Theorems · Theorem · group theory
eq_inv_mul_iff_mul_eq
∀ {G : Type u_3} [inst : Group G] {a b c : G}, a = b⁻¹ * c ↔ b * a = c- 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_leftproof · cited by 88
- mul_inv_cancel_leftproof · cited by 86
Cited by11
Results whose statement or proof uses this declaration.
- MonoidWithZeroHom.ValueGroup₀.zero_or_exists_mkproof · cited by 3
- SkewMonoidAlgebra.coeff_single_mulproof · cited by 1
- Sylow.conj_eq_normalizer_conj_of_mem_centralizerproof · cited by 1
- Set.inv_mem_centralizerproof · cited by 1
- DoubleCoset.mem_doubleCoset_of_not_disjointproof · cited by 1
- MonoidHom.FixedPointFree.commutatorMap_injectiveproof · cited by 1
- GroupExtension.Section.exists_mul_eq_mul_mul_inlproof · cited by 0
- krullTopology_t2proof · cited by 0
- SimpleGraph.mulCayley_adjproof · cited by 0
- max_inv_oneproof · cited by 0
- GroupExtension.Section.exists_mul_eq_inl_mul_mulproof · cited by 0