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
ModularSetMember(b,c,p,a) ∧ (Lt(r,p) ∧ (ModEq(p,a + d,r) ∧ ¬BetaAt(b,c,r,1)))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
(((exists fms_gap_cd_secondwave_source. fms_gap_cd_secondwave_source + S (a) = (p)) /\ (((exists fs_h_fms_cd_secondwave_source. fs_h_fms_cd_secondwave_source + S (1) = S ((S (a)) * c)) /\ exists fs_q_fms_cd_secondwave_source. b = fs_q_fms_cd_secondwave_source * S ((S (a)) * c) + (1))))) /\ ((exists fms_gap_cd_secondwave_target. fms_gap_cd_secondwave_target + S (r) = (p)) /\ ((exists fms_u_cd_secondwave_shift fms_v_cd_secondwave_shift. (a+d) + (p) * fms_u_cd_secondwave_shift = (r) + (p) * fms_v_cd_secondwave_shift) /\ ~(((exists fs_h_cd_secondwave_outside. fs_h_cd_secondwave_outside + S (1) = S ((S (r)) * c)) /\ exists fs_q_cd_secondwave_outside. b = fs_q_cd_secondwave_outside * S ((S (r)) * c) + (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
CD0034 · finite_modular_orbit_member_or_boundaryCD0035 · prime_modular_set_translation_boundary_existsCD003C · finite_modular_dyson_lower_boundary_nonmemberCD003E · finite_modular_dyson_strict_sizesCD0041 · prime_modular_normalized_boundary_existsCD0042 · prime_cauchy_davenport_normalized_bounded_induction