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
Lt(a,p) ∧ (Lt(b,p) ∧ CanonicalModularResidue(p,a · b,c))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
((exists pfa_gap_bottomlayerleft. pfa_gap_bottomlayerleft + S ((a)) = ((p))) /\ (((exists pfa_gap_bottomlayerright. pfa_gap_bottomlayerright + S ((b)) = ((p))) /\ ((((exists pfa_gap_bottomlayerresultbound. pfa_gap_bottomlayerresultbound + S ((c)) = ((p))) /\ ((exists pfa_offset_left_bottomlayerresultcongruence pfa_offset_right_bottomlayerresultcongruence. (((a)) * ((b))) + ((p)) * pfa_offset_left_bottomlayerresultcongruence = ((c)) + ((p)) * pfa_offset_right_bottomlayerresultcongruence))))))))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
PP0016 · prime_field_polynomial_scale_entryPP0017 · prime_field_polynomial_scale_boundedPP0019 · prime_field_polynomial_scale_transportPP001D · prime_field_polynomial_scale_associativePP0020 · prime_field_polynomial_horner_canonical_stepPP0021 · prime_field_polynomial_horner_trace_from_normalizationPP0025 · prime_field_polynomial_horner_successor_decomposePP0027 · prime_field_polynomial_horner_normalization_residuePP002C · prime_field_polynomial_horner_successor_construct