Theorems · Theorem · group theory
inv_mul_eq_div
∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b : α), a⁻¹ * b = b / a- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- DivisionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- div_eq_mul_invproof · cited by 715
- DivisionCommMonoidstatement and proof · cited by 80
Cited by26
Results whose statement or proof uses this declaration.
- PeriodPair.ω₁_div_two_notMem_latticeproof · cited by 10
- EuclideanGeometry.Sphere.isDiameter_ofDiameterproof · cited by 3
- Manifold.exists_lt_locally_constant_of_riemannianEDist_ltproof · cited by 3
- Real.Angle.tan_eq_inv_of_two_nsmul_add_two_nsmul_eq_piproof · cited by 1
- Behrend.dValue_posproof · cited by 1
- tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_supportproof · cited by 1
- tendsto_integral_mul_one_add_inv_smul_sq_powproof · cited by 1
- NormedSpace.closedBall_inv_subset_polar_closedBallproof · cited by 1
- Behrend.roth_lower_bound_explicitproof · cited by 1
- ContinuousLinearMap.opNorm_le_of_re_inner_leproof · cited by 1
- PeriodPair.ω₂_div_two_notMem_latticeproof · cited by 1
- ContinuousLinearMap.antilipschitz_of_forall_le_inner_mapproof · cited by 1