Theorems · Theorem · group theory
AddSubgroup.pointwise_smul_def
∀ {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 = AddSubgroup.map ((DistribMulAction.toAddMonoidEnd M A) a) S- Defined in
- Mathlib.Algebra.GroupWithZero.Subgroup
- 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- Monoidstatement and proof · cited by 3,887
- MonoidHomstatement · cited by 3,629
- AddSubgroupstatement and proof · cited by 3,232
- DistribMulActionstatement and proof · cited by 584
- AddSubgroup.mapstatement · cited by 189
- AddMonoid.Endstatement · cited by 64
- AddSubgroup.pointwiseMulActionstatement · cited by 24
- DistribMulAction.toAddMonoidEndstatement · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.relIndex_pointwise_smulproof · cited by 0