Theorems · Theorem · group theory

AddMonoidHom.injective_codRestrict

∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {S : Type u_5} [inst_2 : SetLike S N]
  [inst_3 : AddSubmonoidClass S N] (f : M →+ N) (s : S) (h : ∀ (x : M), f x ∈ s),
  Function.Injective ⇑(f.codRestrict s h) ↔ Function.Injective ⇑f

Defined in: Mathlib.Algebra.Group.Submonoid.Operations
Cited by: 0 results in Mathlib
Foundations: Depth 14 from the axioms · uses no axioms
Assumes: AddZeroClass AddZeroClass SetLike AddSubmonoidClass

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DFunLike.coestatement and proof · cited by 62,936
AddMonoidHomstatement and proof · cited by 3,230
AddZeroClassstatement and proof · cited by 1,237
SetLikestatement and proof · cited by 1,084
AddSubmonoidClassstatement and proof · cited by 346
AddMonoidHom.codRestrictstatement and proof · cited by 5

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