Theorems · Theorem · group theory
Associated.symm
∀ {M : Type u_1} [inst : Monoid M] {x y : M}, Associated x y → Associated y x- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 87 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- Associatedstatement and proof · cited by 296
- Units.mul_invproof · cited by 67
Cited by87
Results whose statement or proof uses this declaration.
- associated_one_iff_isUnitproof · cited by 14
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11
- Associated.irreducibleproof · cited by 10
- UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvdproof · cited by 8
- Associated.commproof · cited by 7
- Associated.dvd'proof · cited by 7
- normalize_associatedproof · cited by 7
- Polynomial.associated_content_mulproof · cited by 6
- Irreducible.associated_of_dvdproof · cited by 6
- IsDiscreteValuationRing.eq_unit_mul_pow_irreducibleproof · cited by 6
- Associated.of_mul_leftproof · cited by 6
- normalize_eq_normalize_iff_associatedproof · cited by 5