presieveOfCoveringAux — Mathlib

English

A dependent pair (V, f) belonging to presieveOfCovering U f corresponds to an index i with V = U_i.

Русский

Значение пары (V, f) в presieveOfCovering U соответствует индексу i с V = U_i.

LaTeX

$$$\\text{homOfIndex}(i) = (U_i,\\; i,\\; \\text{proof})$ and $f$ matches.$$

Lean4

/-- Given a family of opens `U : ι → Opens X` and any open `Y : Opens X`, we obtain a presieve
on `Y` by declaring that a morphism `f : V ⟶ Y` is a member of the presieve if and only if
there exists an index `i : ι` such that `V = U i`.
-/
def presieveOfCoveringAux {ι : Type v} (U : ι → Opens X) (Y : Opens X) : Presieve Y := fun V _ => ∃ i, V = U i

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