Theorems · Theorem · commutative algebra
Associated.card_factors_eq
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a b : α},
Associated a b → (UniqueFactorizationMonoid.factors a).card = (UniqueFactorizationMonoid.factors b).card- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.cardstatement and proof · cited by 375
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associated.symmproof · cited by 87
- UniqueFactorizationMonoid.factorsstatement · cited by 55
- Associated.transproof · cited by 22
- UniqueFactorizationMonoid.factors_prodproof · cited by 18
- UniqueFactorizationMonoid.factors_uniqueproof · cited by 14
- UniqueFactorizationMonoid.irreducible_of_factorproof · cited by 13
- Multiset.card_eq_card_of_relproof · cited by 5
- UniqueFactorizationMonoid.factors_zeroproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Associated.moebius_eqproof · cited by 1