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
∀ fp_i_defined_injective_prefix. ∀ fp_j_defined_injective_prefix. ∀ fp_value_defined_injective_prefix. Lt(fp_i_defined_injective_prefix,l) → Lt(fp_j_defined_injective_prefix,l) → BetaAt(b,c,fp_i_defined_injective_prefix,fp_value_defined_injective_prefix) → BetaAt(b,c,fp_j_defined_injective_prefix,fp_value_defined_injective_prefix) → fp_i_defined_injective_prefix = fp_j_defined_injective_prefixOnly definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall fp_i_defined_injective_prefix fp_j_defined_injective_prefix fp_value_defined_injective_prefix. (exists fp_gap_defined_injective_prefix_i. fp_gap_defined_injective_prefix_i + S fp_i_defined_injective_prefix = l) -> (exists fp_gap_defined_injective_prefix_j. fp_gap_defined_injective_prefix_j + S fp_j_defined_injective_prefix = l) -> (((exists ff_h_defined_injective_prefix_left. ff_h_defined_injective_prefix_left + S (fp_value_defined_injective_prefix) = S ((S (fp_i_defined_injective_prefix)) * c)) /\ exists ff_q_defined_injective_prefix_left. b = ff_q_defined_injective_prefix_left * S ((S (fp_i_defined_injective_prefix)) * c) + (fp_value_defined_injective_prefix))) -> (((exists ff_h_defined_injective_prefix_right. ff_h_defined_injective_prefix_right + S (fp_value_defined_injective_prefix) = S ((S (fp_j_defined_injective_prefix)) * c)) /\ exists ff_q_defined_injective_prefix_right. b = ff_q_defined_injective_prefix_right * S ((S (fp_j_defined_injective_prefix)) * c) + (fp_value_defined_injective_prefix))) -> fp_i_defined_injective_prefix = fp_j_defined_injective_prefixThe unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.