English
The preimage of the basic open under the map fromSpec corresponds to the basic open defined by a projective basic open condition.
Русский
Предобраз базовой открытой под отображением FromSpec соответствует базовой открытой, определяемой условиями проективной открытой.
LaTeX
$$$\text{preimage}_{FromSpec}(\text{basicOpen}) = \text{projective basicOpen}$$$
Lean4
/-- Pretty printer defined by `notation3` command. -/
@[local delab✝ app.AlgebraicGeometry.PresheafedSpace.carrier]
public meta def
«_aux_Mathlib_AlgebraicGeometry_ProjectiveSpectrum_Scheme___delab_app__private_Mathlib_AlgebraicGeometry_ProjectiveSpectrum_Scheme_0_AlgebraicGeometry_termProj.T_1» :
Delab✝ :=
whenPPOption✝ getPPNotation✝ <|
whenNotPPOption✝ getPPExplicit✝ <|
withOverApp✝ 3
(getExpr✝ >>= fun e✝ =>
(matchApp✝
(matchApp✝
(matchApp✝ (matchExpr✝ (Expr.isConstOf✝ · `AlgebraicGeometry.PresheafedSpace.carrier))
(matchExpr✝ (Expr.isConstOf✝ · `CommRingCat)))
pure✝)
(matchApp✝
(matchApp✝
(matchApp✝ (matchExpr✝ (Expr.isConstOf✝ · `AlgebraicGeometry.SheafedSpace.toPresheafedSpace))
(matchExpr✝ (Expr.isConstOf✝ · `CommRingCat)))
pure✝)
(matchApp✝ (matchExpr✝ (Expr.isConstOf✝ · `AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace))
(matchApp✝
(matchApp✝
(matchApp✝
(matchApp✝
(matchApp✝
(matchApp✝
(matchApp✝
(matchExpr✝ (Expr.isConstOf✝ · `AlgebraicGeometry.Proj.toLocallyRingedSpace))
(matchFVar✝ `R (matchExpr✝ isType'✝)))
(matchFVar✝ `A (matchExpr✝ isType'✝)))
pure✝)
pure✝)
pure✝)
(matchFVar✝ `𝒜
(matchForall✝ (matchExpr✝ (Expr.isConstOf✝ · `Nat))
(fun n✝ =>
matchApp✝¹
(matchApp✝¹
(matchApp✝¹
(matchApp✝¹
(matchApp✝¹ (matchExpr✝¹ (Expr.isConstOf✝¹ · `Submodule))
(matchFVar✝¹ `R (matchExpr✝¹ isType'✝¹)))
(matchFVar✝¹ `A (matchExpr✝¹ isType'✝¹)))
pure✝¹)
pure✝¹)
pure✝¹))))
pure✝))) >=>
pure✝)
MatchState.empty✝ >>=
fun s✝ => withHeadRefIfTagAppFns✝ `(Proj.T))
