Mathlib Map

Theorems · Definition · group theory

AddSubmonoid.map

{M : Type u_1} →
  {N : Type u_2} →
    [inst : AddZeroClass M] →
      [inst_1 : AddZeroClass N] →
        {F : Type u_4} → [inst_2 : FunLike F M N] → [mc : AddMonoidHomClass F M N] → F → AddSubmonoid M → AddSubmonoid N

The image of an AddSubmonoid along an AddMonoidHom is an AddSubmonoid.

Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
99 results in Mathlib
Foundations
Depth 14 from the axioms, rests on 61 definitions · uses no axioms
Assumes
AddZeroClassAddZeroClassFunLikeAddMonoidHomClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Submodule.map · cited by 614Submodule.mapAddSubgroup.map · cited by 189AddSubgroup.mapAddMonoidHom.mrange · cited by 61AddMonoidHom.mrangeAddSubgroup.ofAddUnits · cited by 30AddSubgroup.ofAddUnitsSubsemiring.map · cited by 29Subsemiring.mapNonUnitalSubsemiring.map · cited by 22NonUnitalSubsemiring.mapAddSubmonoid.mul · cited by 18AddSubmonoid.mulAddSubmonoid.gc_map_comap · cited by 16AddSubmonoid.gc_map_comapAddMonoidHom.mrange_eq_map · cited by 15AddMonoidHom.mrange_eq_mapAddMonoidHom.map_mclosure · cited by 12AddMonoidHom.map_mclosureAddSubmonoid.smul · cited by 11AddSubmonoid.smulAddSubmonoid.gciMapComap · cited by 9AddSubmonoid.gciMapComapAddSubmonoid.giMapComap · cited by 9AddSubmonoid.giMapComapAddSubmonoid.smul_le · cited by 8AddSubmonoid.smul_leAddSubmonoid.smul_mem_smul · cited by 8AddSubmonoid.smul_mem_smulDFunLike.coe · cited by 62936DFunLike.coeSetLike.coe · cited by 8199SetLike.coeSet.image · cited by 5609Set.imageFunLike · cited by 2560FunLikeAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddMonoidHomClass · cited by 252AddMonoidHomClassAddSubmonoid.mapCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by118

Results whose statement or proof uses this declaration.