Theorems · Theorem · number theory
Nat.prime_def_minFac
∀ {p : ℕ}, Nat.Prime p ↔ 2 ≤ p ∧ p.minFac = p- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement and proof · cited by 2,059
- ne_of_gtproof · cited by 637
- Nat.Prime.one_ltproof · cited by 118
- Nat.minFacstatement and proof · cited by 72
- Nat.Prime.two_leproof · cited by 53
- Nat.minFac_primeproof · cited by 31
- Nat.dvd_primeproof · cited by 18
- Nat.minFac_has_propproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Nat.primeFactorsList_primeproof · cited by 5
- Nat.Prime.minFac_eqproof · cited by 4
- Nat.not_prime_iff_minFac_ltproof · cited by 2
- Nat.decidablePrime'proof · cited by 1
- Nat.minFac_le_divproof · cited by 1