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 original first-admission records.
Definition in prerequisite notation
∀ fp_i_defined_bounded_prefix. Lt(fp_i_defined_bounded_prefix,l) → ∃ x. BetaAt(b,c,fp_i_defined_bounded_prefix,x) ∧ Lt(x,l)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall fp_i_defined_bounded_prefix. (exists fp_gap_defined_bounded_prefix_index. fp_gap_defined_bounded_prefix_index + S fp_i_defined_bounded_prefix = l) -> exists fp_value_defined_bounded_prefix. ((((exists ff_h_defined_bounded_prefix_entry. ff_h_defined_bounded_prefix_entry + S (fp_value_defined_bounded_prefix) = S ((S (fp_i_defined_bounded_prefix)) * c)) /\ exists ff_q_defined_bounded_prefix_entry. b = ff_q_defined_bounded_prefix_entry * S ((S (fp_i_defined_bounded_prefix)) * c) + (fp_value_defined_bounded_prefix))) /\ (exists fp_gap_defined_bounded_prefix_value. fp_gap_defined_bounded_prefix_value + S fp_value_defined_bounded_prefix = l))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
none directly; see definition consumers