Theorems · Theorem · group theory
AddSubgroup.pointwise_smul_toAddSubmonoid
∀ {M : Type u_3} {A : Type u_4} [inst : Monoid M] [inst_1 : AddGroup A] [inst_2 : DistribMulAction M A] (a : M)
(S : AddSubgroup A), (a • S).toAddSubmonoid = a • S.toAddSubmonoid- Defined in
- Mathlib.Algebra.GroupWithZero.Subgroup
- Cited by
- 0 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.
Cites8
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
- AddSubmonoidstatement · cited by 1,178
- DistribMulActionstatement and proof · cited by 584
- AddSubgroup.toAddSubmonoidstatement · cited by 91
- AddSubgroup.pointwiseMulActionstatement · cited by 24
- AddSubmonoid.pointwiseMulActionstatement · cited by 23
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.