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
∀ pft_index_bottomlayer. Lt(pft_index_bottomlayer,l) → ∃ x. BetaAt(b,c,pft_index_bottomlayer,x) ∧ FpAdd(p,pft_index_bottomlayer,x,0)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall pft_index_bottomlayer. (exists pfa_gap_bottomlayerprefix. pfa_gap_bottomlayerprefix + S (pft_index_bottomlayer) = ((l))) -> exists pft_value_bottomlayer. (((((exists ff_h_pft_bottomlayerpointentry. ff_h_pft_bottomlayerpointentry + S (pft_value_bottomlayer) = S ((S (pft_index_bottomlayer)) * (c))) /\ exists ff_q_pft_bottomlayerpointentry. (b) = ff_q_pft_bottomlayerpointentry * S ((S (pft_index_bottomlayer)) * (c)) + (pft_value_bottomlayer))) /\ ((((exists pfa_gap_bottomlayerpointvalueadditionleft. pfa_gap_bottomlayerpointvalueadditionleft + S (pft_index_bottomlayer) = ((p))) /\ (((exists pfa_gap_bottomlayerpointvalueadditionright. pfa_gap_bottomlayerpointvalueadditionright + S (pft_value_bottomlayer) = ((p))) /\ ((((exists pfa_gap_bottomlayerpointvalueadditionresultbound. pfa_gap_bottomlayerpointvalueadditionresultbound + S (0) = ((p))) /\ ((exists pfa_offset_left_bottomlayerpointvalueadditionresultcongruence pfa_offset_right_bottomlayerpointvalueadditionresultcongruence. ((pft_index_bottomlayer) + (pft_value_bottomlayer)) + ((p)) * pfa_offset_left_bottomlayerpointvalueadditionresultcongruence = (0) + ((p)) * pfa_offset_right_bottomlayerpointvalueadditionresultcongruence))))))))))))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.