Theorems · Theorem · group theory
mul_inv_eq_one
∀ {G : Type u_3} [inst : Group G] {a b : G}, a * b⁻¹ = 1 ↔ a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 20 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_invproof · cited by 494
- mul_eq_one_iff_eq_invproof · cited by 12
Cited by20
Results whose statement or proof uses this declaration.
- injective_iff_map_eq_oneproof · cited by 9
- Subgroup.upperCentralSeries_oneproof · cited by 7
- zpow_eq_zpow_iff_modEqproof · cited by 5
- Subgroup.lowerCentralSeries_succ_eq_botproof · cited by 3
- commutatorElement_eq_one_iff_mul_commproof · cited by 3
- Subgroup.disjoint_iff_mul_eq_oneproof · cited by 2
- Subgroup.mul_injective_of_disjointproof · cited by 2
- AddChar.wInner_cWeight_eq_booleproof · cited by 2
- MonoidHom.liftOfRightInverseAux_comp_applyproof · cited by 1
- Subgroup.IsComplement.coe_equiv_fst_eq_one_iff_memproof · cited by 1
- conj_eq_one_iffproof · cited by 1
- NumberField.IsCMField.unitsMulComplexConjInv_kerproof · cited by 1