Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.factors_one
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α],
UniqueFactorizationMonoid.factors 1 = 0- Cited by
- 2 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.
- Multisetstatement · cited by 2,627
- Nontrivialproof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- one_ne_zeroproof · cited by 885
- Multiset.prodproof · cited by 528
- Associatedproof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
- UniqueFactorizationMonoid.factors_prodproof · cited by 18
- Multiset.notMem_zeroproof · cited by 17
- UniqueFactorizationMonoid.factors_uniqueproof · cited by 14
- UniqueFactorizationMonoid.irreducible_of_factorproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.moebius_oneproof · cited by 2
- UniqueFactorizationMonoid.factors_of_isUnitproof · cited by 1