Theorems · Theorem · group theory
AddSubgroup.smul_mem_pointwise_smul_iff
∀ {G : Type u_2} {A : Type u_4} [inst : Group G] [inst_1 : AddGroup A] [inst_2 : DistribMulAction G A]
{S : AddSubgroup A} {a : G} {x : A}, a • x ∈ a • S ↔ x ∈ S- Defined in
- Mathlib.Algebra.GroupWithZero.Subgroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- DistribMulActionstatement and proof · cited by 584
- AddSubgroup.pointwiseMulActionstatement · cited by 24
- Set.smul_mem_smul_set_iffproof · cited by 14
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