Theorems · Theorem · group theory
eq_mul_inv_iff_mul_eq
∀ {G : Type u_3} [inst : Group G] {a b c : G}, a = b * c⁻¹ ↔ a * c = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 11 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 by11
Results whose statement or proof uses this declaration.
- eq_div_iff_mul_eq'proof · cited by 6
- Finset.prod_Ico_eq_mul_invproof · cited by 1
- Sylow.conj_eq_normalizer_conj_of_mem_centralizerproof · cited by 1
- DoubleCoset.mem_doubleCoset_of_not_disjointproof · cited by 1
- Rep.indToCoindAux_snd_mul_invproof · cited by 1
- SkewMonoidAlgebra.coeff_mul_singleproof · cited by 1
- ProfiniteGrp.closedSubgroup_eq_sInf_openproof · cited by 0
- GroupExtension.Section.exists_mul_eq_mul_mul_inlproof · cited by 0
- ConjAct.stabilizer_eq_centralizerproof · cited by 0
- Rack.ad_conjproof · cited by 0
- GroupExtension.Section.exists_mul_eq_inl_mul_mulproof · cited by 0