Theorems · Theorem · number theory
Nat.factors_multiset_prod_of_irreducible
∀ {s : Multiset ℕ}, (∀ x ∈ s, Irreducible x) → UniqueFactorizationMonoid.normalizedFactors s.prod = s- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement · cited by 2,804
- Multisetstatement and proof · cited by 2,627
- Multiset.prodstatement and proof · cited by 528
- Irreduciblestatement and proof · cited by 496
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- Multiset.Relproof · cited by 47
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- UniqueFactorizationMonoid.irreducible_of_normalized_factorproof · cited by 15
- UniqueFactorizationMonoid.factors_uniqueproof · cited by 14
- Multiset.prod_eq_zero_iffproof · cited by 7
- associated_eq_eqproof · cited by 6
- Multiset.rel_eqproof · cited by 6
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