Theorems · Theorem · number theory
Nat.Prime.dvd_iff_one_le_factorization
∀ {p n : ℕ}, Nat.Prime p → n ≠ 0 → (p ∣ n ↔ 1 ≤ n.factorization p)- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsuppstatement · cited by 5,255
- Nat.Primestatement and proof · cited by 2,059
- pow_oneproof · cited by 894
- Nat.factorizationstatement · cited by 215
- Nat.Prime.pow_dvd_iff_le_factorizationproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Nat.not_dvd_ordComplproof · cited by 4
- Nat.factorization_eq_one_of_squarefreeproof · cited by 0
- Nat.Squarefree.ext_iffproof · cited by 0