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
∀ fms_i_secondwave. Lt(fms_i_secondwave,p) → (BetaAt(u,v,fms_i_secondwave,1) → BetaAt(b,c,fms_i_secondwave,1) ∧ BetaAt(d,e,fms_i_secondwave,1)) ∧ (BetaAt(b,c,fms_i_secondwave,1) ∧ BetaAt(d,e,fms_i_secondwave,1) → BetaAt(u,v,fms_i_secondwave,1))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall fms_i_secondwave. (exists fms_gap_secondwave. fms_gap_secondwave + S (fms_i_secondwave) = (p)) -> ((((((exists fs_h_fms_secondwave_result. fs_h_fms_secondwave_result + S (1) = S ((S (fms_i_secondwave)) * v)) /\ exists fs_q_fms_secondwave_result. u = fs_q_fms_secondwave_result * S ((S (fms_i_secondwave)) * v) + (1))) -> (((((exists fs_h_fms_secondwave_left. fs_h_fms_secondwave_left + S (1) = S ((S (fms_i_secondwave)) * c)) /\ exists fs_q_fms_secondwave_left. b = fs_q_fms_secondwave_left * S ((S (fms_i_secondwave)) * c) + (1))) /\ (((exists fs_h_fms_secondwave_right. fs_h_fms_secondwave_right + S (1) = S ((S (fms_i_secondwave)) * e)) /\ exists fs_q_fms_secondwave_right. d = fs_q_fms_secondwave_right * S ((S (fms_i_secondwave)) * e) + (1)))))) /\ ((((((exists fs_h_fms_secondwave_left. fs_h_fms_secondwave_left + S (1) = S ((S (fms_i_secondwave)) * c)) /\ exists fs_q_fms_secondwave_left. b = fs_q_fms_secondwave_left * S ((S (fms_i_secondwave)) * c) + (1))) /\ (((exists fs_h_fms_secondwave_right. fs_h_fms_secondwave_right + S (1) = S ((S (fms_i_secondwave)) * e)) /\ exists fs_q_fms_secondwave_right. d = fs_q_fms_secondwave_right * S ((S (fms_i_secondwave)) * e) + (1))))) -> (((exists fs_h_fms_secondwave_result. fs_h_fms_secondwave_result + S (1) = S ((S (fms_i_secondwave)) * v)) /\ exists fs_q_fms_secondwave_result. u = fs_q_fms_secondwave_result * S ((S (fms_i_secondwave)) * v) + (1))))))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
none
Checked theorems using this definition
CD0011 · finite_bit_intersection_from_productCD0012 · finite_bit_intersection_existsCD0015 · finite_bit_union_of_complementsCD0016 · finite_bit_union_existsCD001B · finite_bit_union_intersection_count_balanceCD0037 · finite_modular_dyson_lower_from_pullbackCD0038 · finite_modular_dyson_transform_exists