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Theorems · Theorem · group theory

AddSubmonoid.mem_map_of_mem

∀ {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 : F) {S : AddSubmonoid M} {x : M},
  x ∈ S → f x ∈ AddSubmonoid.map f S
Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
3 results in Mathlib
Foundations
Depth 15 from the axioms · uses no axioms
Assumes
AddZeroClassAddZeroClassFunLikeAddMonoidHomClass
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Around this declaration

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

AddSubmonoid.apply_coe_mem_map · cited by 2AddSubmonoid.apply_coe_me…AddSubmonoid.pi_le_iff · cited by 2AddSubmonoid.pi_le_iffAddSubmonoid.iSup_map_single · cited by 1AddSubmonoid.iSup_map_sin…DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidSet.mem_image_of_mem · cited by 371Set.mem_image_of_memAddMonoidHomClass · cited by 252AddMonoidHomClassAddSubmonoid.map · cited by 99AddSubmonoid.mapAddSubmonoid.mem_map_of_memCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.