Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.card_factors_of_irreducible
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a : α},
Irreducible a → (UniqueFactorizationMonoid.factors a).card = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetproof · cited by 2,627
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodproof · cited by 528
- Irreduciblestatement and proof · cited by 496
- Multiset.cardstatement and proof · cited by 375
- Multiset.consproof · cited by 313
- Associatedproof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Multiset.prod_consproof · cited by 68
- UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
- Irreducible.ne_zeroproof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.factors_eq_singleton_of_irreducibleproof · cited by 0
- Irreducible.moebius_eqproof · cited by 0