Theorems · Theorem · group theory
mul_dvd_mul
∀ {α : Type u_1} [inst : CommSemigroup α] {a b c d : α}, a ∣ b → c ∣ d → a * c ∣ b * d- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- CommSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- mul_left_commproof · cited by 184
- CommSemigroupstatement and proof · cited by 62
Cited by24
Results whose statement or proof uses this declaration.
- pow_dvd_pow_of_dvdproof · cited by 12
- mul_dvd_mul_rightproof · cited by 7
- multiplicity_mulproof · cited by 5
- Nat.coprime_of_squarefree_mulproof · cited by 4
- gcd_mul_dvd_mul_gcdproof · cited by 2
- Nat.totient_dvd_of_dvdproof · cited by 2
- Nat.totient_gcd_mul_totient_mulproof · cited by 2
- IsRelPrime.of_squarefree_mulproof · cited by 2
- divRadical_dvd_derivativeproof · cited by 1
- Multiset.prod_dvd_prod_of_dvdproof · cited by 1
- MvPolynomial.dvd_monomial_mul_iff_existsproof · cited by 1
- Subgroup.card_commutator_dvd_index_center_powproof · cited by 1