codRestrict — Mathlib

English

The codomain restriction map from a range is surjective onto the target type: every element of the codomain is attained by restricting the range.

Русский

Отображение ограничения кодом диапазона достигает каждое значение целевой области.

LaTeX

$$$((\\operatorname{range} f).\\codRestrict f (mem\\_range\\_self)).Surjective$$$

Lean4

/-- Restrict codomain of a function `f` to a set `s`. Same as `Subtype.coind` but this version
has codomain `↥s` instead of `Subtype s`. -/
def codRestrict (f : ι → α) (s : Set α) (h : ∀ x, f x ∈ s) : ι → s := fun x => ⟨f x, h x⟩

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