Theorems · Theorem · group theory
mul_eq_one_iff_eq_inv
∀ {G : Type u_3} [inst : Group G] {a b : G}, a * b = 1 ↔ a = b⁻¹- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 12 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_mul_cancelproof · cited by 107
- eq_inv_of_mul_eq_one_leftproof · cited by 15
Cited by12
Results whose statement or proof uses this declaration.
- mul_inv_eq_oneproof · cited by 20
- inv_mul_eq_oneproof · cited by 11
- eq_inv_iff_mul_eq_oneproof · cited by 5
- mul_eq_one_iff_inv_eqproof · cited by 4
- self_eq_invproof · cited by 2
- RootPairing.reflectionPerm_invproof · cited by 1
- groupCohomology.map_inv_of_isMulCocycle₁proof · cited by 0
- IsKleinFour.mul_selfproof · cited by 0
- RootPairing.reflection_sqproof · cited by 0
- mul_eq_one_iff_inv_eq'proof · cited by 0
- Subgroup.commute_of_normal_of_disjointproof · cited by 0
- RootPairing.coreflection_sqproof · cited by 0