Theorems · Theorem · group theory
mul_inv_rev
∀ {G : Type u_1} [inst : DivisionMonoid G] (a b : G), (a * b)⁻¹ = b⁻¹ * a⁻¹- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 270 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 31 definitions · uses no axioms
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DivisionMonoidstatement and proof · cited by 201
- DivisionMonoid.mul_inv_revproof · cited by 1
Cited by270
Results whose statement or proof uses this declaration.
- inv_divproof · cited by 92
- div_divproof · cited by 56
- mul_invproof · cited by 50
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- div_mul_div_commproof · cited by 24
- zpow_add_oneproof · cited by 18
- div_div_eq_mul_divproof · cited by 12
- mul_div_mul_commproof · cited by 11
- div_mul_eq_div_divproof · cited by 9
- zpow_add_one₀proof · cited by 9
- div_mul_eq_div_div_swapproof · cited by 8
- taylorWithinEval_selfproof · cited by 7
Showing the 200 most cited of 270.