algebraic_geometry.morphisms.open_immersion ⟷ Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -74,12 +74,12 @@ theorem isOpenImmersion_is_local_at_target : PropertyIsLocalAtTarget @IsOpenImme
         ((is_open_immersion_respects_iso.arrow_iso_iff
                 (morphism_restrict_opens_range f (𝒰.map i))).mpr
             (H i)).1
-      rwa [arrow.mk_hom, morphism_restrict_val_base] at this 
+      rwa [arrow.mk_hom, morphism_restrict_val_base] at this
     · intro x
       have :=
         arrow.iso_w
           (morphism_restrict_stalk_map f (𝒰.map <| 𝒰.f <| f.1 x).opensRange ⟨x, 𝒰.covers _⟩)
-      dsimp only [arrow.mk_hom] at this 
+      dsimp only [arrow.mk_hom] at this
       rw [this]
       haveI : is_open_immersion (f ∣_ (𝒰.map <| 𝒰.f <| f.1 x).opensRange) :=
         (is_open_immersion_respects_iso.arrow_iso_iff

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 -/
-import Mathbin.Topology.LocalAtTarget
-import Mathbin.AlgebraicGeometry.Morphisms.Basic
+import Topology.LocalAtTarget
+import AlgebraicGeometry.Morphisms.Basic
 
 #align_import algebraic_geometry.morphisms.open_immersion from "leanprover-community/mathlib"@"728ef9dbb281241906f25cbeb30f90d83e0bb451"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.morphisms.open_immersion
-! leanprover-community/mathlib commit 728ef9dbb281241906f25cbeb30f90d83e0bb451
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.LocalAtTarget
 import Mathbin.AlgebraicGeometry.Morphisms.Basic
 
+#align_import algebraic_geometry.morphisms.open_immersion from "leanprover-community/mathlib"@"728ef9dbb281241906f25cbeb30f90d83e0bb451"
+
 /-!
 
 # Open immersions

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module algebraic_geometry.morphisms.open_immersion
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 728ef9dbb281241906f25cbeb30f90d83e0bb451
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.AlgebraicGeometry.Morphisms.Basic
 
 # Open immersions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A morphism is an open immersions if the underlying map of spaces is an open embedding
 `f : X ⟶ U ⊆ Y`, and the sheaf map `Y(V) ⟶ f _* X(V)` is an iso for each `V ⊆ U`.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -34,26 +34,33 @@ namespace AlgebraicGeometry
 
 variable {X Y Z : Scheme.{u}} (f : X ⟶ Y) (g : Y ⟶ Z)
 
-theorem isOpenImmersionCat_iff_stalk {f : X ⟶ Y} :
+#print AlgebraicGeometry.isOpenImmersion_iff_stalk /-
+theorem isOpenImmersion_iff_stalk {f : X ⟶ Y} :
     IsOpenImmersionCat f ↔ OpenEmbedding f.1.base ∧ ∀ x, IsIso (PresheafedSpace.stalkMap f.1 x) :=
   by
   constructor
   · intro h; exact ⟨h.1, inferInstance⟩
   · rintro ⟨h₁, h₂⟩; exact is_open_immersion.of_stalk_iso f h₁
-#align algebraic_geometry.is_open_immersion_iff_stalk AlgebraicGeometry.isOpenImmersionCat_iff_stalk
+#align algebraic_geometry.is_open_immersion_iff_stalk AlgebraicGeometry.isOpenImmersion_iff_stalk
+-/
 
-theorem isOpenImmersionCat_stableUnderComposition :
+#print AlgebraicGeometry.isOpenImmersion_stableUnderComposition /-
+theorem isOpenImmersion_stableUnderComposition :
     MorphismProperty.StableUnderComposition @IsOpenImmersionCat := by intro X Y Z f g h₁ h₂;
   infer_instance
-#align algebraic_geometry.is_open_immersion_stable_under_composition AlgebraicGeometry.isOpenImmersionCat_stableUnderComposition
+#align algebraic_geometry.is_open_immersion_stable_under_composition AlgebraicGeometry.isOpenImmersion_stableUnderComposition
+-/
 
-theorem isOpenImmersionCat_respectsIso : MorphismProperty.RespectsIso @IsOpenImmersionCat :=
+#print AlgebraicGeometry.isOpenImmersion_respectsIso /-
+theorem isOpenImmersion_respectsIso : MorphismProperty.RespectsIso @IsOpenImmersionCat :=
   by
   apply is_open_immersion_stable_under_composition.respects_iso
   intro _ _ _; infer_instance
-#align algebraic_geometry.is_open_immersion_respects_iso AlgebraicGeometry.isOpenImmersionCat_respectsIso
+#align algebraic_geometry.is_open_immersion_respects_iso AlgebraicGeometry.isOpenImmersion_respectsIso
+-/
 
-theorem isOpenImmersionCat_is_local_at_target : PropertyIsLocalAtTarget @IsOpenImmersionCat :=
+#print AlgebraicGeometry.isOpenImmersion_is_local_at_target /-
+theorem isOpenImmersion_is_local_at_target : PropertyIsLocalAtTarget @IsOpenImmersionCat :=
   by
   constructor
   · exact is_open_immersion_respects_iso
@@ -79,9 +86,11 @@ theorem isOpenImmersionCat_is_local_at_target : PropertyIsLocalAtTarget @IsOpenI
               (morphism_restrict_opens_range f (𝒰.map _))).mpr
           (H _)
       infer_instance
-#align algebraic_geometry.is_open_immersion_is_local_at_target AlgebraicGeometry.isOpenImmersionCat_is_local_at_target
+#align algebraic_geometry.is_open_immersion_is_local_at_target AlgebraicGeometry.isOpenImmersion_is_local_at_target
+-/
 
-theorem IsOpenImmersionCat.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
+#print AlgebraicGeometry.IsOpenImmersion.openCover_TFAE /-
+theorem IsOpenImmersion.openCover_TFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
     TFAE
       [IsOpenImmersionCat f,
         ∃ 𝒰 : Scheme.OpenCover.{u} Y,
@@ -93,20 +102,24 @@ theorem IsOpenImmersionCat.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
           IsOpenImmersionCat (pullback.snd : pullback f g ⟶ _),
         ∃ (ι : Type u) (U : ι → Opens Y.carrier) (hU : iSup U = ⊤),
           ∀ i, IsOpenImmersionCat (f ∣_ U i)] :=
-  isOpenImmersionCat_is_local_at_target.openCover_TFAE f
-#align algebraic_geometry.is_open_immersion.open_cover_tfae AlgebraicGeometry.IsOpenImmersionCat.openCover_tFAE
+  isOpenImmersion_is_local_at_target.openCover_TFAE f
+#align algebraic_geometry.is_open_immersion.open_cover_tfae AlgebraicGeometry.IsOpenImmersion.openCover_TFAE
+-/
 
-theorem IsOpenImmersionCat.openCover_iff {X Y : Scheme.{u}} (𝒰 : Scheme.OpenCover.{u} Y)
-    (f : X ⟶ Y) :
+#print AlgebraicGeometry.IsOpenImmersion.openCover_iff /-
+theorem IsOpenImmersion.openCover_iff {X Y : Scheme.{u}} (𝒰 : Scheme.OpenCover.{u} Y) (f : X ⟶ Y) :
     IsOpenImmersionCat f ↔ ∀ i, IsOpenImmersionCat (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
-  isOpenImmersionCat_is_local_at_target.openCover_iff f 𝒰
-#align algebraic_geometry.is_open_immersion.open_cover_iff AlgebraicGeometry.IsOpenImmersionCat.openCover_iff
+  isOpenImmersion_is_local_at_target.openCover_iff f 𝒰
+#align algebraic_geometry.is_open_immersion.open_cover_iff AlgebraicGeometry.IsOpenImmersion.openCover_iff
+-/
 
-theorem isOpenImmersionCat_stableUnderBaseChange :
+#print AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange /-
+theorem isOpenImmersion_stableUnderBaseChange :
     MorphismProperty.StableUnderBaseChange @IsOpenImmersionCat :=
-  MorphismProperty.StableUnderBaseChange.mk isOpenImmersionCat_respectsIso <| by intro X Y Z f g H;
+  MorphismProperty.StableUnderBaseChange.mk isOpenImmersion_respectsIso <| by intro X Y Z f g H;
     infer_instance
-#align algebraic_geometry.is_open_immersion_stable_under_base_change AlgebraicGeometry.isOpenImmersionCat_stableUnderBaseChange
+#align algebraic_geometry.is_open_immersion_stable_under_base_change AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
+-/
 
 end AlgebraicGeometry
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -53,7 +53,7 @@ theorem isOpenImmersionCat_respectsIso : MorphismProperty.RespectsIso @IsOpenImm
   intro _ _ _; infer_instance
 #align algebraic_geometry.is_open_immersion_respects_iso AlgebraicGeometry.isOpenImmersionCat_respectsIso
 
-theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersionCat :=
+theorem isOpenImmersionCat_is_local_at_target : PropertyIsLocalAtTarget @IsOpenImmersionCat :=
   by
   constructor
   · exact is_open_immersion_respects_iso
@@ -79,7 +79,7 @@ theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersio
               (morphism_restrict_opens_range f (𝒰.map _))).mpr
           (H _)
       infer_instance
-#align algebraic_geometry.is_open_immersion_is_local_at_target AlgebraicGeometry.isOpenImmersionIsLocalAtTarget
+#align algebraic_geometry.is_open_immersion_is_local_at_target AlgebraicGeometry.isOpenImmersionCat_is_local_at_target
 
 theorem IsOpenImmersionCat.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
     TFAE
@@ -93,13 +93,13 @@ theorem IsOpenImmersionCat.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
           IsOpenImmersionCat (pullback.snd : pullback f g ⟶ _),
         ∃ (ι : Type u) (U : ι → Opens Y.carrier) (hU : iSup U = ⊤),
           ∀ i, IsOpenImmersionCat (f ∣_ U i)] :=
-  isOpenImmersionIsLocalAtTarget.openCover_tFAE f
+  isOpenImmersionCat_is_local_at_target.openCover_TFAE f
 #align algebraic_geometry.is_open_immersion.open_cover_tfae AlgebraicGeometry.IsOpenImmersionCat.openCover_tFAE
 
 theorem IsOpenImmersionCat.openCover_iff {X Y : Scheme.{u}} (𝒰 : Scheme.OpenCover.{u} Y)
     (f : X ⟶ Y) :
     IsOpenImmersionCat f ↔ ∀ i, IsOpenImmersionCat (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
-  isOpenImmersionIsLocalAtTarget.openCover_iff f 𝒰
+  isOpenImmersionCat_is_local_at_target.openCover_iff f 𝒰
 #align algebraic_geometry.is_open_immersion.open_cover_iff AlgebraicGeometry.IsOpenImmersionCat.openCover_iff
 
 theorem isOpenImmersionCat_stableUnderBaseChange :

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -34,26 +34,26 @@ namespace AlgebraicGeometry
 
 variable {X Y Z : Scheme.{u}} (f : X ⟶ Y) (g : Y ⟶ Z)
 
-theorem isOpenImmersion_iff_stalk {f : X ⟶ Y} :
-    IsOpenImmersion f ↔ OpenEmbedding f.1.base ∧ ∀ x, IsIso (PresheafedSpace.stalkMap f.1 x) :=
+theorem isOpenImmersionCat_iff_stalk {f : X ⟶ Y} :
+    IsOpenImmersionCat f ↔ OpenEmbedding f.1.base ∧ ∀ x, IsIso (PresheafedSpace.stalkMap f.1 x) :=
   by
   constructor
   · intro h; exact ⟨h.1, inferInstance⟩
   · rintro ⟨h₁, h₂⟩; exact is_open_immersion.of_stalk_iso f h₁
-#align algebraic_geometry.is_open_immersion_iff_stalk AlgebraicGeometry.isOpenImmersion_iff_stalk
+#align algebraic_geometry.is_open_immersion_iff_stalk AlgebraicGeometry.isOpenImmersionCat_iff_stalk
 
-theorem isOpenImmersion_stableUnderComposition :
-    MorphismProperty.StableUnderComposition @IsOpenImmersion := by intro X Y Z f g h₁ h₂;
+theorem isOpenImmersionCat_stableUnderComposition :
+    MorphismProperty.StableUnderComposition @IsOpenImmersionCat := by intro X Y Z f g h₁ h₂;
   infer_instance
-#align algebraic_geometry.is_open_immersion_stable_under_composition AlgebraicGeometry.isOpenImmersion_stableUnderComposition
+#align algebraic_geometry.is_open_immersion_stable_under_composition AlgebraicGeometry.isOpenImmersionCat_stableUnderComposition
 
-theorem isOpenImmersion_respectsIso : MorphismProperty.RespectsIso @IsOpenImmersion :=
+theorem isOpenImmersionCat_respectsIso : MorphismProperty.RespectsIso @IsOpenImmersionCat :=
   by
   apply is_open_immersion_stable_under_composition.respects_iso
   intro _ _ _; infer_instance
-#align algebraic_geometry.is_open_immersion_respects_iso AlgebraicGeometry.isOpenImmersion_respectsIso
+#align algebraic_geometry.is_open_immersion_respects_iso AlgebraicGeometry.isOpenImmersionCat_respectsIso
 
-theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersion :=
+theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersionCat :=
   by
   constructor
   · exact is_open_immersion_respects_iso
@@ -81,31 +81,32 @@ theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersio
       infer_instance
 #align algebraic_geometry.is_open_immersion_is_local_at_target AlgebraicGeometry.isOpenImmersionIsLocalAtTarget
 
-theorem IsOpenImmersion.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
+theorem IsOpenImmersionCat.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
     TFAE
-      [IsOpenImmersion f,
+      [IsOpenImmersionCat f,
         ∃ 𝒰 : Scheme.OpenCover.{u} Y,
-          ∀ i : 𝒰.J, IsOpenImmersion (pullback.snd : (𝒰.pullbackCover f).obj i ⟶ 𝒰.obj i),
+          ∀ i : 𝒰.J, IsOpenImmersionCat (pullback.snd : (𝒰.pullbackCover f).obj i ⟶ 𝒰.obj i),
         ∀ (𝒰 : Scheme.OpenCover.{u} Y) (i : 𝒰.J),
-          IsOpenImmersion (pullback.snd : (𝒰.pullbackCover f).obj i ⟶ 𝒰.obj i),
-        ∀ U : Opens Y.carrier, IsOpenImmersion (f ∣_ U),
-        ∀ {U : Scheme} (g : U ⟶ Y) [IsOpenImmersion g],
-          IsOpenImmersion (pullback.snd : pullback f g ⟶ _),
+          IsOpenImmersionCat (pullback.snd : (𝒰.pullbackCover f).obj i ⟶ 𝒰.obj i),
+        ∀ U : Opens Y.carrier, IsOpenImmersionCat (f ∣_ U),
+        ∀ {U : Scheme} (g : U ⟶ Y) [IsOpenImmersionCat g],
+          IsOpenImmersionCat (pullback.snd : pullback f g ⟶ _),
         ∃ (ι : Type u) (U : ι → Opens Y.carrier) (hU : iSup U = ⊤),
-          ∀ i, IsOpenImmersion (f ∣_ U i)] :=
+          ∀ i, IsOpenImmersionCat (f ∣_ U i)] :=
   isOpenImmersionIsLocalAtTarget.openCover_tFAE f
-#align algebraic_geometry.is_open_immersion.open_cover_tfae AlgebraicGeometry.IsOpenImmersion.openCover_tFAE
+#align algebraic_geometry.is_open_immersion.open_cover_tfae AlgebraicGeometry.IsOpenImmersionCat.openCover_tFAE
 
-theorem IsOpenImmersion.openCover_iff {X Y : Scheme.{u}} (𝒰 : Scheme.OpenCover.{u} Y) (f : X ⟶ Y) :
-    IsOpenImmersion f ↔ ∀ i, IsOpenImmersion (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
+theorem IsOpenImmersionCat.openCover_iff {X Y : Scheme.{u}} (𝒰 : Scheme.OpenCover.{u} Y)
+    (f : X ⟶ Y) :
+    IsOpenImmersionCat f ↔ ∀ i, IsOpenImmersionCat (pullback.snd : pullback f (𝒰.map i) ⟶ _) :=
   isOpenImmersionIsLocalAtTarget.openCover_iff f 𝒰
-#align algebraic_geometry.is_open_immersion.open_cover_iff AlgebraicGeometry.IsOpenImmersion.openCover_iff
+#align algebraic_geometry.is_open_immersion.open_cover_iff AlgebraicGeometry.IsOpenImmersionCat.openCover_iff
 
-theorem isOpenImmersion_stableUnderBaseChange :
-    MorphismProperty.StableUnderBaseChange @IsOpenImmersion :=
-  MorphismProperty.StableUnderBaseChange.mk isOpenImmersion_respectsIso <| by intro X Y Z f g H;
+theorem isOpenImmersionCat_stableUnderBaseChange :
+    MorphismProperty.StableUnderBaseChange @IsOpenImmersionCat :=
+  MorphismProperty.StableUnderBaseChange.mk isOpenImmersionCat_respectsIso <| by intro X Y Z f g H;
     infer_instance
-#align algebraic_geometry.is_open_immersion_stable_under_base_change AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
+#align algebraic_geometry.is_open_immersion_stable_under_base_change AlgebraicGeometry.isOpenImmersionCat_stableUnderBaseChange
 
 end AlgebraicGeometry
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -57,7 +57,7 @@ theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersio
   by
   constructor
   · exact is_open_immersion_respects_iso
-  · intros ; infer_instance
+  · intros; infer_instance
   · intro X Y f 𝒰 H
     rw [is_open_immersion_iff_stalk]
     constructor
@@ -67,12 +67,12 @@ theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersio
         ((is_open_immersion_respects_iso.arrow_iso_iff
                 (morphism_restrict_opens_range f (𝒰.map i))).mpr
             (H i)).1
-      rwa [arrow.mk_hom, morphism_restrict_val_base] at this
+      rwa [arrow.mk_hom, morphism_restrict_val_base] at this 
     · intro x
       have :=
         arrow.iso_w
           (morphism_restrict_stalk_map f (𝒰.map <| 𝒰.f <| f.1 x).opensRange ⟨x, 𝒰.covers _⟩)
-      dsimp only [arrow.mk_hom] at this
+      dsimp only [arrow.mk_hom] at this 
       rw [this]
       haveI : is_open_immersion (f ∣_ (𝒰.map <| 𝒰.f <| f.1 x).opensRange) :=
         (is_open_immersion_respects_iso.arrow_iso_iff
@@ -91,7 +91,7 @@ theorem IsOpenImmersion.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
         ∀ U : Opens Y.carrier, IsOpenImmersion (f ∣_ U),
         ∀ {U : Scheme} (g : U ⟶ Y) [IsOpenImmersion g],
           IsOpenImmersion (pullback.snd : pullback f g ⟶ _),
-        ∃ (ι : Type u)(U : ι → Opens Y.carrier)(hU : iSup U = ⊤),
+        ∃ (ι : Type u) (U : ι → Opens Y.carrier) (hU : iSup U = ⊤),
           ∀ i, IsOpenImmersion (f ∣_ U i)] :=
   isOpenImmersionIsLocalAtTarget.openCover_tFAE f
 #align algebraic_geometry.is_open_immersion.open_cover_tfae AlgebraicGeometry.IsOpenImmersion.openCover_tFAE

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -38,10 +38,8 @@ theorem isOpenImmersion_iff_stalk {f : X ⟶ Y} :
     IsOpenImmersion f ↔ OpenEmbedding f.1.base ∧ ∀ x, IsIso (PresheafedSpace.stalkMap f.1 x) :=
   by
   constructor
-  · intro h
-    exact ⟨h.1, inferInstance⟩
-  · rintro ⟨h₁, h₂⟩
-    exact is_open_immersion.of_stalk_iso f h₁
+  · intro h; exact ⟨h.1, inferInstance⟩
+  · rintro ⟨h₁, h₂⟩; exact is_open_immersion.of_stalk_iso f h₁
 #align algebraic_geometry.is_open_immersion_iff_stalk AlgebraicGeometry.isOpenImmersion_iff_stalk
 
 theorem isOpenImmersion_stableUnderComposition :
@@ -59,8 +57,7 @@ theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersio
   by
   constructor
   · exact is_open_immersion_respects_iso
-  · intros
-    infer_instance
+  · intros ; infer_instance
   · intro X Y f 𝒰 H
     rw [is_open_immersion_iff_stalk]
     constructor
@@ -106,9 +103,7 @@ theorem IsOpenImmersion.openCover_iff {X Y : Scheme.{u}} (𝒰 : Scheme.OpenCove
 
 theorem isOpenImmersion_stableUnderBaseChange :
     MorphismProperty.StableUnderBaseChange @IsOpenImmersion :=
-  MorphismProperty.StableUnderBaseChange.mk isOpenImmersion_respectsIso <|
-    by
-    intro X Y Z f g H
+  MorphismProperty.StableUnderBaseChange.mk isOpenImmersion_respectsIso <| by intro X Y Z f g H;
     infer_instance
 #align algebraic_geometry.is_open_immersion_stable_under_base_change AlgebraicGeometry.isOpenImmersion_stableUnderBaseChange
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -64,7 +64,7 @@ theorem isOpenImmersionIsLocalAtTarget : PropertyIsLocalAtTarget @IsOpenImmersio
   · intro X Y f 𝒰 H
     rw [is_open_immersion_iff_stalk]
     constructor
-    · apply (openEmbedding_iff_openEmbedding_of_supᵢ_eq_top 𝒰.supr_opens_range f.1.base.2).mpr
+    · apply (openEmbedding_iff_openEmbedding_of_iSup_eq_top 𝒰.supr_opens_range f.1.base.2).mpr
       intro i
       have :=
         ((is_open_immersion_respects_iso.arrow_iso_iff
@@ -94,7 +94,7 @@ theorem IsOpenImmersion.openCover_tFAE {X Y : Scheme.{u}} (f : X ⟶ Y) :
         ∀ U : Opens Y.carrier, IsOpenImmersion (f ∣_ U),
         ∀ {U : Scheme} (g : U ⟶ Y) [IsOpenImmersion g],
           IsOpenImmersion (pullback.snd : pullback f g ⟶ _),
-        ∃ (ι : Type u)(U : ι → Opens Y.carrier)(hU : supᵢ U = ⊤),
+        ∃ (ι : Type u)(U : ι → Opens Y.carrier)(hU : iSup U = ⊤),
           ∀ i, IsOpenImmersion (f ∣_ U i)] :=
   isOpenImmersionIsLocalAtTarget.openCover_tFAE f
 #align algebraic_geometry.is_open_immersion.open_cover_tfae AlgebraicGeometry.IsOpenImmersion.openCover_tFAE

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
 
 ! This file was ported from Lean 3 source module algebraic_geometry.morphisms.open_immersion
-! leanprover-community/mathlib commit 68fa0fd2d0aa7061ad59baa5ec17cf0ff1e6d036
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.AlgebraicGeometry.Morphisms.RingHomProperties
 import Mathbin.Topology.LocalAtTarget
+import Mathbin.AlgebraicGeometry.Morphisms.Basic
 
 /-!
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

The type class MorphismProperty.HasTwoOutOfThreeProperty is introduced. The structure StableUnderComposition is also changed into a type class IsStableUnderComposition.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

@@ -38,14 +38,16 @@ theorem isOpenImmersion_iff_stalk {f : X ⟶ Y} : IsOpenImmersion f ↔
   · rintro ⟨h₁, h₂⟩; exact IsOpenImmersion.of_stalk_iso f h₁
 #align algebraic_geometry.is_open_immersion_iff_stalk AlgebraicGeometry.isOpenImmersion_iff_stalk
 
-theorem isOpenImmersion_stableUnderComposition :
-    MorphismProperty.StableUnderComposition @IsOpenImmersion := by
-  intro X Y Z f g h₁ h₂; exact LocallyRingedSpace.IsOpenImmersion.comp f g
-#align algebraic_geometry.is_open_immersion_stable_under_composition AlgebraicGeometry.isOpenImmersion_stableUnderComposition
+instance isOpenImmersion_isStableUnderComposition :
+    MorphismProperty.IsStableUnderComposition @IsOpenImmersion where
+  comp_mem f g _ _ := LocallyRingedSpace.IsOpenImmersion.comp f g
+#align algebraic_geometry.is_open_immersion_stable_under_composition AlgebraicGeometry.isOpenImmersion_isStableUnderComposition
 
 theorem isOpenImmersion_respectsIso : MorphismProperty.RespectsIso @IsOpenImmersion := by
-  apply isOpenImmersion_stableUnderComposition.respectsIso
-  intro _ _ _; infer_instance
+  apply MorphismProperty.respectsIso_of_isStableUnderComposition
+  intro _ _ f (hf : IsIso f)
+  have : IsIso f := hf
+  infer_instance
 #align algebraic_geometry.is_open_immersion_respects_iso AlgebraicGeometry.isOpenImmersion_respectsIso
 
 theorem isOpenImmersion_is_local_at_target : PropertyIsLocalAtTarget @IsOpenImmersion := by

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Andrew Yang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Andrew Yang
-
-! This file was ported from Lean 3 source module algebraic_geometry.morphisms.open_immersion
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.LocalAtTarget
 import Mathlib.AlgebraicGeometry.Morphisms.Basic
 
+#align_import algebraic_geometry.morphisms.open_immersion from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 
 # Open immersions