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) ∧ (a = 0 ∧ b = 0 ∨ FpInv(p,a,b)))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
((exists pfa_gap_bottomlayerinput. pfa_gap_bottomlayerinput + S ((a)) = ((p))) /\ (((exists pfa_gap_bottomlayeroutput. pfa_gap_bottomlayeroutput + S ((b)) = ((p))) /\ (((((a)) = 0 /\ ((b)) = 0) \/ (((~(((a)) = 0)) /\ ((((exists pfa_gap_bottomlayernonzeromultiplicationleft. pfa_gap_bottomlayernonzeromultiplicationleft + S ((a)) = ((p))) /\ (((exists pfa_gap_bottomlayernonzeromultiplicationright. pfa_gap_bottomlayernonzeromultiplicationright + S ((b)) = ((p))) /\ ((((exists pfa_gap_bottomlayernonzeromultiplicationresultbound. pfa_gap_bottomlayernonzeromultiplicationresultbound + S (1) = ((p))) /\ ((exists pfa_offset_left_bottomlayernonzeromultiplicationresultcongruence pfa_offset_right_bottomlayernonzeromultiplicationresultcongruence. (((a)) * ((b))) + ((p)) * pfa_offset_left_bottomlayernonzeromultiplicationresultcongruence = (1) + ((p)) * pfa_offset_right_bottomlayernonzeromultiplicationresultcongruence)))))))))))))))))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.