inverse_tables_sourceleftvaluefoldresultdecode))) /\ ((dst_positive_sum_inverse_tables_sourceleftvaluefold) + ge_balance_negative_inverse_tables_sourceleftvaluefoldresult = (dst_negative_sum_inverse_tables_sourceleftvaluefold) + ge_balance_positive_inverse_tables_sourceleftvaluefoldresult)))))))))))))))))))) /\ (((exists dst_positive_code_inverse_tables_sourcerightleft dst_positive_scale_inverse_tables_sourcerightleft dst_negative_code_inverse_tables_sourcerightleft dst_negative_scale_inverse_tables_sourcerightleft. (((G) = (((((dst_positive_code_inverse_tables_sourcerightleft) + (dst_positive_scale_inverse_tables_sourcerightleft)) * S ((dst_positive_code_inverse_tables_sourcerightleft) + (dst_positive_scale_inverse_tables_sourcerightleft)) + ((dst_positive_scale_inverse_tables_sourcerightleft) + (dst_positive_scale_inverse_tables_sourcerightleft))) + (((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) * S ((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) + ((dst_negative_scale_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)))) * S ((((dst_positive_code_inverse_tables_sourcerightleft) + (dst_positive_scale_inverse_tables_sourcerightleft)) * S ((dst_positive_code_inverse_tables_sourcerightleft) + (dst_positive_scale_inverse_tables_sourcerightleft)) + ((dst_positive_scale_inverse_tables_sourcerightleft) + (dst_positive_scale_inverse_tables_sourcerightleft))) + (((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) * S ((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) + ((dst_negative_scale_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)))) + ((((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) * S ((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) + ((dst_negative_scale_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft))) + (((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) * S ((dst_negative_code_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)) + ((dst_negative_scale_inverse_tables_sourcerightleft) + (dst_negative_scale_inverse_tables_sourcerightleft)))))) /\ (forall dst_index_inverse_tables_sourcerightleft. (exists pvs_le_gap_inverse_tables_sourcerightleftdomain. pvs_le_gap_inverse_tables_sourcerightleftdomain + (dst_index_inverse_tables_sourcerightleft) = (N)) -> exists dst_positive_inverse_tables_sourcerightleft dst_negative_inverse_tables_sourcerightleft dst_value_inverse_tables_sourcerightleft. ((((exists ff_h_pvs_inverse_tables_sourcerightleftentrypositive. ff_h_pvs_inverse_tables_sourcerightleftentrypositive + S (dst_positive_inverse_tables_sourcerightleft) = S ((S (dst_index_inverse_tables_sourcerightleft)) * dst_positive_scale_inverse_tables_sourcerightleft)) /\ exists ff_q_pvs_inverse_tables_sourcerightleftentrypositive. dst_positive_code_inverse_tables_sourcerightleft = ff_q_pvs_inverse_tables_sourcerightleftentrypositive * S ((S (dst_index_inverse_tables_sourcerightleft)) * dst_positive_scale_inverse_tables_sourcerightleft) + (dst_positive_inverse_tables_sourcerightleft))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightleftentrynegative. ff_h_pvs_inverse_tables_sourcerightleftentrynegative + S (dst_negative_inverse_tables_sourcerightleft) = S ((S (dst_index_inverse_tables_sourcerightleft)) * dst_negative_scale_inverse_tables_sourcerightleft)) /\ exists ff_q_pvs_inverse_tables_sourcerightleftentrynegative. dst_negative_code_inverse_tables_sourcerightleft = ff_q_pvs_inverse_tables_sourcerightleftentrynegative * S ((S (dst_index_inverse_tables_sourcerightleft)) * dst_negative_scale_inverse_tables_sourcerightleft) + (dst_negative_inverse_tables_sourcerightleft))) /\ (exists ge_balance_positive_inverse_tables_sourcerightleftentryvalue ge_balance_negative_inverse_tables_sourcerightleftentryvalue. (((((dst_value_inverse_tables_sourcerightleft) = 2 * (ge_balance_positive_inverse_tables_sourcerightleftentryvalue) /\ (ge_balance_negative_inverse_tables_sourcerightleftentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightleftentryvaluedecode. (((dst_value_inverse_tables_sourcerightleft) = 2 * ge_signed_half_inverse_tables_sourcerightleftentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightleftentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightleftentryvalue) = S ge_signed_half_inverse_tables_sourcerightleftentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerightleft) + ge_balance_negative_inverse_tables_sourcerightleftentryvalue = (dst_negative_inverse_tables_sourcerightleft) + ge_balance_positive_inverse_tables_sourcerightleftentryvalue))))))))) /\ (((exists dst_positive_code_inverse_tables_sourcerightright dst_positive_scale_inverse_tables_sourcerightright dst_negative_code_inverse_tables_sourcerightright dst_negative_scale_inverse_tables_sourcerightright. (((F) = (((((dst_positive_code_inverse_tables_sourcerightright) + (dst_positive_scale_inverse_tables_sourcerightright)) * S ((dst_positive_code_inverse_tables_sourcerightright) + (dst_positive_scale_inverse_tables_sourcerightright)) + ((dst_positive_scale_inverse_tables_sourcerightright) + (dst_positive_scale_inverse_tables_sourcerightright))) + (((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) * S ((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) + ((dst_negative_scale_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)))) * S ((((dst_positive_code_inverse_tables_sourcerightright) + (dst_positive_scale_inverse_tables_sourcerightright)) * S ((dst_positive_code_inverse_tables_sourcerightright) + (dst_positive_scale_inverse_tables_sourcerightright)) + ((dst_positive_scale_inverse_tables_sourcerightright) + (dst_positive_scale_inverse_tables_sourcerightright))) + (((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) * S ((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) + ((dst_negative_scale_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)))) + ((((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) * S ((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) + ((dst_negative_scale_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright))) + (((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) * S ((dst_negative_code_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)) + ((dst_negative_scale_inverse_tables_sourcerightright) + (dst_negative_scale_inverse_tables_sourcerightright)))))) /\ (forall dst_index_inverse_tables_sourcerightright. (exists pvs_le_gap_inverse_tables_sourcerightrightdomain. pvs_le_gap_inverse_tables_sourcerightrightdomain + (dst_index_inverse_tables_sourcerightright) = (N)) -> exists dst_positive_inverse_tables_sourcerightright dst_negative_inverse_tables_sourcerightright dst_value_inverse_tables_sourcerightright. ((((exists ff_h_pvs_inverse_tables_sourcerightrightentrypositive. ff_h_pvs_inverse_tables_sourcerightrightentrypositive + S (dst_positive_inverse_tables_sourcerightright) = S ((S (dst_index_inverse_tables_sourcerightright)) * dst_positive_scale_inverse_tables_sourcerightright)) /\ exists ff_q_pvs_inverse_tables_sourcerightrightentrypositive. dst_positive_code_inverse_tables_sourcerightright = ff_q_pvs_inverse_tables_sourcerightrightentrypositive * S ((S (dst_index_inverse_tables_sourcerightright)) * dst_positive_scale_inverse_tables_sourcerightright) + (dst_positive_inverse_tables_sourcerightright))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightrightentrynegative. ff_h_pvs_inverse_tables_sourcerightrightentrynegative + S (dst_negative_inverse_tables_sourcerightright) = S ((S (dst_index_inverse_tables_sourcerightright)) * dst_negative_scale_inverse_tables_sourcerightright)) /\ exists ff_q_pvs_inverse_tables_sourcerightrightentrynegative. dst_negative_code_inverse_tables_sourcerightright = ff_q_pvs_inverse_tables_sourcerightrightentrynegative * S ((S (dst_index_inverse_tables_sourcerightright)) * dst_negative_scale_inverse_tables_sourcerightright) + (dst_negative_inverse_tables_sourcerightright))) /\ (exists ge_balance_positive_inverse_tables_sourcerightrightentryvalue ge_balance_negative_inverse_tables_sourcerightrightentryvalue. (((((dst_value_inverse_tables_sourcerightright) = 2 * (ge_balance_positive_inverse_tables_sourcerightrightentryvalue) /\ (ge_balance_negative_inverse_tables_sourcerightrightentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightrightentryvaluedecode. (((dst_value_inverse_tables_sourcerightright) = 2 * ge_signed_half_inverse_tables_sourcerightrightentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightrightentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightrightentryvalue) = S ge_signed_half_inverse_tables_sourcerightrightentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerightright) + ge_balance_negative_inverse_tables_sourcerightrightentryvalue = (dst_negative_inverse_tables_sourcerightright) + ge_balance_positive_inverse_tables_sourcerightrightentryvalue))))))))) /\ (((exists dst_positive_code_inverse_tables_sourcerighttable dst_positive_scale_inverse_tables_sourcerighttable dst_negative_code_inverse_tables_sourcerighttable dst_negative_scale_inverse_tables_sourcerighttable. (((di_delta_inverse_tables_source) = (((((dst_positive_code_inverse_tables_sourcerighttable) + (dst_positive_scale_inverse_tables_sourcerighttable)) * S ((dst_positive_code_inverse_tables_sourcerighttable) + (dst_positive_scale_inverse_tables_sourcerighttable)) + ((dst_positive_scale_inverse_tables_sourcerighttable) + (dst_positive_scale_inverse_tables_sourcerighttable))) + (((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) * S ((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) + ((dst_negative_scale_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)))) * S ((((dst_positive_code_inverse_tables_sourcerighttable) + (dst_positive_scale_inverse_tables_sourcerighttable)) * S ((dst_positive_code_inverse_tables_sourcerighttable) + (dst_positive_scale_inverse_tables_sourcerighttable)) + ((dst_positive_scale_inverse_tables_sourcerighttable) + (dst_positive_scale_inverse_tables_sourcerighttable))) + (((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) * S ((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) + ((dst_negative_scale_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)))) + ((((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) * S ((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) + ((dst_negative_scale_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable))) + (((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) * S ((dst_negative_code_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)) + ((dst_negative_scale_inverse_tables_sourcerighttable) + (dst_negative_scale_inverse_tables_sourcerighttable)))))) /\ (forall dst_index_inverse_tables_sourcerighttable. (exists pvs_le_gap_inverse_tables_sourcerighttabledomain. pvs_le_gap_inverse_tables_sourcerighttabledomain + (dst_index_inverse_tables_sourcerighttable) = (N)) -> exists dst_positive_inverse_tables_sourcerighttable dst_negative_inverse_tables_sourcerighttable dst_value_inverse_tables_sourcerighttable. ((((exists ff_h_pvs_inverse_tables_sourcerighttableentrypositive. ff_h_pvs_inverse_tables_sourcerighttableentrypositive + S (dst_positive_inverse_tables_sourcerighttable) = S ((S (dst_index_inverse_tables_sourcerighttable)) * dst_positive_scale_inverse_tables_sourcerighttable)) /\ exists ff_q_pvs_inverse_tables_sourcerighttableentrypositive. dst_positive_code_inverse_tables_sourcerighttable = ff_q_pvs_inverse_tables_sourcerighttableentrypositive * S ((S (dst_index_inverse_tables_sourcerighttable)) * dst_positive_scale_inverse_tables_sourcerighttable) + (dst_positive_inverse_tables_sourcerighttable))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerighttableentrynegative. ff_h_pvs_inverse_tables_sourcerighttableentrynegative + S (dst_negative_inverse_tables_sourcerighttable) = S ((S (dst_index_inverse_tables_sourcerighttable)) * dst_negative_scale_inverse_tables_sourcerighttable)) /\ exists ff_q_pvs_inverse_tables_sourcerighttableentrynegative. dst_negative_code_inverse_tables_sourcerighttable = ff_q_pvs_inverse_tables_sourcerighttableentrynegative * S ((S (dst_index_inverse_tables_sourcerighttable)) * dst_negative_scale_inverse_tables_sourcerighttable) + (dst_negative_inverse_tables_sourcerighttable))) /\ (exists ge_balance_positive_inverse_tables_sourcerighttableentryvalue ge_balance_negative_inverse_tables_sourcerighttableentryvalue. (((((dst_value_inverse_tables_sourcerighttable) = 2 * (ge_balance_positive_inverse_tables_sourcerighttableentryvalue) /\ (ge_balance_negative_inverse_tables_sourcerighttableentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerighttableentryvaluedecode. (((dst_value_inverse_tables_sourcerighttable) = 2 * ge_signed_half_inverse_tables_sourcerighttableentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerighttableentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerighttableentryvalue) = S ge_signed_half_inverse_tables_sourcerighttableentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerighttable) + ge_balance_negative_inverse_tables_sourcerighttableentryvalue = (dst_negative_inverse_tables_sourcerighttable) + ge_balance_positive_inverse_tables_sourcerighttableentryvalue))))))))) /\ (forall dc_input_inverse_tables_sourceright dc_output_inverse_tables_sourceright. ~(dc_input_inverse_tables_sourceright=0) -> (exists pvs_le_gap_inverse_tables_sourcerightdomain. pvs_le_gap_inverse_tables_sourcerightdomain + (dc_input_inverse_tables_sourceright) = (N)) -> (exists dst_positive_code_inverse_tables_sourcerightlookup dst_positive_scale_inverse_tables_sourcerightlookup dst_negative_code_inverse_tables_sourcerightlookup dst_negative_scale_inverse_tables_sourcerightlookup dst_positive_inverse_tables_sourcerightlookup dst_negative_inverse_tables_sourcerightlookup. (((di_delta_inverse_tables_source) = (((((dst_positive_code_inverse_tables_sourcerightlookup) + (dst_positive_scale_inverse_tables_sourcerightlookup)) * S ((dst_positive_code_inverse_tables_sourcerightlookup) + (dst_positive_scale_inverse_tables_sourcerightlookup)) + ((dst_positive_scale_inverse_tables_sourcerightlookup) + (dst_positive_scale_inverse_tables_sourcerightlookup))) + (((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) * S ((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) + ((dst_negative_scale_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)))) * S ((((dst_positive_code_inverse_tables_sourcerightlookup) + (dst_positive_scale_inverse_tables_sourcerightlookup)) * S ((dst_positive_code_inverse_tables_sourcerightlookup) + (dst_positive_scale_inverse_tables_sourcerightlookup)) + ((dst_positive_scale_inverse_tables_sourcerightlookup) + (dst_positive_scale_inverse_tables_sourcerightlookup))) + (((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) * S ((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) + ((dst_negative_scale_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)))) + ((((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) * S ((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) + ((dst_negative_scale_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup))) + (((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) * S ((dst_negative_code_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)) + ((dst_negative_scale_inverse_tables_sourcerightlookup) + (dst_negative_scale_inverse_tables_sourcerightlookup)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightlookuppositive. ff_h_pvs_inverse_tables_sourcerightlookuppositive + S (dst_positive_inverse_tables_sourcerightlookup) = S ((S (dc_input_inverse_tables_sourceright)) * dst_positive_scale_inverse_tables_sourcerightlookup)) /\ exists ff_q_pvs_inverse_tables_sourcerightlookuppositive. dst_positive_code_inverse_tables_sourcerightlookup = ff_q_pvs_inverse_tables_sourcerightlookuppositive * S ((S (dc_input_inverse_tables_sourceright)) * dst_positive_scale_inverse_tables_sourcerightlookup) + (dst_positive_inverse_tables_sourcerightlookup))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightlookupnegative. ff_h_pvs_inverse_tables_sourcerightlookupnegative + S (dst_negative_inverse_tables_sourcerightlookup) = S ((S (dc_input_inverse_tables_sourceright)) * dst_negative_scale_inverse_tables_sourcerightlookup)) /\ exists ff_q_pvs_inverse_tables_sourcerightlookupnegative. dst_negative_code_inverse_tables_sourcerightlookup = ff_q_pvs_inverse_tables_sourcerightlookupnegative * S ((S (dc_input_inverse_tables_sourceright)) * dst_negative_scale_inverse_tables_sourcerightlookup) + (dst_negative_inverse_tables_sourcerightlookup))) /\ (exists ge_balance_positive_inverse_tables_sourcerightlookupvalue ge_balance_negative_inverse_tables_sourcerightlookupvalue. (((((dc_output_inverse_tables_sourceright) = 2 * (ge_balance_positive_inverse_tables_sourcerightlookupvalue) /\ (ge_balance_negative_inverse_tables_sourcerightlookupvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightlookupvaluedecode. (((dc_output_inverse_tables_sourceright) = 2 * ge_signed_half_inverse_tables_sourcerightlookupvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightlookupvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightlookupvalue) = S ge_signed_half_inverse_tables_sourcerightlookupvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerightlookup) + ge_balance_negative_inverse_tables_sourcerightlookupvalue = (dst_negative_inverse_tables_sourcerightlookup) + ge_balance_positive_inverse_tables_sourcerightlookupvalue))))))))) -> (((~((dc_input_inverse_tables_sourceright)=0)) /\ (exists dc_mask_inverse_tables_sourcerightvalue. ((((exists dst_positive_code_inverse_tables_sourcerightvaluemasktable dst_positive_scale_inverse_tables_sourcerightvaluemasktable dst_negative_code_inverse_tables_sourcerightvaluemasktable dst_negative_scale_inverse_tables_sourcerightvaluemasktable. (((dc_mask_inverse_tables_sourcerightvalue) = (((((dst_positive_code_inverse_tables_sourcerightvaluemasktable) + (dst_positive_scale_inverse_tables_sourcerightvaluemasktable)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemasktable) + (dst_positive_scale_inverse_tables_sourcerightvaluemasktable)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemasktable) + (dst_positive_scale_inverse_tables_sourcerightvaluemasktable))) + (((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)))) * S ((((dst_positive_code_inverse_tables_sourcerightvaluemasktable) + (dst_positive_scale_inverse_tables_sourcerightvaluemasktable)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemasktable) + (dst_positive_scale_inverse_tables_sourcerightvaluemasktable)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemasktable) + (dst_positive_scale_inverse_tables_sourcerightvaluemasktable))) + (((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)))) + ((((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable))) + (((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasktable) + (dst_negative_scale_inverse_tables_sourcerightvaluemasktable)))))) /\ (forall dst_index_inverse_tables_sourcerightvaluemasktable. (exists pvs_le_gap_inverse_tables_sourcerightvaluemasktabledomain. pvs_le_gap_inverse_tables_sourcerightvaluemasktabledomain + (dst_index_inverse_tables_sourcerightvaluemasktable) = (dc_input_inverse_tables_sourceright)) -> exists dst_positive_inverse_tables_sourcerightvaluemasktable dst_negative_inverse_tables_sourcerightvaluemasktable dst_value_inverse_tables_sourcerightvaluemasktable. ((((exists ff_h_pvs_inverse_tables_sourcerightvaluemasktableentrypositive. ff_h_pvs_inverse_tables_sourcerightvaluemasktableentrypositive + S (dst_positive_inverse_tables_sourcerightvaluemasktable) = S ((S (dst_index_inverse_tables_sourcerightvaluemasktable)) * dst_positive_scale_inverse_tables_sourcerightvaluemasktable)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemasktableentrypositive. dst_positive_code_inverse_tables_sourcerightvaluemasktable = ff_q_pvs_inverse_tables_sourcerightvaluemasktableentrypositive * S ((S (dst_index_inverse_tables_sourcerightvaluemasktable)) * dst_positive_scale_inverse_tables_sourcerightvaluemasktable) + (dst_positive_inverse_tables_sourcerightvaluemasktable))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightvaluemasktableentrynegative. ff_h_pvs_inverse_tables_sourcerightvaluemasktableentrynegative + S (dst_negative_inverse_tables_sourcerightvaluemasktable) = S ((S (dst_index_inverse_tables_sourcerightvaluemasktable)) * dst_negative_scale_inverse_tables_sourcerightvaluemasktable)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemasktableentrynegative. dst_negative_code_inverse_tables_sourcerightvaluemasktable = ff_q_pvs_inverse_tables_sourcerightvaluemasktableentrynegative * S ((S (dst_index_inverse_tables_sourcerightvaluemasktable)) * dst_negative_scale_inverse_tables_sourcerightvaluemasktable) + (dst_negative_inverse_tables_sourcerightvaluemasktable))) /\ (exists ge_balance_positive_inverse_tables_sourcerightvaluemasktableentryvalue ge_balance_negative_inverse_tables_sourcerightvaluemasktableentryvalue. (((((dst_value_inverse_tables_sourcerightvaluemasktable) = 2 * (ge_balance_positive_inverse_tables_sourcerightvaluemasktableentryvalue) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemasktableentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluemasktableentryvaluedecode. (((dst_value_inverse_tables_sourcerightvaluemasktable) = 2 * ge_signed_half_inverse_tables_sourcerightvaluemasktableentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightvaluemasktableentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemasktableentryvalue) = S ge_signed_half_inverse_tables_sourcerightvaluemasktableentryvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerightvaluemasktable) + ge_balance_negative_inverse_tables_sourcerightvaluemasktableentryvalue = (dst_negative_inverse_tables_sourcerightvaluemasktable) + ge_balance_positive_inverse_tables_sourcerightvaluemasktableentryvalue))))))))) /\ (forall dc_index_inverse_tables_sourcerightvaluemask dc_value_inverse_tables_sourcerightvaluemask. (exists pvs_le_gap_inverse_tables_sourcerightvaluemaskdomain. pvs_le_gap_inverse_tables_sourcerightvaluemaskdomain + (dc_index_inverse_tables_sourcerightvaluemask) = (dc_input_inverse_tables_sourceright)) -> (exists dst_positive_code_inverse_tables_sourcerightvaluemasklookup dst_positive_scale_inverse_tables_sourcerightvaluemasklookup dst_negative_code_inverse_tables_sourcerightvaluemasklookup dst_negative_scale_inverse_tables_sourcerightvaluemasklookup dst_positive_inverse_tables_sourcerightvaluemasklookup dst_negative_inverse_tables_sourcerightvaluemasklookup. (((dc_mask_inverse_tables_sourcerightvalue) = (((((dst_positive_code_inverse_tables_sourcerightvaluemasklookup) + (dst_positive_scale_inverse_tables_sourcerightvaluemasklookup)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemasklookup) + (dst_positive_scale_inverse_tables_sourcerightvaluemasklookup)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_positive_scale_inverse_tables_sourcerightvaluemasklookup))) + (((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)))) * S ((((dst_positive_code_inverse_tables_sourcerightvaluemasklookup) + (dst_positive_scale_inverse_tables_sourcerightvaluemasklookup)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemasklookup) + (dst_positive_scale_inverse_tables_sourcerightvaluemasklookup)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_positive_scale_inverse_tables_sourcerightvaluemasklookup))) + (((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)))) + ((((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup))) + (((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightvaluemasklookuppositive. ff_h_pvs_inverse_tables_sourcerightvaluemasklookuppositive + S (dst_positive_inverse_tables_sourcerightvaluemasklookup) = S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_positive_scale_inverse_tables_sourcerightvaluemasklookup)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemasklookuppositive. dst_positive_code_inverse_tables_sourcerightvaluemasklookup = ff_q_pvs_inverse_tables_sourcerightvaluemasklookuppositive * S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_positive_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_positive_inverse_tables_sourcerightvaluemasklookup))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightvaluemasklookupnegative. ff_h_pvs_inverse_tables_sourcerightvaluemasklookupnegative + S (dst_negative_inverse_tables_sourcerightvaluemasklookup) = S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_negative_scale_inverse_tables_sourcerightvaluemasklookup)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemasklookupnegative. dst_negative_code_inverse_tables_sourcerightvaluemasklookup = ff_q_pvs_inverse_tables_sourcerightvaluemasklookupnegative * S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_negative_scale_inverse_tables_sourcerightvaluemasklookup) + (dst_negative_inverse_tables_sourcerightvaluemasklookup))) /\ (exists ge_balance_positive_inverse_tables_sourcerightvaluemasklookupvalue ge_balance_negative_inverse_tables_sourcerightvaluemasklookupvalue. (((((dc_value_inverse_tables_sourcerightvaluemask) = 2 * (ge_balance_positive_inverse_tables_sourcerightvaluemasklookupvalue) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemasklookupvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluemasklookupvaluedecode. (((dc_value_inverse_tables_sourcerightvaluemask) = 2 * ge_signed_half_inverse_tables_sourcerightvaluemasklookupvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightvaluemasklookupvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemasklookupvalue) = S ge_signed_half_inverse_tables_sourcerightvaluemasklookupvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerightvaluemasklookup) + ge_balance_negative_inverse_tables_sourcerightvaluemasklookupvalue = (dst_negative_inverse_tables_sourcerightvaluemasklookup) + ge_balance_positive_inverse_tables_sourcerightvaluemasklookupvalue))))))))) -> ((((~((dc_index_inverse_tables_sourcerightvaluemask)=0)) /\ (exists dc_quotient_inverse_tables_sourcerightvaluemaskentry dc_left_inverse_tables_sourcerightvaluemaskentry dc_right_inverse_tables_sourcerightvaluemaskentry. (((dc_input_inverse_tables_sourceright)=(dc_index_inverse_tables_sourcerightvaluemask)*dc_quotient_inverse_tables_sourcerightvaluemaskentry) /\ (((exists dst_positive_code_inverse_tables_sourcerightvaluemaskentryleft dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft dst_positive_inverse_tables_sourcerightvaluemaskentryleft dst_negative_inverse_tables_sourcerightvaluemaskentryleft. (((G) = (((((dst_positive_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft))) + (((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)))) * S ((((dst_positive_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft))) + (((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)))) + ((((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft))) + (((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightvaluemaskentryleftpositive. ff_h_pvs_inverse_tables_sourcerightvaluemaskentryleftpositive + S (dst_positive_inverse_tables_sourcerightvaluemaskentryleft) = S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemaskentryleftpositive. dst_positive_code_inverse_tables_sourcerightvaluemaskentryleft = ff_q_pvs_inverse_tables_sourcerightvaluemaskentryleftpositive * S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_positive_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_positive_inverse_tables_sourcerightvaluemaskentryleft))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightvaluemaskentryleftnegative. ff_h_pvs_inverse_tables_sourcerightvaluemaskentryleftnegative + S (dst_negative_inverse_tables_sourcerightvaluemaskentryleft) = S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemaskentryleftnegative. dst_negative_code_inverse_tables_sourcerightvaluemaskentryleft = ff_q_pvs_inverse_tables_sourcerightvaluemaskentryleftnegative * S ((S (dc_index_inverse_tables_sourcerightvaluemask)) * dst_negative_scale_inverse_tables_sourcerightvaluemaskentryleft) + (dst_negative_inverse_tables_sourcerightvaluemaskentryleft))) /\ (exists ge_balance_positive_inverse_tables_sourcerightvaluemaskentryleftvalue ge_balance_negative_inverse_tables_sourcerightvaluemaskentryleftvalue. (((((dc_left_inverse_tables_sourcerightvaluemaskentry) = 2 * (ge_balance_positive_inverse_tables_sourcerightvaluemaskentryleftvalue) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemaskentryleftvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluemaskentryleftvaluedecode. (((dc_left_inverse_tables_sourcerightvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourcerightvaluemaskentryleftvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightvaluemaskentryleftvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemaskentryleftvalue) = S ge_signed_half_inverse_tables_sourcerightvaluemaskentryleftvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerightvaluemaskentryleft) + ge_balance_negative_inverse_tables_sourcerightvaluemaskentryleftvalue = (dst_negative_inverse_tables_sourcerightvaluemaskentryleft) + ge_balance_positive_inverse_tables_sourcerightvaluemaskentryleftvalue))))))))) /\ (((exists dst_positive_code_inverse_tables_sourcerightvaluemaskentryright dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright dst_negative_code_inverse_tables_sourcerightvaluemaskentryright dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright dst_positive_inverse_tables_sourcerightvaluemaskentryright dst_negative_inverse_tables_sourcerightvaluemaskentryright. (((F) = (((((dst_positive_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright))) + (((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)))) * S ((((dst_positive_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright)) * S ((dst_positive_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright)) + ((dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright))) + (((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)))) + ((((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright))) + (((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) * S ((dst_negative_code_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) + ((dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)))))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightvaluemaskentryrightpositive. ff_h_pvs_inverse_tables_sourcerightvaluemaskentryrightpositive + S (dst_positive_inverse_tables_sourcerightvaluemaskentryright) = S ((S (dc_quotient_inverse_tables_sourcerightvaluemaskentry)) * dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemaskentryrightpositive. dst_positive_code_inverse_tables_sourcerightvaluemaskentryright = ff_q_pvs_inverse_tables_sourcerightvaluemaskentryrightpositive * S ((S (dc_quotient_inverse_tables_sourcerightvaluemaskentry)) * dst_positive_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_positive_inverse_tables_sourcerightvaluemaskentryright))) /\ (((((exists ff_h_pvs_inverse_tables_sourcerightvaluemaskentryrightnegative. ff_h_pvs_inverse_tables_sourcerightvaluemaskentryrightnegative + S (dst_negative_inverse_tables_sourcerightvaluemaskentryright) = S ((S (dc_quotient_inverse_tables_sourcerightvaluemaskentry)) * dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright)) /\ exists ff_q_pvs_inverse_tables_sourcerightvaluemaskentryrightnegative. dst_negative_code_inverse_tables_sourcerightvaluemaskentryright = ff_q_pvs_inverse_tables_sourcerightvaluemaskentryrightnegative * S ((S (dc_quotient_inverse_tables_sourcerightvaluemaskentry)) * dst_negative_scale_inverse_tables_sourcerightvaluemaskentryright) + (dst_negative_inverse_tables_sourcerightvaluemaskentryright))) /\ (exists ge_balance_positive_inverse_tables_sourcerightvaluemaskentryrightvalue ge_balance_negative_inverse_tables_sourcerightvaluemaskentryrightvalue. (((((dc_right_inverse_tables_sourcerightvaluemaskentry) = 2 * (ge_balance_positive_inverse_tables_sourcerightvaluemaskentryrightvalue) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemaskentryrightvalue) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluemaskentryrightvaluedecode. (((dc_right_inverse_tables_sourcerightvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourcerightvaluemaskentryrightvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightvaluemaskentryrightvalue) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightvaluemaskentryrightvalue) = S ge_signed_half_inverse_tables_sourcerightvaluemaskentryrightvaluedecode))) /\ ((dst_positive_inverse_tables_sourcerightvaluemaskentryright) + ge_balance_negative_inverse_tables_sourcerightvaluemaskentryrightvalue = (dst_negative_inverse_tables_sourcerightvaluemaskentryright) + ge_balance_positive_inverse_tables_sourcerightvaluemaskentryrightvalue))))))))) /\ (exists sto_ap_inverse_tables_sourcerightvaluemaskentryproduct sto_an_inverse_tables_sourcerightvaluemaskentryproduct sto_bp_inverse_tables_sourcerightvaluemaskentryproduct sto_bn_inverse_tables_sourcerightvaluemaskentryproduct sto_cp_inverse_tables_sourcerightvaluemaskentryproduct sto_cn_inverse_tables_sourcerightvaluemaskentryproduct. (((((dc_left_inverse_tables_sourcerightvaluemaskentry) = 2 * (sto_ap_inverse_tables_sourcerightvaluemaskentryproduct) /\ (sto_an_inverse_tables_sourcerightvaluemaskentryproduct) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductleft. (((dc_left_inverse_tables_sourcerightvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductleft + 1 /\ (sto_ap_inverse_tables_sourcerightvaluemaskentryproduct) = 0) /\ (sto_an_inverse_tables_sourcerightvaluemaskentryproduct) = S ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductleft))) /\ ((((((dc_right_inverse_tables_sourcerightvaluemaskentry) = 2 * (sto_bp_inverse_tables_sourcerightvaluemaskentryproduct) /\ (sto_bn_inverse_tables_sourcerightvaluemaskentryproduct) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductright. (((dc_right_inverse_tables_sourcerightvaluemaskentry) = 2 * ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductright + 1 /\ (sto_bp_inverse_tables_sourcerightvaluemaskentryproduct) = 0) /\ (sto_bn_inverse_tables_sourcerightvaluemaskentryproduct) = S ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductright))) /\ ((((((dc_value_inverse_tables_sourcerightvaluemask) = 2 * (sto_cp_inverse_tables_sourcerightvaluemaskentryproduct) /\ (sto_cn_inverse_tables_sourcerightvaluemaskentryproduct) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductoutput. (((dc_value_inverse_tables_sourcerightvaluemask) = 2 * ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductoutput + 1 /\ (sto_cp_inverse_tables_sourcerightvaluemaskentryproduct) = 0) /\ (sto_cn_inverse_tables_sourcerightvaluemaskentryproduct) = S ge_signed_half_inverse_tables_sourcerightvaluemaskentryproductoutput))) /\ ((sto_ap_inverse_tables_sourcerightvaluemaskentryproduct * sto_bp_inverse_tables_sourcerightvaluemaskentryproduct + sto_an_inverse_tables_sourcerightvaluemaskentryproduct * sto_bn_inverse_tables_sourcerightvaluemaskentryproduct) + sto_cn_inverse_tables_sourcerightvaluemaskentryproduct = (sto_ap_inverse_tables_sourcerightvaluemaskentryproduct * sto_bn_inverse_tables_sourcerightvaluemaskentryproduct + sto_an_inverse_tables_sourcerightvaluemaskentryproduct * sto_bp_inverse_tables_sourcerightvaluemaskentryproduct) + sto_cp_inverse_tables_sourcerightvaluemaskentryproduct))))))))))))))) \/ ((((dc_index_inverse_tables_sourcerightvaluemask)=0 \/ ~(exists pvs_factor_inverse_tables_sourcerightvaluemaskentrynondivisor. (dc_input_inverse_tables_sourceright) = (dc_index_inverse_tables_sourcerightvaluemask) * pvs_factor_inverse_tables_sourcerightvaluemaskentrynondivisor)) /\ ((dc_value_inverse_tables_sourcerightvaluemask)=0))))))) /\ (exists dst_positive_code_inverse_tables_sourcerightvaluefold dst_positive_scale_inverse_tables_sourcerightvaluefold dst_negative_code_inverse_tables_sourcerightvaluefold dst_negative_scale_inverse_tables_sourcerightvaluefold dst_positive_sum_inverse_tables_sourcerightvaluefold dst_negative_sum_inverse_tables_sourcerightvaluefold. (((dc_mask_inverse_tables_sourcerightvalue) = (((((dst_positive_code_inverse_tables_sourcerightvaluefold) + (dst_positive_scale_inverse_tables_sourcerightvaluefold)) * S ((dst_positive_code_inverse_tables_sourcerightvaluefold) + (dst_positive_scale_inverse_tables_sourcerightvaluefold)) + ((dst_positive_scale_inverse_tables_sourcerightvaluefold) + (dst_positive_scale_inverse_tables_sourcerightvaluefold))) + (((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) * S ((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) + ((dst_negative_scale_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)))) * S ((((dst_positive_code_inverse_tables_sourcerightvaluefold) + (dst_positive_scale_inverse_tables_sourcerightvaluefold)) * S ((dst_positive_code_inverse_tables_sourcerightvaluefold) + (dst_positive_scale_inverse_tables_sourcerightvaluefold)) + ((dst_positive_scale_inverse_tables_sourcerightvaluefold) + (dst_positive_scale_inverse_tables_sourcerightvaluefold))) + (((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) * S ((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) + ((dst_negative_scale_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)))) + ((((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) * S ((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) + ((dst_negative_scale_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold))) + (((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) * S ((dst_negative_code_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)) + ((dst_negative_scale_inverse_tables_sourcerightvaluefold) + (dst_negative_scale_inverse_tables_sourcerightvaluefold)))))) /\ (((exists fs_u_dst_inverse_tables_sourcerightvaluefoldpositive fs_v_dst_inverse_tables_sourcerightvaluefoldpositive. ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_start. fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_start + S (0) = S ((S (0)) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_start. fs_u_dst_inverse_tables_sourcerightvaluefoldpositive = fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_start * S ((S (0)) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive) + (0))) /\ ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_terminal. fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_terminal + S (dst_positive_sum_inverse_tables_sourcerightvaluefold) = S ((S (S (dc_input_inverse_tables_sourceright))) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_terminal. fs_u_dst_inverse_tables_sourcerightvaluefoldpositive = fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_terminal * S ((S (S (dc_input_inverse_tables_sourceright))) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive) + (dst_positive_sum_inverse_tables_sourcerightvaluefold))) /\ forall fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps. (exists fs_lt_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_bound. fs_lt_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_bound + S fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps = S (dc_input_inverse_tables_sourceright)) -> exists fs_a_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps fs_r_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps fs_s_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps. ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_summand. fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_summand + S (fs_a_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps) = S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps)) * dst_positive_scale_inverse_tables_sourcerightvaluefold)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_summand. dst_positive_code_inverse_tables_sourcerightvaluefold = fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_summand * S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps)) * dst_positive_scale_inverse_tables_sourcerightvaluefold) + (fs_a_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_partial. fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_partial + S (fs_r_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps) = S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_partial. fs_u_dst_inverse_tables_sourcerightvaluefoldpositive = fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_partial * S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive) + (fs_r_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_successor. fs_h_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_successor + S (fs_s_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps) = S ((S (S fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_successor. fs_u_dst_inverse_tables_sourcerightvaluefoldpositive = fs_q_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps_successor * S ((S (S fs_i_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldpositive) + (fs_s_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps))) /\ fs_s_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps = fs_r_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps + fs_a_dst_inverse_tables_sourcerightvaluefoldpositive_body_steps)))))) /\ (((exists fs_u_dst_inverse_tables_sourcerightvaluefoldnegative fs_v_dst_inverse_tables_sourcerightvaluefoldnegative. ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_start. fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_start + S (0) = S ((S (0)) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_start. fs_u_dst_inverse_tables_sourcerightvaluefoldnegative = fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_start * S ((S (0)) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative) + (0))) /\ ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_terminal. fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_terminal + S (dst_negative_sum_inverse_tables_sourcerightvaluefold) = S ((S (S (dc_input_inverse_tables_sourceright))) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_terminal. fs_u_dst_inverse_tables_sourcerightvaluefoldnegative = fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_terminal * S ((S (S (dc_input_inverse_tables_sourceright))) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative) + (dst_negative_sum_inverse_tables_sourcerightvaluefold))) /\ forall fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps. (exists fs_lt_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_bound. fs_lt_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_bound + S fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps = S (dc_input_inverse_tables_sourceright)) -> exists fs_a_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps fs_r_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps fs_s_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps. ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_summand. fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_summand + S (fs_a_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps) = S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps)) * dst_negative_scale_inverse_tables_sourcerightvaluefold)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_summand. dst_negative_code_inverse_tables_sourcerightvaluefold = fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_summand * S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps)) * dst_negative_scale_inverse_tables_sourcerightvaluefold) + (fs_a_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_partial. fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_partial + S (fs_r_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps) = S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_partial. fs_u_dst_inverse_tables_sourcerightvaluefoldnegative = fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_partial * S ((S (fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative) + (fs_r_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps))) /\ ((((exists fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_successor. fs_h_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_successor + S (fs_s_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps) = S ((S (S fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative)) /\ exists fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_successor. fs_u_dst_inverse_tables_sourcerightvaluefoldnegative = fs_q_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps_successor * S ((S (S fs_i_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps)) * fs_v_dst_inverse_tables_sourcerightvaluefoldnegative) + (fs_s_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps))) /\ fs_s_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps = fs_r_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps + fs_a_dst_inverse_tables_sourcerightvaluefoldnegative_body_steps)))))) /\ (exists ge_balance_positive_inverse_tables_sourcerightvaluefoldresult ge_balance_negative_inverse_tables_sourcerightvaluefoldresult. (((((dc_output_inverse_tables_sourceright) = 2 * (ge_balance_positive_inverse_tables_sourcerightvaluefoldresult) /\ (ge_balance_negative_inverse_tables_sourcerightvaluefoldresult) = 0) \/ exists ge_signed_half_inverse_tables_sourcerightvaluefoldresultdecode. (((dc_output_inverse_tables_sourceright) = 2 * ge_signed_half_inverse_tables_sourcerightvaluefoldresultdecode + 1 /\ (ge_balance_positive_inverse_tables_sourcerightvaluefoldresult) = 0) /\ (ge_balance_negative_inverse_tables_sourcerightvaluefoldresult) = S ge_signed_half_inverse_tables_sourcerightvaluefoldresultdecode))) /\ ((dst_positive_sum_inverse_tables_sourcerightvaluefold) + ge_balance_negative_inverse_tables_sourcerightvaluefoldresult = (dst_negative_sum_inverse_tables_sourcerightvaluefold) + ge_balance_positive_inverse_tables_sourcerightvaluefoldresult)))))))))))))))))))))))) -> ((exists dst_positive_code_inverse_tables_left dst_positive_scale_inverse_tables_left dst_negative_code_inverse_tables_left dst_negative_scale_inverse_tables_left. (((F) = (((((dst_positive_code_inverse_tables_left) + (dst_positive_scale_inverse_tables_left)) * S ((dst_positive_code_inverse_tables_left) + (dst_positive_scale_inverse_tables_left)) + ((dst_positive_scale_inverse_tables_left) + (dst_positive_scale_inverse_tables_left))) + (((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) * S ((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) + ((dst_negative_scale_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)))) * S ((((dst_positive_code_inverse_tables_left) + (dst_positive_scale_inverse_tables_left)) * S ((dst_positive_code_inverse_tables_left) + (dst_positive_scale_inverse_tables_left)) + ((dst_positive_scale_inverse_tables_left) + (dst_positive_scale_inverse_tables_left))) + (((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) * S ((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) + ((dst_negative_scale_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)))) + ((((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) * S ((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) + ((dst_negative_scale_inverse_tables_left) + (dst_negative_scale_inverse_tables_left))) + (((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) * S ((dst_negative_code_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)) + ((dst_negative_scale_inverse_tables_left) + (dst_negative_scale_inverse_tables_left)))))) /\ (forall dst_index_inverse_tables_left. (exists pvs_le_gap_inverse_tables_leftdomain. pvs_le_gap_inverse_tables_leftdomain + (dst_index_inverse_tables_left) = (N)) -> exists dst_positive_inverse_tables_left dst_negative_inverse_tables_left dst_value_inverse_tables_left. ((((exists ff_h_pvs_inverse_tables_leftentrypositive. ff_h_pvs_inverse_tables_leftentrypositive + S (dst_positive_inverse_tables_left) = S ((S (dst_index_inverse_tables_left)) * dst_positive_scale_inverse_tables_left)) /\ exists ff_q_pvs_inverse_tables_leftentrypositive. dst_positive_code_inverse_tables_left = ff_q_pvs_inverse_tables_leftentrypositive * S ((S (dst_index_inverse_tables_left)) * dst_positive_scale_inverse_tables_left) + (dst_positive_inverse_tables_left))) /\ (((((exists ff_h_pvs_inverse_tables_leftentrynegative. ff_h_pvs_inverse_tables_leftentrynegative + S (dst_negative_inverse_tables_left) = S ((S (dst_index_inverse_tables_left)) * dst_negative_scale_inverse_tables_left)) /\ exists ff_q_pvs_inverse_tables_leftentrynegative. dst_negative_code_inverse_tables_left = ff_q_pvs_inverse_tables_leftentrynegative * S ((S (dst_index_inverse_tables_left)) * dst_negative_scale_inverse_tables_left) + (dst_negative_inverse_tables_left))) /\ (exists ge_balance_positive_inverse_tables_leftentryvalue ge_balance_negative_inverse_tables_leftentryvalue. (((((dst_value_inverse_tables_left) = 2 * (ge_balance_positive_inverse_tables_leftentryvalue) /\ (ge_balance_negative_inverse_tables_leftentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_leftentryvaluedecode. (((dst_value_inverse_tables_left) = 2 * ge_signed_half_inverse_tables_leftentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_leftentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_leftentryvalue) = S ge_signed_half_inverse_tables_leftentryvaluedecode))) /\ ((dst_positive_inverse_tables_left) + ge_balance_negative_inverse_tables_leftentryvalue = (dst_negative_inverse_tables_left) + ge_balance_positive_inverse_tables_leftentryvalue))))))))) /\ (exists dst_positive_code_inverse_tables_right dst_positive_scale_inverse_tables_right dst_negative_code_inverse_tables_right dst_negative_scale_inverse_tables_right. (((G) = (((((dst_positive_code_inverse_tables_right) + (dst_positive_scale_inverse_tables_right)) * S ((dst_positive_code_inverse_tables_right) + (dst_positive_scale_inverse_tables_right)) + ((dst_positive_scale_inverse_tables_right) + (dst_positive_scale_inverse_tables_right))) + (((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) * S ((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) + ((dst_negative_scale_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)))) * S ((((dst_positive_code_inverse_tables_right) + (dst_positive_scale_inverse_tables_right)) * S ((dst_positive_code_inverse_tables_right) + (dst_positive_scale_inverse_tables_right)) + ((dst_positive_scale_inverse_tables_right) + (dst_positive_scale_inverse_tables_right))) + (((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) * S ((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) + ((dst_negative_scale_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)))) + ((((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) * S ((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) + ((dst_negative_scale_inverse_tables_right) + (dst_negative_scale_inverse_tables_right))) + (((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) * S ((dst_negative_code_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)) + ((dst_negative_scale_inverse_tables_right) + (dst_negative_scale_inverse_tables_right)))))) /\ (forall dst_index_inverse_tables_right. (exists pvs_le_gap_inverse_tables_rightdomain. pvs_le_gap_inverse_tables_rightdomain + (dst_index_inverse_tables_right) = (N)) -> exists dst_positive_inverse_tables_right dst_negative_inverse_tables_right dst_value_inverse_tables_right. ((((exists ff_h_pvs_inverse_tables_rightentrypositive. ff_h_pvs_inverse_tables_rightentrypositive + S (dst_positive_inverse_tables_right) = S ((S (dst_index_inverse_tables_right)) * dst_positive_scale_inverse_tables_right)) /\ exists ff_q_pvs_inverse_tables_rightentrypositive. dst_positive_code_inverse_tables_right = ff_q_pvs_inverse_tables_rightentrypositive * S ((S (dst_index_inverse_tables_right)) * dst_positive_scale_inverse_tables_right) + (dst_positive_inverse_tables_right))) /\ (((((exists ff_h_pvs_inverse_tables_rightentrynegative. ff_h_pvs_inverse_tables_rightentrynegative + S (dst_negative_inverse_tables_right) = S ((S (dst_index_inverse_tables_right)) * dst_negative_scale_inverse_tables_right)) /\ exists ff_q_pvs_inverse_tables_rightentrynegative. dst_negative_code_inverse_tables_right = ff_q_pvs_inverse_tables_rightentrynegative * S ((S (dst_index_inverse_tables_right)) * dst_negative_scale_inverse_tables_right) + (dst_negative_inverse_tables_right))) /\ (exists ge_balance_positive_inverse_tables_rightentryvalue ge_balance_negative_inverse_tables_rightentryvalue. (((((dst_value_inverse_tables_right) = 2 * (ge_balance_positive_inverse_tables_rightentryvalue) /\ (ge_balance_negative_inverse_tables_rightentryvalue) = 0) \/ exists ge_signed_half_inverse_tables_rightentryvaluedecode. (((dst_value_inverse_tables_right) = 2 * ge_signed_half_inverse_tables_rightentryvaluedecode + 1 /\ (ge_balance_positive_inverse_tables_rightentryvalue) = 0) /\ (ge_balance_negative_inverse_tables_rightentryvalue) = S ge_signed_half_inverse_tables_rightentryvaluedecode))) /\ ((dst_positive_inverse_tables_right) + ge_balance_negative_inverse_tables_rightentryvalue = (dst_negative_inverse_tables_right) + ge_balance_positive_inverse_tables_rightentryvalue))))))))))Constructive proof overview
Generated structural guide
The inverse graph entails actual valid input tables; it is never a vacuous equation between missing lookups.
The unchanged tactic script uses 0 declared prerequisites and contains 13 exact native proof lines.
Alpha v34 checked-use · first admitted v31 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
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
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.
01Fix variables and assumptionsL1–4
02Separate the logical casesL5–11
Original exact command ledger · 13 lines
- 0001
intro N - 0002
intro F - 0003
intro G - 0004
intro hi - 0005
cases hi - 0006
cases hi_witness - 0007
cases hi_witness_right - 0008
cases hi_witness_right_left - 0009
cases hi_witness_right_left_right - 0010
cases hi_witness_right_left_right_right - 0011
split - 0012
exact hi_witness_right_left_left - 0013
exact hi_witness_right_left_right_left