Theorems · Theorem · group theory
inv_smul_eq_iff
∀ {G : Type u_3} {α : Type u_5} [inst : Group G] [inst_1 : MulAction G α] {g : G} {a b : α}, g⁻¹ • a = b ↔ a = g • b- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- MulActionstatement and proof · cited by 1,294
- inv_smul_smulproof · cited by 76
- smul_inv_smulproof · cited by 53
Cited by16
Results whose statement or proof uses this declaration.
- inv_smul_eq_iff₀proof · cited by 7
- MulAction.fixedBy_invproof · cited by 4
- span_eq_top_of_isLocalizedModuleproof · cited by 3
- invOf_smul_eq_iffproof · cited by 3
- Subgroup.smul_diff'proof · cited by 2
- IsGaloisGroup.smul_mem_of_normalproof · cited by 2
- MulAction.zpow_smul_eq_iff_period_dvdproof · cited by 2
- Monoid.CoprodI.Word.equivPair_tail_eq_inv_smulproof · cited by 2
- SubMulAction.fixingSubgroup_map_conj_eqproof · cited by 1
- Set.conj_mem_fixingSubgroupproof · cited by 1
- SubMulAction.conjMap_ofFixingSubgroup_bijectiveproof · cited by 1
- smul_mem_fixedPoints_of_normalproof · cited by 0