Theorems · Definition · group theory

AddSubgroupClass.inclusion

{G : Type u_1} →
  [inst : AddGroup G] →
    {S : Type u_4} →
      [inst_1 : SetLike S G] →
        [inst_2 : AddSubgroupClass S G] → [inst_3 : LE S] → [IsConcreteLE S G] → {H K : S} → H ≤ K → ↥H →+ ↥K

The inclusion homomorphism from an additive subgroup H contained in K to K.

Defined in: Mathlib.Algebra.Group.Subgroup.Defs
Cited by: 5 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Quot.sound
Assumes: AddGroup SetLike AddSubgroupClass LE IsConcreteLE

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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
AddMonoidHomstatement · cited by 3,230
SetLikestatement and proof · cited by 1,084
AddSubgroupClassstatement and proof · cited by 240
IsConcreteLEstatement and proof · cited by 28
AddMonoidHom.mk'proof · cited by 25

Cited by5

Results whose statement or proof uses this declaration.

AddSubgroupClass.inclusion_mkstatement · cited by 0
AddSubgroupClass.inclusion_rightstatement and proof · cited by 0
AddSubgroupClass.inclusion_selfstatement and proof · cited by 0
AddSubgroupClass.subtype_comp_inclusionstatement · cited by 0
AddSubgroupClass.coe_inclusionstatement · cited by 0