Theorems · Theorem · commutative algebra
normalize_eq_normalize_iff_associated
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] {a b : α},
normalize a = normalize b ↔ Associated a b- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Nontrivialproof · cited by 2,416
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- MonoidWithZerostatement and proof · cited by 456
- Associatedstatement and proof · cited by 296
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement and proof · cited by 137
- Associated.symmproof · cited by 87
- NormalizationMonoid.normUnitproof · cited by 33
- by_casesproof · cited by 31
Cited by5
Results whose statement or proof uses this declaration.
- normalize_eq_normalizeproof · cited by 5
- Associated.eq_of_normalizedproof · cited by 5
- UniqueFactorizationMonoid.mem_normalizedFactors_iff'proof · cited by 3
- normalize_eq_normalize_iffproof · cited by 3
- Polynomial.content_monomialproof · cited by 0