Theorems · Theorem · group theory
AddSubgroup.smul_mem_pointwise_smul
∀ {M : Type u_3} {A : Type u_4} [inst : Monoid M] [inst_1 : AddGroup A] [inst_2 : DistribMulAction M A] (m : A) (a : M)
(S : AddSubgroup A), m ∈ S → a • m ∈ a • S- Defined in
- Mathlib.Algebra.GroupWithZero.Subgroup
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, 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.
- AddGroupstatement and proof · cited by 4,410
- Monoidstatement and proof · cited by 3,887
- AddSubgroupstatement and proof · cited by 3,232
- DistribMulActionstatement and proof · cited by 584
- Set.smul_mem_smul_setproof · cited by 39
- AddSubgroup.pointwiseMulActionstatement · cited by 24
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