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. ∀ fms_j_secondwave. ∀ fms_s_secondwave. Lt(fms_i_secondwave,p) → Lt(fms_j_secondwave,p) → Lt(fms_s_secondwave,p) → BetaAt(b,c,fms_i_secondwave,1) → BetaAt(d,e,fms_j_secondwave,1) → ModEq(p,fms_i_secondwave + fms_j_secondwave,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_i_secondwave fms_j_secondwave fms_s_secondwave. (exists fms_gap_secondwave_i. fms_gap_secondwave_i + S (fms_i_secondwave) = (p)) -> (exists fms_gap_secondwave_j. fms_gap_secondwave_j + S (fms_j_secondwave) = (p)) -> (exists fms_gap_secondwave_s. fms_gap_secondwave_s + S (fms_s_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 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
Checked theorems using this definition
CD0031 · finite_modular_sumset_coverCD003D · finite_modular_dyson_sum_coverCD003F · finite_modular_zero_sum_left_subsetCD0040 · finite_modular_singleton_cover_boundCD0041 · prime_modular_normalized_boundary_existsCD0042 · prime_cauchy_davenport_normalized_bounded_inductionCD0043 · prime_cauchy_davenport_normalized_cover_boundCD0045 · finite_modular_opposite_translates_sum_coverCD0046 · prime_cauchy_davenport_cover_bound