Theorems · Theorem · group theory
Associated.mul_mul
∀ {M : Type u_1} [inst : CommMonoid M] {a₁ a₂ b₁ b₂ : M},
Associated a₁ b₁ → Associated a₂ b₂ → Associated (a₁ * a₂) (b₁ * b₂)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- Associatedstatement and proof · cited by 296
- Associated.transproof · cited by 22
- Associated.mul_leftproof · cited by 10
- Associated.mul_rightproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11
- irreducible_iff_prime_of_existsUnique_irreducible_factorsproof · cited by 1
- UniqueFactorizationMonoid.factors_mulproof · cited by 1
- WfDvdMonoid.of_exists_prime_factorsproof · cited by 1
- exists_maximalIdeal_pow_eq_of_principalproof · cited by 1
- Associated.pow_powproof · cited by 1
- Associates.out_mul'proof · cited by 0