scheme_eq_of_locallyRingedSpace_eq

English

A simp-lemma form of appIso_inv_app, giving a straightforward equality of composites with the latter map.

Русский

Простейшая форма леммы appIso_inv_app, дающая простое равенство композитов.

LaTeX

$$$$ (f.appIso U).inv ≫ f.app (f.opensFunctor.obj U) = X.presheaf.map (eqToHom (preimage_image_eq f U)).op $$$$

Lean4

theorem scheme_eq_of_locallyRingedSpace_eq {X Y : Scheme.{u}} (H : X.toLocallyRingedSpace = Y.toLocallyRingedSpace) :
    X = Y := by cases X; cases Y; congr

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