Theorems · Theorem · number theory
Nat.ordProj_dvd_ordProj_iff_dvd
∀ {a b : ℕ}, a ≠ 0 → b ≠ 0 → ((∀ (p : ℕ), p ^ a.factorization p ∣ p ^ b.factorization p) ↔ a ∣ b)- Defined in
- Mathlib.Data.Nat.Factorization.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsuppstatement · cited by 5,255
- zero_addproof · cited by 2,366
- pow_zeroproof · cited by 1,094
- Nat.factorizationstatement and proof · cited by 215
- Nat.factorization_le_iff_dvdproof · cited by 18
- Nat.factorization_zero_rightproof · cited by 7
- Finsupp.le_defproof · cited by 3
- Nat.factorization_one_rightproof · cited by 1
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