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
HL0023 · integer_polynomial_prime_power_hensel_lift_exists_uniqueHL0024 · integer_polynomial_prime_power_hensel_iterated_exists_uniqueHL0025 · hensel_prime_blended_nonzero_derivative_is_unitHL0026 · hensel_prime_signed_nonzero_derivative_is_unitHL0027 · hensel_prime_nonsingular_root_is_simpleHL0028 · integer_polynomial_prime_simple_root_lifts_all_positive_powers