finite_of_toPiLocalization_pi_surjective

English

If f is bijective, then the induced map on PiLocalization is bijective.

Русский

Если f биективно, то индуцированное отображение на PiLocalization биективно.

LaTeX

$$$\mathrm{mapPiLocalization}(f) \text{ bijective for bijective } f$$$

Lean4

theorem finite_of_toPiLocalization_pi_surjective (h : Function.Surjective (toPiLocalization (Π i, R i))) : Finite ι :=
  by
  contrapose! h
  exact toPiLocalization_not_surjective_of_infinite _

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