Theorems · Theorem · group theory
mul_inv_cancel_comm
∀ {G : Type u_1} [inst : CommGroup G] (a b : G), a * b * a⁻¹ = b- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- CommGroup
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
- CommGroupstatement and proof · cited by 990
- inv_mul_cancel_leftproof · cited by 88
Cited by13
Results whose statement or proof uses this declaration.
- inf_mul_supproof · cited by 3
- HasProd.hasProd_compl_iffproof · cited by 3
- CategoryTheory.isCommMonObj_iff_commutator_eq_toUnit_ηproof · cited by 2
- MeasureTheory.StronglyMeasurable.mul_iff_rightproof · cited by 1
- CoxeterSystem.IsReflection.length_mul_left_neproof · cited by 1
- Measurable.mul_iff_rightproof · cited by 1
- MeasureTheory.AEStronglyMeasurable.mul_iff_rightproof · cited by 1
- AEMeasurable.mul_iff_rightproof · cited by 1
- IsTopologicalGroup.of_comm_of_nhds_oneproof · cited by 0
- CategoryTheory.GrpObj.conj_eq_snd_of_isCommMonObjproof · cited by 0
- CommGroup.normalizer_eq_topproof · cited by 0
- CoxeterSystem.IsReflection.length_mul_right_neproof · cited by 0