Theorems · Theorem · number theory
Nat.eq_factorization_iff
∀ {n : ℕ} {f : ℕ →₀ ℕ},
n ≠ 0 → (∀ p ∈ f.support, Nat.Prime p) → (f = n.factorization ↔ (f.prod fun x1 x2 => x1 ^ x2) = n)- Defined in
- Mathlib.Data.Nat.Factorization.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Finsuppstatement and proof · cited by 5,255
- Nat.Primestatement and proof · cited by 2,059
- Finsupp.supportstatement and proof · cited by 828
- Finsupp.prodstatement and proof · cited by 231
- Nat.factorizationstatement and proof · cited by 215
- Nat.prod_factorization_pow_eq_selfproof · cited by 22
- Nat.prod_pow_factorization_eq_selfproof · cited by 4
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