Theorems · Theorem · commutative algebra
normalize_eq_normalize_iff
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] [IsLeftCancelMulZero α] {x y : α},
normalize x = normalize y ↔ x ∣ y ∧ y ∣ x- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidWithZerostatement and proof · cited by 456
- Associatedproof · cited by 296
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement · cited by 137
- IsLeftCancelMulZerostatement and proof · cited by 48
- dvd_dvd_iff_associatedproof · cited by 5
- normalize_eq_normalize_iff_associatedproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_irreducibleproof · cited by 10
- UniqueFactorizationMonoid.prod_normalizedFactors_eqproof · cited by 1
- UniqueFactorizationMonoid.mem_normalizedFactors_eq_of_associatedproof · cited by 0