Theorems · Theorem · group theory
mul_inv_eq_iff_eq_mul
∀ {G : Type u_3} [inst : Group G] {a b c : G}, a * b⁻¹ = c ↔ a = c * b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 13 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_cancel_rightproof · cited by 70
- mul_inv_cancel_rightproof · cited by 53
Cited by13
Results whose statement or proof uses this declaration.
- isConj_iffproof · cited by 16
- div_eq_iff_eq_mulproof · cited by 7
- Subgroup.upperCentralSeries_oneproof · cited by 7
- oneLePart_div_leOnePartproof · cited by 6
- commutatorElement_eq_one_iff_mul_commproof · cited by 3
- Equiv.Perm.isConj_of_support_equivproof · cited by 2
- card_comm_eq_card_conjClasses_mul_cardproof · cited by 2
- Subgroup.centralizer_eq_comap_stabilizerproof · cited by 1
- Set.inv_mem_centralizerproof · cited by 1
- Unitary.mul_inv_mem_iffproof · cited by 1
- ConjClasses.mk_bijOnproof · cited by 1
- Subgroup.mem_centralizer_iff_commutator_eq_one'proof · cited by 0