Theorems · Theorem · group theory
Associated.of_mul_left
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {a b c d : M},
Associated (a * b) (c * d) → Associated a c → a ≠ 0 → Associated b d- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- mul_commproof · cited by 2,262
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- mul_left_commproof · cited by 184
- IsCancelMulZerostatement and proof · cited by 177
- Associated.symmproof · cited by 87
- mul_left_cancel₀proof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- isUnit_gcd_of_eq_mul_gcdproof · cited by 3
- prime_factors_uniqueproof · cited by 3
- Polynomial.associated_primPart_mulproof · cited by 2
- Multiset.extract_gcd'proof · cited by 1
- Finset.extract_gcd'proof · cited by 1
- Associated.of_mul_rightproof · cited by 0