Theorems · Theorem · group theory
inv_mul_eq_one
∀ {G : Type u_3} [inst : Group G] {a b : G}, a⁻¹ * b = 1 ↔ a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- inv_injproof · cited by 25
- mul_eq_one_iff_eq_invproof · cited by 12
Cited by11
Results whose statement or proof uses this declaration.
- MonoidHom.ker_eq_bot_iffproof · cited by 16
- Subgroup.mul_injective_of_disjointproof · cited by 2
- MeasureTheory.Measure.pairwise_aedisjoint_of_aedisjoint_forall_ne_oneproof · cited by 2
- Monoid.PushoutI.NormalWord.ext_smulproof · cited by 1
- FixedPoints.toAlgAut_surjectiveproof · cited by 1
- MonoidHom.FixedPointFree.commutatorMap_injectiveproof · cited by 1
- cauchy_davenport_minOrder_mulproof · cited by 1
- isCancelSMul_iff_eq_one_of_smul_eqproof · cited by 1
- MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eqproof · cited by 0
- Subgroup.IsComplement.coe_equiv_snd_eq_one_iff_memproof · cited by 0
- NonarchimedeanGroup.exists_openSubgroup_separatingproof · cited by 0