Theorems · Theorem · group theory
eq_inv_smul_iff
∀ {G : Type u_3} {α : Type u_5} [inst : Group G] [inst_1 : MulAction G α] {g : G} {a b : α}, a = g⁻¹ • b ↔ g • a = b- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 12 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 by12
Results whose statement or proof uses this declaration.
- smul_eq_iff_eq_inv_smulproof · cited by 9
- eq_inv_smul_iff₀proof · cited by 5
- SubMulAction.IsPretransitive.isPretransitive_ofFixingSubgroup_interproof · cited by 2
- SubMulAction.ofStabilizer.conjMap_bijectiveproof · cited by 2
- SubMulAction.ofStabilizer.inv_conjMap_comp_applystatement · cited by 1
- MonoidAlgebra.mem_smulAntidiagonal_of_groupproof · cited by 1
- MulAction.IsPreprimitive.exists_mem_smul_and_notMem_smulproof · cited by 1
- Finset.pow_ssubset_pow_succ_of_pow_ne_closureproof · cited by 1
- continuousSMul_iff_stabilizer_isOpenproof · cited by 0
- ModularGroup.stabilizer_ρproof · cited by 0
- MulAction.stabilizerEquivStabilizer_symmstatement · cited by 0
- SubMulAction.ofStabilizer.conjMap_comp_inv_applystatement · cited by 0