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
∃ k. n = d · kOnly definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists k. n = d * kThe 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
Checked theorems using this definition
HL0007 · hensel_lift_correction_of_rootHL0008 · hensel_canonical_horner_lift_exists_uniqueHL000A · beta_horner_simple_root_hensel_lift_exists_uniqueHL000C · beta_horner_root_mod_weakenHL000F · hensel_positive_power_factorHL0010 · beta_horner_prime_power_hensel_lift_exists_uniqueHL0013 · beta_horner_prime_power_iterated_lifts_exists_uniqueHL0018 · hensel_signed_blend_mod_iffHL0019 · hensel_signed_blend_zero_iffHL001A · hensel_signed_blend_unit_coprimeHL001B · beta_signed_horner_blend_root_equivalenceHL0021 · beta_signed_horner_prime_power_hensel_lift_exists_uniqueHL0022 · beta_signed_horner_prime_power_iterated_lifts_exists_unique