Theorems · Theorem · group theory
Commute.div_mul_div_comm
∀ {G : Type u_1} [inst : DivisionMonoid G] {a b c d : G},
Commute b d → Commute b⁻¹ c → a / b * (c / d) = a * c / (b * d)- Defined in
- Mathlib.Algebra.Group.Commute.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- div_eq_mul_invproof · cited by 715
- Commutestatement and proof · cited by 639
- mul_inv_revproof · cited by 270
- DivisionMonoidstatement and proof · cited by 201
- Commute.eqproof · cited by 91
- Commute.symmproof · cited by 79
- Commute.mul_mul_mul_commproof · cited by 8
- Commute.inv_invproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Rat.cast_mul_of_ne_zeroproof · cited by 1
- NNRat.cast_mul_of_ne_zeroproof · cited by 1
- NNRat.cast_div_of_ne_zeroproof · cited by 0
- Rat.cast_div_of_ne_zeroproof · cited by 0
- Commute.mul_div_mul_commproof · cited by 0