Theorems · Theorem · group theory
div_mul_div_comm
∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b c d : α), a / b * (c / d) = a * c / (b * d)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- DivisionCommMonoid
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.
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- div_eq_mul_invproof · cited by 715
- mul_inv_revproof · cited by 270
- mul_left_commproof · cited by 184
- DivisionCommMonoidstatement and proof · cited by 80
Cited by24
Results whose statement or proof uses this declaration.
- EuclideanGeometry.inversion_inversionproof · cited by 5
- NNReal.inner_le_Lp_mul_Lqproof · cited by 5
- RatFunc.denom_dvdproof · cited by 3
- RatFunc.num_denom_mulproof · cited by 2
- RatFunc.num_dvdproof · cited by 2
- mabs_div_sup_mul_mabs_div_infproof · cited by 2
- ENNReal.lintegral_Lp_mul_le_Lq_mul_Lrproof · cited by 2
- Real.summable_pow_div_factorialproof · cited by 1
- HurwitzZeta.jacobiTheta₂'_functional_equation'proof · cited by 1
- Complex.GammaSeq_add_one_leftproof · cited by 1
- RatFunc.denom_mul_dvdproof · cited by 1
- Complex.GammaSeq_mulproof · cited by 1