Theorems · Theorem · group theory
Subgroup.mem_pointwise_smul_iff_inv_smul_mem
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : Group α] [inst_2 : MulDistribMulAction α G] {a : α}
{S : Subgroup G} {x : G}, x ∈ a • S ↔ a⁻¹ • x ∈ S- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Subgroupstatement and proof · cited by 3,593
- MulDistribMulActionstatement and proof · cited by 120
- Subgroup.pointwiseMulActionstatement · cited by 66
- Set.mem_smul_set_iff_inv_smul_memproof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.Normal.of_conjugate_fixedproof · cited by 0
- IsCusp.smul_of_memproof · cited by 0
- Matrix.SpecialLinearGroup.lineStab_smulproof · cited by 0