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Theorems · Theorem · group theory

AddSubsemigroup.mem_map_of_mem

∀ {M : Type u_1} {N : Type u_2} [inst : Add M] [inst_1 : Add N] (f : M →ₙ+ N) {S : AddSubsemigroup M} {x : M},
  x ∈ S → f x ∈ AddSubsemigroup.map f S
Defined in
Mathlib.Algebra.Group.Subsemigroup.Operations
Cited by
1 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
AddAdd
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Around this declaration

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AddSubsemigroup.apply_coe_mem_map · cited by 0AddSubsemigroup.apply_coe…DFunLike.coe · cited by 62936DFunLike.coeSet.mem_image_of_mem · cited by 371Set.mem_image_of_memAddHom · cited by 294AddHomAddSubsemigroup · cited by 262AddSubsemigroupAddSubsemigroup.map · cited by 50AddSubsemigroup.mapAddSubsemigroup.mem_map_of_memCITED BYCITES

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