Theorems · Theorem · group theory
mul_div_mul_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
- 11 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 by11
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addModularCharacterFun_eq_addHaarScalarFactorproof · cited by 3
- MeasureTheory.Measure.modularCharacterFun_eq_haarScalarFactorproof · cited by 3
- Multiset.prod_map_divproof · cited by 2
- Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_powproof · cited by 2
- fermatLastTheoremWith_nat_int_rat_tfaeproof · cited by 2
- IsFractionRing.associated_den_num_invproof · cited by 1
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1
- gaugeRescale_smulproof · cited by 1
- FractionalIdeal.dual_div_dualproof · cited by 0
- Set.smul_div_smul_commproof · cited by 0