equivMapOfInjective — Mathlib

English

Same as above: the range of f is the image of the top subsemiring under f.

Русский

То же самое: образ f равен образу верхнего подполусемиринга по f.

LaTeX

$$$ srange f = (\top : NonUnitalSubsemiring R).map f $$$

Lean4

/-- A non-unital subsemiring is isomorphic to its image under an injective function -/
noncomputable def equivMapOfInjective (f : F) (hf : Function.Injective (f : R → S)) : s ≃+* s.map f :=
  { Equiv.Set.image f s hf with
    map_mul' := fun _ _ => Subtype.ext (map_mul f _ _)
    map_add' := fun _ _ => Subtype.ext (map_add f _ _) }

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