Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.factors_of_isUnit
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {x : α},
IsUnit x → UniqueFactorizationMonoid.factors x = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedproof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
- Multiset.Relproof · cited by 47
- associated_one_iff_isUnitproof · cited by 14
- UniqueFactorizationMonoid.factors_oneproof · cited by 2
- UniqueFactorizationMonoid.factors_rel_of_associatedproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.factors_eq_zeroproof · cited by 1