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
¬p = 1 ∧ (∀ x. ∀ y. p = x · y → x = 1 ∨ y = 1)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
~(p = 1) /\ forall a b. p = a * b -> a = 1 \/ b = 1The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.
Direct definition dependencies
none — first-order arithmetic only
Definitions depending on this notation
none
Checked theorems using this definition
CD0033 · prime_modular_additive_orbit_hitsCD0035 · prime_modular_set_translation_boundary_existsCD0041 · prime_modular_normalized_boundary_existsCD0042 · prime_cauchy_davenport_normalized_bounded_inductionCD0043 · prime_cauchy_davenport_normalized_cover_boundCD0046 · prime_cauchy_davenport_cover_boundCD0047 · prime_cauchy_davenport_sumset_boundCD0048 · prime_cauchy_davenport_sumset_exists