mk — Mathlib · SciLib

English

From equality of mapped arrows, we obtain AreEqualizedByLocalization. Mk constructs the witness given equality.

Русский

Из равенства отображённых стрелок следует AreEqualizedByLocalization; mk строит свидетельство по равенству.

LaTeX

$$$\\text{AreEqualizedByLocalization } W f g \\;\\Longrightarrow\\; \\text{L.map } f = \\text{L.map } g$ (construction provides witness)$$

Lean4

theorem mk (L : C ⥤ D) [L.IsLocalization W] (h : L.map f = L.map g) : AreEqualizedByLocalization W f g :=
  (areEqualizedByLocalization_iff L W f g).2 h

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