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_s_secondwave. Lt(fms_s_secondwave,p) → (BetaAt(u,v,fms_s_secondwave,1) → ∃ x. ∃ y. ModularSetMember(b,c,p,x) ∧ (ModularSetMember(d,e,p,y) ∧ ModEq(p,x + y,fms_s_secondwave))) ∧ ((∃ x. ∃ y. ModularSetMember(b,c,p,x) ∧ (ModularSetMember(d,e,p,y) ∧ ModEq(p,x + y,fms_s_secondwave))) → BetaAt(u,v,fms_s_secondwave,1))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall fms_s_secondwave. (exists fms_gap_secondwave_s. fms_gap_secondwave_s + S (fms_s_secondwave) = (p)) -> ((((((exists fs_h_fms_secondwave_result. fs_h_fms_secondwave_result + S (1) = S ((S (fms_s_secondwave)) * v)) /\ exists fs_q_fms_secondwave_result. u = fs_q_fms_secondwave_result * S ((S (fms_s_secondwave)) * v) + (1))) -> (exists fms_i_secondwave fms_j_secondwave. ((((exists fms_gap_secondwave_left. fms_gap_secondwave_left + S (fms_i_secondwave) = (p)) /\ (((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 fms_gap_secondwave_right. fms_gap_secondwave_right + S (fms_j_secondwave) = (p)) /\ (((exists fs_h_fms_secondwave_right. fs_h_fms_secondwave_right + S (1) = S ((S (fms_j_secondwave)) * e)) /\ exists fs_q_fms_secondwave_right. d = fs_q_fms_secondwave_right * S ((S (fms_j_secondwave)) * e) + (1))))) /\ (exists fms_u_secondwave fms_v_secondwave. (fms_i_secondwave + fms_j_secondwave) + (p) * fms_u_secondwave = (fms_s_secondwave) + (p) * fms_v_secondwave))))) /\ ((exists fms_i_secondwave fms_j_secondwave. ((((exists fms_gap_secondwave_left. fms_gap_secondwave_left + S (fms_i_secondwave) = (p)) /\ (((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 fms_gap_secondwave_right. fms_gap_secondwave_right + S (fms_j_secondwave) = (p)) /\ (((exists fs_h_fms_secondwave_right. fs_h_fms_secondwave_right + S (1) = S ((S (fms_j_secondwave)) * e)) /\ exists fs_q_fms_secondwave_right. d = fs_q_fms_secondwave_right * S ((S (fms_j_secondwave)) * e) + (1))))) /\ (exists fms_u_secondwave fms_v_secondwave. (fms_i_secondwave + fms_j_secondwave) + (p) * fms_u_secondwave = (fms_s_secondwave) + (p) * fms_v_secondwave)))) -> (((exists fs_h_fms_secondwave_result. fs_h_fms_secondwave_result + S (1) = S ((S (fms_s_secondwave)) * v)) /\ exists fs_q_fms_secondwave_result. u = fs_q_fms_secondwave_result * S ((S (fms_s_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