Theorems · Theorem · group theory
Commute.div_div_div_comm
∀ {G : Type u_1} [inst : DivisionMonoid G] {a b c d : G},
Commute b c → Commute b⁻¹ d → Commute c⁻¹ d → a / b / (c / d) = a / c / (b / d)- Defined in
- Mathlib.Algebra.Group.Commute.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- DivisionMonoid
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Cites9
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
- inv_invproof · cited by 494
- 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
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