Theorems · Theorem · group theory
Associated.trans
∀ {M : Type u_1} [inst : Monoid M] {x y z : M}, Associated x y → Associated y z → Associated x z- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- Associatedstatement and proof · cited by 296
- Units.val_mulproof · cited by 22
Cited by22
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11
- Associated.mul_mulproof · cited by 7
- dvd_prime_powproof · cited by 6
- Finset.gcd_mul_left'proof · cited by 5
- normalize_eq_normalize_iff_associatedproof · cited by 5
- Polynomial.associated_content_C_mulproof · cited by 4
- associated_mul_isUnit_left_iffproof · cited by 4
- exists_associated_pow_of_mul_eq_powproof · cited by 3
- UniqueFactorizationMonoid.factors_rel_of_associatedproof · cited by 2
- UniqueFactorizationMonoid.factors_mulproof · cited by 1