Theorems · Theorem · group theory
Subgroup.smul_mem_pointwise_smul_iff
∀ {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}, a • x ∈ a • S ↔ x ∈ S- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
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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_mem_smul_set_iffproof · cited by 14
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