indexOfHom — Mathlib

English

For any f = (V, (f, proof)) in presieveOfCovering U f, the first projection of f equals U applied to presieveOfCovering.

Русский

Для всякой f = (V, (f, доказательство)) в presieveOfCovering U, первая проекция f равна U применено к presieveOfCovering.

LaTeX

$$f.1 = U (presieveOfCovering.indexOfHom U f)$$

Lean4

/-- By using the axiom of choice, a dependent pair `(V, f)` where `f : V ⟶ iSup U` is a member of
`presieveOfCovering U f` can be turned into an index `i : ι`, such that `V = U i`.
-/
def indexOfHom (f : Σ V, { f : V ⟶ iSup U // presieveOfCovering U f }) : ι :=
  f.2.2.choose

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