Theorems · Theorem · group theory
Subgroup.pointwise_smul_subset_iff
∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : Group α] [inst_2 : MulDistribMulAction α G] {a : α}
{S T : Subgroup G}, a • S ≤ T ↔ S ≤ a⁻¹ • T- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 1 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.smul_set_subset_iff_subset_inv_smul_setproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- CongruenceSubgroup.IsCongruenceSubgroup.conjGLproof · cited by 0