Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.PartialMap.casesOn

{X Y : AlgebraicGeometry.Scheme} →
  {motive : X.PartialMap Y → Sort u_1} →
    (t : X.PartialMap Y) →
      ((domain : X.Opens) →
          (dense_domain : Dense ↑domain) →
            (hom : ↑domain ⟶ Y) → motive { domain := domain, dense_domain := dense_domain, hom := hom }) →
        motive t

Defined in: Mathlib.AlgebraicGeometry.Birational.RationalMap
Cited by: 2 results in Mathlib
Foundations: Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
AlgebraicGeometry.Scheme.Opens.toSchemestatement and proof · cited by 433
Densestatement and proof · cited by 359

Cited by4

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.PartialMap.ext_iffproof · cited by 2
AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_domain_eq_of_isSeparatedproof · cited by 1
AlgebraicGeometry.Scheme.PartialMap.noConfusionproof · cited by 0
AlgebraicGeometry.Scheme.PartialMap.noConfusionTypeproof · cited by 0