Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Definition in prerequisite notation
∃ dst_positive_code_bottomlayer. ∃ dst_positive_scale_bottomlayer. ∃ dst_negative_code_bottomlayer. ∃ dst_negative_scale_bottomlayer. ∃ dst_positive_bottomlayer. ∃ dst_negative_bottomlayer. MatrixMinorFourCode(F,dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer) ∧ (BetaAt(dst_positive_code_bottomlayer,dst_positive_scale_bottomlayer,i,dst_positive_bottomlayer) ∧ (BetaAt(dst_negative_code_bottomlayer,dst_negative_scale_bottomlayer,i,dst_negative_bottomlayer) ∧ SignedBalance(z,dst_positive_bottomlayer,dst_negative_bottomlayer)))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists dst_positive_code_bottomlayer dst_positive_scale_bottomlayer dst_negative_code_bottomlayer dst_negative_scale_bottomlayer dst_positive_bottomlayer dst_negative_bottomlayer. ((((F)) = (((((dst_positive_code_bottomlayer) + (dst_positive_scale_bottomlayer)) * S ((dst_positive_code_bottomlayer) + (dst_positive_scale_bottomlayer)) + ((dst_positive_scale_bottomlayer) + (dst_positive_scale_bottomlayer))) + (((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) * S ((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) + ((dst_negative_scale_bottomlayer) + (dst_negative_scale_bottomlayer)))) * S ((((dst_positive_code_bottomlayer) + (dst_positive_scale_bottomlayer)) * S ((dst_positive_code_bottomlayer) + (dst_positive_scale_bottomlayer)) + ((dst_positive_scale_bottomlayer) + (dst_positive_scale_bottomlayer))) + (((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) * S ((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) + ((dst_negative_scale_bottomlayer) + (dst_negative_scale_bottomlayer)))) + ((((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) * S ((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) + ((dst_negative_scale_bottomlayer) + (dst_negative_scale_bottomlayer))) + (((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) * S ((dst_negative_code_bottomlayer) + (dst_negative_scale_bottomlayer)) + ((dst_negative_scale_bottomlayer) + (dst_negative_scale_bottomlayer)))))) /\ (((((exists ff_h_pvs_bottomlayerpositive. ff_h_pvs_bottomlayerpositive + S (dst_positive_bottomlayer) = S ((S ((i))) * dst_positive_scale_bottomlayer)) /\ exists ff_q_pvs_bottomlayerpositive. dst_positive_code_bottomlayer = ff_q_pvs_bottomlayerpositive * S ((S ((i))) * dst_positive_scale_bottomlayer) + (dst_positive_bottomlayer))) /\ (((((exists ff_h_pvs_bottomlayernegative. ff_h_pvs_bottomlayernegative + S (dst_negative_bottomlayer) = S ((S ((i))) * dst_negative_scale_bottomlayer)) /\ exists ff_q_pvs_bottomlayernegative. dst_negative_code_bottomlayer = ff_q_pvs_bottomlayernegative * S ((S ((i))) * dst_negative_scale_bottomlayer) + (dst_negative_bottomlayer))) /\ (exists ge_balance_positive_bottomlayervalue ge_balance_negative_bottomlayervalue. ((((((z)) = 2 * (ge_balance_positive_bottomlayervalue) /\ (ge_balance_negative_bottomlayervalue) = 0) \/ exists ge_signed_half_bottomlayervaluedecode. ((((z)) = 2 * ge_signed_half_bottomlayervaluedecode + 1 /\ (ge_balance_positive_bottomlayervalue) = 0) /\ (ge_balance_negative_bottomlayervalue) = S ge_signed_half_bottomlayervaluedecode))) /\ ((dst_positive_bottomlayer) + ge_balance_negative_bottomlayervalue = (dst_negative_bottomlayer) + ge_balance_positive_bottomlayervalue))))))))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.
Direct definition dependencies
Definitions depending on this notation
Checked theorems using this definition
WS0002 · signed_table_lookup_anyWS0003 · signed_table_add_lookupWS0006 · signed_table_add_extensional_uniqueWS0007 · signed_table_multiply_lookupWS000A · signed_table_multiply_extensional_uniqueWS000B · signed_table_scalar_lookupWS000E · signed_table_scalar_extensional_uniqueWS000F · signed_table_add_extendWS0010 · signed_table_add_existsWS0012 · signed_table_multiply_extendWS0013 · signed_table_multiply_existsWS0015 · signed_table_scalar_extendWS0016 · signed_table_scalar_existsWS001B · signed_prefix_sum_pointwise_addWS001C · signed_prefix_sum_scalar_multiplyWS0024 · signed_table_weighted_add_distributiveWS0026 · signed_table_weighted_scalar_commute