of_bijective — Mathlib

English

A dual statement to Span equivalence in the span-target setting.

Русский

Семантически двойственный факт для настройки SpanTarget и его конечной версии.

LaTeX

$$$\\forall P,\\; \\RingHom.OfLocalizationSpanTarget P \\;\\Leftrightarrow \\RingHom.OfLocalizationFiniteSpanTarget P$$$

Lean4

theorem of_bijective (H : RingHom.HoldsForLocalizationAway P) (hf : Function.Bijective f) : P f :=
  by
  letI := f.toAlgebra
  have := IsLocalization.at_units (.powers (1 : R)) (by simp)
  have := IsLocalization.isLocalization_of_algEquiv (.powers (1 : R)) (AlgEquiv.ofBijective (Algebra.ofId R S) hf)
  exact H _ 1

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