topology.sheaves.sheaf_condition.opens_le_cover

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

85d6221d

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

61db041a

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Topology.Sheaves.SheafCondition.Sites
+import Topology.Sheaves.SheafCondition.Sites
 
 #align_import topology.sheaves.sheaf_condition.opens_le_cover from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"

61db041a

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.sheaves.sheaf_condition.opens_le_cover
-! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Sheaves.SheafCondition.Sites
 
+#align_import topology.sheaves.sheaf_condition.opens_le_cover from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
+
 /-!
 # Another version of the sheaf condition.

61db041a

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -79,14 +79,17 @@ def index (V : OpensLeCover U) : ι :=
 #align Top.presheaf.sheaf_condition.opens_le_cover.index TopCat.Presheaf.SheafCondition.OpensLeCover.index
 -/
 
+#print TopCat.Presheaf.SheafCondition.OpensLeCover.homToIndex /-
 /-- The morphism from `V` to `U i` for some `i`.
 -/
 def homToIndex (V : OpensLeCover U) : V.obj ⟶ U (index V) :=
   V.property.choose_spec.Hom
 #align Top.presheaf.sheaf_condition.opens_le_cover.hom_to_index TopCat.Presheaf.SheafCondition.OpensLeCover.homToIndex
+-/
 
 end OpensLeCover
 
+#print TopCat.Presheaf.SheafCondition.opensLeCoverCocone /-
 /-- `supr U` as a cocone over the opens sets contained in some element of the cover.
 
 (In fact this is a colimit cocone.)
@@ -96,6 +99,7 @@ def opensLeCoverCocone : Cocone (fullSubcategoryInclusion _ : OpensLeCover U ⥤
   pt := iSup U
   ι := { app := fun V : OpensLeCover U => V.homToIndex ≫ Opens.leSupr U _ }
 #align Top.presheaf.sheaf_condition.opens_le_cover_cocone TopCat.Presheaf.SheafCondition.opensLeCoverCocone
+-/
 
 end SheafCondition
 
@@ -119,6 +123,7 @@ section
 
 variable {Y : Opens X} (hY : Y = iSup U)
 
+#print TopCat.Presheaf.generateEquivalenceOpensLe /-
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
@@ -149,7 +154,9 @@ def generateEquivalenceOpensLe :
       CategoryTheory.Functor.ext (by rintro ⟨⟨_, _⟩, _⟩; dsimp; congr <;> ext) (by intros; ext)
   counitIso := eqToIso <| CategoryTheory.Functor.hext (by intro; ext; rfl) (by intros; rfl)
 #align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLe
+-/
 
+#print TopCat.Presheaf.whiskerIsoMapGenerateCocone /-
 /-- Given a family of opens `opens_le_cover_cocone U` is essentially the natural cocone
     associated to the sieve generated by the presieve associated to `U` with indexing
     category changed using the above equivalence. -/
@@ -167,7 +174,9 @@ def whiskerIsoMapGenerateCocone :
   hom_inv_id' := by ext; simp [eq_to_hom_map]
   inv_hom_id' := by ext; simp [eq_to_hom_map]
 #align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCocone
+-/
 
+#print TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ /-
 /-- Given a presheaf `F` on the topological space `X` and a family of opens `U` of `X`,
     the natural cone associated to `F` and `U` used in the definition of
     `F.is_sheaf_opens_le_cover` is a limit cone iff the natural cone associated to `F`
@@ -178,7 +187,9 @@ def isLimitOpensLeEquivGenerate₁ :
   (IsLimit.whiskerEquivalenceEquiv (generateEquivalenceOpensLe U hY).op).trans
     (IsLimit.equivIsoLimit (whiskerIsoMapGenerateCocone F U hY))
 #align Top.presheaf.is_limit_opens_le_equiv_generate₁ TopCat.Presheaf.isLimitOpensLeEquivGenerate₁
+-/
 
+#print TopCat.Presheaf.isLimitOpensLeEquivGenerate₂ /-
 /-- Given a presheaf `F` on the topological space `X` and a presieve `R` whose generated sieve
     is covering for the associated Grothendieck topology (equivalently, the presieve is covering
     for the associated pretopology), the natural cone associated to `F` and the family of opens
@@ -197,6 +208,7 @@ def isLimitOpensLeEquivGenerate₂ (R : Presieve Y)
       2 <;>
     rw [covering_presieve_eq_self R]
 #align Top.presheaf.is_limit_opens_le_equiv_generate₂ TopCat.Presheaf.isLimitOpensLeEquivGenerate₂
+-/
 
 #print TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover /-
 /-- A presheaf `(opens X)ᵒᵖ ⥤ C` on a topological space `X` is a sheaf on the site `opens X` iff

61db041a

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -191,7 +191,8 @@ def isLimitOpensLeEquivGenerate₂ (R : Presieve Y)
     IsLimit (F.mapCone (opensLeCoverCocone (coveringOfPresieve Y R)).op) ≃
       IsLimit (F.mapCone (Sieve.generate R).arrows.Cocone.op) :=
   by
-  convert is_limit_opens_le_equiv_generate₁ F (covering_of_presieve Y R)
+  convert
+      is_limit_opens_le_equiv_generate₁ F (covering_of_presieve Y R)
         (covering_of_presieve.supr_eq_of_mem_grothendieck Y R hR).symm using
       2 <;>
     rw [covering_presieve_eq_self R]

61db041a

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -59,7 +59,8 @@ namespace SheafCondition
 /-- The category of open sets contained in some element of the cover.
 -/
 def OpensLeCover : Type w :=
-  FullSubcategory fun V : Opens X => ∃ i, V ≤ U i deriving Category
+  FullSubcategory fun V : Opens X => ∃ i, V ≤ U i
+deriving Category
 #align Top.presheaf.sheaf_condition.opens_le_cover TopCat.Presheaf.SheafCondition.OpensLeCover
 -/
 
@@ -145,8 +146,8 @@ def generateEquivalenceOpensLe :
       map := fun _ _ g => Over.homMk g }
   unitIso :=
     eqToIso <|
-      CategoryTheory.Functor.ext (by rintro ⟨⟨_, _⟩, _⟩; dsimp; congr <;> ext) (by intros ; ext)
-  counitIso := eqToIso <| CategoryTheory.Functor.hext (by intro ; ext; rfl) (by intros ; rfl)
+      CategoryTheory.Functor.ext (by rintro ⟨⟨_, _⟩, _⟩; dsimp; congr <;> ext) (by intros; ext)
+  counitIso := eqToIso <| CategoryTheory.Functor.hext (by intro; ext; rfl) (by intros; rfl)
 #align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLe
 
 /-- Given a family of opens `opens_le_cover_cocone U` is essentially the natural cocone

61db041a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -78,12 +78,6 @@ def index (V : OpensLeCover U) : ι :=
 #align Top.presheaf.sheaf_condition.opens_le_cover.index TopCat.Presheaf.SheafCondition.OpensLeCover.index
 -/
 
-/- warning: Top.presheaf.sheaf_condition.opens_le_cover.hom_to_index -> TopCat.Presheaf.SheafCondition.OpensLeCover.homToIndex is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {X : TopCat.{u1}} {ι : Type.{u1}} {U : ι -> (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))} (V : TopCat.Presheaf.SheafCondition.OpensLeCover.{u1} X ι U), Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.FullSubcategory.obj.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))) V) (U (TopCat.Presheaf.SheafCondition.OpensLeCover.index.{u1} X ι U V))
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition.opens_le_cover.hom_to_index TopCat.Presheaf.SheafCondition.OpensLeCover.homToIndexₓ'. -/
 /-- The morphism from `V` to `U i` for some `i`.
 -/
 def homToIndex (V : OpensLeCover U) : V.obj ⟶ U (index V) :=
@@ -92,9 +86,6 @@ def homToIndex (V : OpensLeCover U) : V.obj ⟶ U (index V) :=
 
 end OpensLeCover
 
-/- warning: Top.presheaf.sheaf_condition.opens_le_cover_cocone -> TopCat.Presheaf.SheafCondition.opensLeCoverCocone is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition.opens_le_cover_cocone TopCat.Presheaf.SheafCondition.opensLeCoverCoconeₓ'. -/
 /-- `supr U` as a cocone over the opens sets contained in some element of the cover.
 
 (In fact this is a colimit cocone.)
@@ -127,9 +118,6 @@ section
 
 variable {Y : Opens X} (hY : Y = iSup U)
 
-/- warning: Top.presheaf.generate_equivalence_opens_le -> TopCat.Presheaf.generateEquivalenceOpensLe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLeₓ'. -/
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
@@ -161,9 +149,6 @@ def generateEquivalenceOpensLe :
   counitIso := eqToIso <| CategoryTheory.Functor.hext (by intro ; ext; rfl) (by intros ; rfl)
 #align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLe
 
-/- warning: Top.presheaf.whisker_iso_map_generate_cocone -> TopCat.Presheaf.whiskerIsoMapGenerateCocone is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCoconeₓ'. -/
 /-- Given a family of opens `opens_le_cover_cocone U` is essentially the natural cocone
     associated to the sieve generated by the presieve associated to `U` with indexing
     category changed using the above equivalence. -/
@@ -182,9 +167,6 @@ def whiskerIsoMapGenerateCocone :
   inv_hom_id' := by ext; simp [eq_to_hom_map]
 #align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCocone
 
-/- warning: Top.presheaf.is_limit_opens_le_equiv_generate₁ -> TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_limit_opens_le_equiv_generate₁ TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ₓ'. -/
 /-- Given a presheaf `F` on the topological space `X` and a family of opens `U` of `X`,
     the natural cone associated to `F` and `U` used in the definition of
     `F.is_sheaf_opens_le_cover` is a limit cone iff the natural cone associated to `F`
@@ -196,9 +178,6 @@ def isLimitOpensLeEquivGenerate₁ :
     (IsLimit.equivIsoLimit (whiskerIsoMapGenerateCocone F U hY))
 #align Top.presheaf.is_limit_opens_le_equiv_generate₁ TopCat.Presheaf.isLimitOpensLeEquivGenerate₁
 
-/- warning: Top.presheaf.is_limit_opens_le_equiv_generate₂ -> TopCat.Presheaf.isLimitOpensLeEquivGenerate₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_limit_opens_le_equiv_generate₂ TopCat.Presheaf.isLimitOpensLeEquivGenerate₂ₓ'. -/
 /-- Given a presheaf `F` on the topological space `X` and a presieve `R` whose generated sieve
     is covering for the associated Grothendieck topology (equivalently, the presieve is covering
     for the associated pretopology), the natural cone associated to `F` and the family of opens

61db041a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -157,24 +157,8 @@ def generateEquivalenceOpensLe :
       map := fun _ _ g => Over.homMk g }
   unitIso :=
     eqToIso <|
-      CategoryTheory.Functor.ext
-        (by
-          rintro ⟨⟨_, _⟩, _⟩
-          dsimp
-          congr <;> ext)
-        (by
-          intros
-          ext)
-  counitIso :=
-    eqToIso <|
-      CategoryTheory.Functor.hext
-        (by
-          intro
-          ext
-          rfl)
-        (by
-          intros
-          rfl)
+      CategoryTheory.Functor.ext (by rintro ⟨⟨_, _⟩, _⟩; dsimp; congr <;> ext) (by intros ; ext)
+  counitIso := eqToIso <| CategoryTheory.Functor.hext (by intro ; ext; rfl) (by intros ; rfl)
 #align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLe
 
 /- warning: Top.presheaf.whisker_iso_map_generate_cocone -> TopCat.Presheaf.whiskerIsoMapGenerateCocone is a dubious translation:
@@ -190,20 +174,12 @@ def whiskerIsoMapGenerateCocone :
     where
   Hom :=
     { Hom := F.map (eqToHom (congr_arg op hY.symm))
-      w' := fun j => by
-        erw [← F.map_comp]
-        congr }
+      w' := fun j => by erw [← F.map_comp]; congr }
   inv :=
     { Hom := F.map (eqToHom (congr_arg op hY))
-      w' := fun j => by
-        erw [← F.map_comp]
-        congr }
-  hom_inv_id' := by
-    ext
-    simp [eq_to_hom_map]
-  inv_hom_id' := by
-    ext
-    simp [eq_to_hom_map]
+      w' := fun j => by erw [← F.map_comp]; congr }
+  hom_inv_id' := by ext; simp [eq_to_hom_map]
+  inv_hom_id' := by ext; simp [eq_to_hom_map]
 #align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCocone
 
 /- warning: Top.presheaf.is_limit_opens_le_equiv_generate₁ -> TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ is a dubious translation:
@@ -250,15 +226,10 @@ theorem isSheaf_iff_isSheafOpensLeCover : F.IsSheaf ↔ F.IsSheafOpensLeCover :=
   by
   refine' (presheaf.is_sheaf_iff_is_limit _ _).trans _
   constructor
-  · intro h ι U
-    rw [(is_limit_opens_le_equiv_generate₁ F U rfl).nonempty_congr]
-    apply h
-    apply presieve_of_covering.mem_grothendieck_topology
-  · intro h Y S
-    rw [← sieve.generate_sieve S]
-    intro hS
-    rw [← (is_limit_opens_le_equiv_generate₂ F S hS).nonempty_congr]
-    apply h
+  · intro h ι U; rw [(is_limit_opens_le_equiv_generate₁ F U rfl).nonempty_congr]
+    apply h; apply presieve_of_covering.mem_grothendieck_topology
+  · intro h Y S; rw [← sieve.generate_sieve S]; intro hS
+    rw [← (is_limit_opens_le_equiv_generate₂ F S hS).nonempty_congr]; apply h
 #align Top.presheaf.is_sheaf_iff_is_sheaf_opens_le_cover TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover
 -/

61db041a

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -93,10 +93,7 @@ def homToIndex (V : OpensLeCover U) : V.obj ⟶ U (index V) :=
 end OpensLeCover
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition.opens_le_cover_cocone TopCat.Presheaf.SheafCondition.opensLeCoverCoconeₓ'. -/
 /-- `supr U` as a cocone over the opens sets contained in some element of the cover.
 
@@ -131,10 +128,7 @@ section
 variable {Y : Opens X} (hY : Y = iSup U)
 
 /- warning: Top.presheaf.generate_equivalence_opens_le -> TopCat.Presheaf.generateEquivalenceOpensLe is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLeₓ'. -/
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
@@ -184,10 +178,7 @@ def generateEquivalenceOpensLe :
 #align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLe
 
 /- warning: Top.presheaf.whisker_iso_map_generate_cocone -> TopCat.Presheaf.whiskerIsoMapGenerateCocone is a dubious translation:
-lean 3 declaration is
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(CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.fromPUnit.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y) f)))) C _inst_1 (CategoryTheory.Functor.comp.{u1, u1, u2, u1, u1, u3} (Opposite.{succ u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} 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(CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (CategoryTheory.FullSubcategory.category.{u1, 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u1, u1, u3} (Opposite.{succ u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (CategoryTheory.Category.opposite.{u1, u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) 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(TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 F (CategoryTheory.Functor.op.{u1, u1, u1, u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (CategoryTheory.FullSubcategory.category.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCoconeₓ'. -/
 /-- Given a family of opens `opens_le_cover_cocone U` is essentially the natural cocone
     associated to the sieve generated by the presieve associated to `U` with indexing
@@ -216,10 +207,7 @@ def whiskerIsoMapGenerateCocone :
 #align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCocone
 
 /- warning: Top.presheaf.is_limit_opens_le_equiv_generate₁ -> TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ is a dubious translation:
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(CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} 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(CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} 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(CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_limit_opens_le_equiv_generate₁ TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ₓ'. -/
 /-- Given a presheaf `F` on the topological space `X` and a family of opens `U` of `X`,
     the natural cone associated to `F` and `U` used in the definition of
@@ -233,10 +221,7 @@ def isLimitOpensLeEquivGenerate₁ :
 #align Top.presheaf.is_limit_opens_le_equiv_generate₁ TopCat.Presheaf.isLimitOpensLeEquivGenerate₁
 
 /- warning: Top.presheaf.is_limit_opens_le_equiv_generate₂ -> TopCat.Presheaf.isLimitOpensLeEquivGenerate₂ is a dubious translation:
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=> R V f))) (fun (i : Sigma.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Subtype.{succ u1} (Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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Y) => R V f))) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V 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(fun (f : Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (CategoryTheory.Functor.id.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} 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(TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y) f))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (CategoryTheory.Presieve.diagram.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y (CategoryTheory.Sieve.arrows.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y (CategoryTheory.Sieve.generate.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y R))) (CategoryTheory.Presieve.cocone.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y (CategoryTheory.Sieve.arrows.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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(Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y R)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_limit_opens_le_equiv_generate₂ TopCat.Presheaf.isLimitOpensLeEquivGenerate₂ₓ'. -/
 /-- Given a presheaf `F` on the topological space `X` and a presieve `R` whose generated sieve
     is covering for the associated Grothendieck topology (equivalently, the presieve is covering

61db041a

bump to nightly-2023-05-25-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

2175c3c2

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module topology.sheaves.sheaf_condition.opens_le_cover
-! leanprover-community/mathlib commit 85d6221d32c37e68f05b2e42cde6cee658dae5e9
+! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Topology.Sheaves.SheafCondition.Sites
 /-!
 # Another version of the sheaf condition.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a family of open sets `U : ι → opens X` we can form the subcategory
 `{ V : opens X // ∃ i, V ≤ U i }`, which has `supr U` as a cocone.

85d6221d

bump to nightly-2023-05-23-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

869439c6

Diff

@@ -52,11 +52,13 @@ namespace Presheaf
 
 namespace SheafCondition
 
+#print TopCat.Presheaf.SheafCondition.OpensLeCover /-
 /-- The category of open sets contained in some element of the cover.
 -/
 def OpensLeCover : Type w :=
   FullSubcategory fun V : Opens X => ∃ i, V ≤ U i deriving Category
 #align Top.presheaf.sheaf_condition.opens_le_cover TopCat.Presheaf.SheafCondition.OpensLeCover
+-/
 
 instance [Inhabited ι] : Inhabited (OpensLeCover U) :=
   ⟨⟨⊥, default, bot_le⟩⟩
@@ -65,12 +67,20 @@ namespace OpensLeCover
 
 variable {U}
 
+#print TopCat.Presheaf.SheafCondition.OpensLeCover.index /-
 /-- An arbitrarily chosen index such that `V ≤ U i`.
 -/
 def index (V : OpensLeCover U) : ι :=
   V.property.some
 #align Top.presheaf.sheaf_condition.opens_le_cover.index TopCat.Presheaf.SheafCondition.OpensLeCover.index
+-/
 
+/- warning: Top.presheaf.sheaf_condition.opens_le_cover.hom_to_index -> TopCat.Presheaf.SheafCondition.OpensLeCover.homToIndex is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition.opens_le_cover.hom_to_index TopCat.Presheaf.SheafCondition.OpensLeCover.homToIndexₓ'. -/
 /-- The morphism from `V` to `U i` for some `i`.
 -/
 def homToIndex (V : OpensLeCover U) : V.obj ⟶ U (index V) :=
@@ -79,6 +89,12 @@ def homToIndex (V : OpensLeCover U) : V.obj ⟶ U (index V) :=
 
 end OpensLeCover
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align Top.presheaf.sheaf_condition.opens_le_cover_cocone TopCat.Presheaf.SheafCondition.opensLeCoverCoconeₓ'. -/
 /-- `supr U` as a cocone over the opens sets contained in some element of the cover.
 
 (In fact this is a colimit cocone.)
@@ -93,6 +109,7 @@ end SheafCondition
 
 open SheafCondition
 
+#print TopCat.Presheaf.IsSheafOpensLeCover /-
 /-- An equivalent formulation of the sheaf condition
 (which we prove equivalent to the usual one below as
 `is_sheaf_iff_is_sheaf_opens_le_cover`).
@@ -104,11 +121,18 @@ mapping down to any `V` which is contained in some `U i`.)
 def IsSheafOpensLeCover : Prop :=
   ∀ ⦃ι : Type w⦄ (U : ι → Opens X), Nonempty (IsLimit (F.mapCone (opensLeCoverCocone U).op))
 #align Top.presheaf.is_sheaf_opens_le_cover TopCat.Presheaf.IsSheafOpensLeCover
+-/
 
 section
 
 variable {Y : Opens X} (hY : Y = iSup U)
 
+/- warning: Top.presheaf.generate_equivalence_opens_le -> TopCat.Presheaf.generateEquivalenceOpensLe is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))))) (CategoryTheory.Comma.left.{u1, u1, u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} 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(Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.fromPUnit.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y) f)) (CategoryTheory.Comma.hom.{u1, u1, u1, u1, u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.fromPUnit.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y) f))) (TopCat.Presheaf.SheafCondition.instCategoryOpensLeCover.{u1} X ι U))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLeₓ'. -/
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
@@ -156,6 +180,12 @@ def generateEquivalenceOpensLe :
           rfl)
 #align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLe
 
+/- warning: Top.presheaf.whisker_iso_map_generate_cocone -> TopCat.Presheaf.whiskerIsoMapGenerateCocone is a dubious translation:
+lean 3 declaration is
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(CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (CategoryTheory.Functor.id.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) (CategoryTheory.Functor.fromPUnit.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y) f)))) C _inst_1 (CategoryTheory.Functor.comp.{u1, u1, u2, u1, u1, u3} (Opposite.{succ u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (CategoryTheory.Category.opposite.{u1, u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (CategoryTheory.FullSubcategory.category.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) (CategoryTheory.Category.opposite.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))))))) C _inst_1 (CategoryTheory.Functor.op.{u1, u1, u1, u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (CategoryTheory.FullSubcategory.category.{u1, 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(CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} 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u1, u1, u3} (Opposite.{succ u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (CategoryTheory.Category.opposite.{u1, u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) 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(TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i))))) (Opposite.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} 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F (CategoryTheory.Functor.op.{u1, u1, u1, u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} ι (fun (i : ι) => LE.le.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.toLE.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (CategoryTheory.FullSubcategory.category.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} 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+Case conversion may be inaccurate. Consider using '#align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCoconeₓ'. -/
 /-- Given a family of opens `opens_le_cover_cocone U` is essentially the natural cocone
     associated to the sieve generated by the presieve associated to `U` with indexing
     category changed using the above equivalence. -/
@@ -182,6 +212,12 @@ def whiskerIsoMapGenerateCocone :
     simp [eq_to_hom_map]
 #align Top.presheaf.whisker_iso_map_generate_cocone TopCat.Presheaf.whiskerIsoMapGenerateCocone
 
+/- warning: Top.presheaf.is_limit_opens_le_equiv_generate₁ -> TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {ι : Type.{u1}} (U : ι -> (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X))) {Y : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)}, (Eq.{succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) Y (iSup.{u1, succ u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (ConditionallyCompleteLattice.toSupSet.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, 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(TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) V (U i)))) (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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+Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_limit_opens_le_equiv_generate₁ TopCat.Presheaf.isLimitOpensLeEquivGenerate₁ₓ'. -/
 /-- Given a presheaf `F` on the topological space `X` and a family of opens `U` of `X`,
     the natural cone associated to `F` and `U` used in the definition of
     `F.is_sheaf_opens_le_cover` is a limit cone iff the natural cone associated to `F`
@@ -193,6 +229,12 @@ def isLimitOpensLeEquivGenerate₁ :
     (IsLimit.equivIsoLimit (whiskerIsoMapGenerateCocone F U hY))
 #align Top.presheaf.is_limit_opens_le_equiv_generate₁ TopCat.Presheaf.isLimitOpensLeEquivGenerate₁
 
+/- warning: Top.presheaf.is_limit_opens_le_equiv_generate₂ -> TopCat.Presheaf.isLimitOpensLeEquivGenerate₂ is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {X : TopCat.{u1}} (F : TopCat.Presheaf.{u1, u2, u3} C _inst_1 X) {Y : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)} (R : CategoryTheory.Presieve.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y), (Membership.mem.{u1, u1} (CategoryTheory.Sieve.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} 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(TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) (Opens.grothendieckTopology.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) Y)) -> (Equiv.{max (max (succ u3) (succ u1)) (succ u2), max (max (succ u3) (succ u1)) (succ u2)} (CategoryTheory.Limits.IsLimit.{u1, u2, u1, u3} (Opposite.{succ u1} (CategoryTheory.FullSubcategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Exists.{succ u1} (Sigma.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} 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=> R V f))) (fun (i : Sigma.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (fun (V : TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) => Subtype.{succ u1} (Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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(fun (f : Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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(fun (f : Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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(fun (f : Quiver.Hom.{succ u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) 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(Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y R))) (CategoryTheory.Presieve.cocone.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y (CategoryTheory.Sieve.arrows.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y (CategoryTheory.Sieve.generate.{u1, u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (Preorder.smallCategory.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (PartialOrder.toPreorder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteSemilatticeInf.toPartialOrder.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (TopologicalSpace.Opens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} X) (TopCat.topologicalSpace_coe.{u1} X)))))) Y R)))))))
+Case conversion may be inaccurate. Consider using '#align Top.presheaf.is_limit_opens_le_equiv_generate₂ TopCat.Presheaf.isLimitOpensLeEquivGenerate₂ₓ'. -/
 /-- Given a presheaf `F` on the topological space `X` and a presieve `R` whose generated sieve
     is covering for the associated Grothendieck topology (equivalently, the presieve is covering
     for the associated pretopology), the natural cone associated to `F` and the family of opens
@@ -211,6 +253,7 @@ def isLimitOpensLeEquivGenerate₂ (R : Presieve Y)
     rw [covering_presieve_eq_self R]
 #align Top.presheaf.is_limit_opens_le_equiv_generate₂ TopCat.Presheaf.isLimitOpensLeEquivGenerate₂
 
+#print TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover /-
 /-- A presheaf `(opens X)ᵒᵖ ⥤ C` on a topological space `X` is a sheaf on the site `opens X` iff
     it satisfies the `is_sheaf_opens_le_cover` sheaf condition. The latter is not the
     official definition of sheaves on spaces, but has the advantage that it does not
@@ -229,6 +272,7 @@ theorem isSheaf_iff_isSheafOpensLeCover : F.IsSheaf ↔ F.IsSheafOpensLeCover :=
     rw [← (is_limit_opens_le_equiv_generate₂ F S hS).nonempty_congr]
     apply h
 #align Top.presheaf.is_sheaf_iff_is_sheaf_opens_le_cover TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover
+-/
 
 end

85d6221d

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -85,7 +85,7 @@ end OpensLeCover
 -/
 def opensLeCoverCocone : Cocone (fullSubcategoryInclusion _ : OpensLeCover U ⥤ Opens X)
     where
-  pt := supᵢ U
+  pt := iSup U
   ι := { app := fun V : OpensLeCover U => V.homToIndex ≫ Opens.leSupr U _ }
 #align Top.presheaf.sheaf_condition.opens_le_cover_cocone TopCat.Presheaf.SheafCondition.opensLeCoverCocone
 
@@ -107,7 +107,7 @@ def IsSheafOpensLeCover : Prop :=
 
 section
 
-variable {Y : Opens X} (hY : Y = supᵢ U)
+variable {Y : Opens X} (hY : Y = iSup U)
 
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
@@ -130,9 +130,9 @@ def generateEquivalenceOpensLe :
         ⟨Over.mk
             (hY.substr
                 (let ⟨i, h⟩ := V.2
-                h.trans (le_supᵢ U i))).Hom,
+                h.trans (le_iSup U i))).Hom,
           let ⟨i, h⟩ := V.2
-          ⟨U i, h.Hom, (hY.substr (le_supᵢ U i)).Hom, ⟨i, rfl⟩, rfl⟩⟩
+          ⟨U i, h.Hom, (hY.substr (le_iSup U i)).Hom, ⟨i, rfl⟩, rfl⟩⟩
       map := fun _ _ g => Over.homMk g }
   unitIso :=
     eqToIso <|

85d6221d

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -205,8 +205,7 @@ def isLimitOpensLeEquivGenerate₂ (R : Presieve Y)
     IsLimit (F.mapCone (opensLeCoverCocone (coveringOfPresieve Y R)).op) ≃
       IsLimit (F.mapCone (Sieve.generate R).arrows.Cocone.op) :=
   by
-  convert
-      is_limit_opens_le_equiv_generate₁ F (covering_of_presieve Y R)
+  convert is_limit_opens_le_equiv_generate₁ F (covering_of_presieve Y R)
         (covering_of_presieve.supr_eq_of_mem_grothendieck Y R hR).symm using
       2 <;>
     rw [covering_presieve_eq_self R]

85d6221d

bump to nightly-2023-02-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

1fb1623f

Diff

@@ -85,7 +85,7 @@ end OpensLeCover
 -/
 def opensLeCoverCocone : Cocone (fullSubcategoryInclusion _ : OpensLeCover U ⥤ Opens X)
     where
-  x := supᵢ U
+  pt := supᵢ U
   ι := { app := fun V : OpensLeCover U => V.homToIndex ≫ Opens.leSupr U _ }
 #align Top.presheaf.sheaf_condition.opens_le_cover_cocone TopCat.Presheaf.SheafCondition.opensLeCoverCocone

85d6221d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

85d6221d

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -42,7 +42,6 @@ open CategoryTheory CategoryTheory.Limits TopologicalSpace TopologicalSpace.Open
 namespace TopCat
 
 variable {C : Type u} [Category.{v} C]
-
 variable {X : TopCat.{w}} (F : Presheaf C X) {ι : Type w} (U : ι → Opens X)
 
 namespace Presheaf

85d6221d

style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

86b84c52

Diff

@@ -56,7 +56,7 @@ def OpensLeCover : Type w :=
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.sheaf_condition.opens_le_cover TopCat.Presheaf.SheafCondition.OpensLeCover
 
--- Porting note : failed to derive `category`
+-- Porting note: failed to derive `category`
 instance : Category (OpensLeCover U) := FullSubcategory.category _
 
 instance [h : Nonempty ι] : Inhabited (OpensLeCover U) :=
@@ -113,7 +113,7 @@ section
 
 variable {Y : Opens X} (hY : Y = iSup U)
 
--- Porting note : split it out to prevent timeout
+-- Porting note: split it out to prevent timeout
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
@@ -129,7 +129,7 @@ def generateEquivalenceOpensLe_functor' :
       ⟨i, hY ▸ h.le⟩⟩
   map := fun {_ _} g => g.left }
 
--- Porting note : split it out to prevent timeout
+-- Porting note: split it out to prevent timeout
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
@@ -162,7 +162,7 @@ def generateEquivalenceOpensLe_inverse' :
 def generateEquivalenceOpensLe :
     (FullSubcategory fun f : Over Y => (Sieve.generate (presieveOfCoveringAux U Y)).arrows f.hom) ≌
     OpensLeCover U where
-  -- Porting note : split it out to prevent timeout
+  -- Porting note: split it out to prevent timeout
   functor := generateEquivalenceOpensLe_functor' _ _
   inverse := generateEquivalenceOpensLe_inverse' _ _
   unitIso := eqToIso <| CategoryTheory.Functor.ext

85d6221d

chore(Topology): Inhabited -> Nonempty (#10647)

996ae393

Diff

@@ -59,8 +59,8 @@ set_option linter.uppercaseLean3 false in
 -- Porting note : failed to derive `category`
 instance : Category (OpensLeCover U) := FullSubcategory.category _
 
-instance [Inhabited ι] : Inhabited (OpensLeCover U) :=
-  ⟨⟨⊥, default, bot_le⟩⟩
+instance [h : Nonempty ι] : Inhabited (OpensLeCover U) :=
+  ⟨⟨⊥, let ⟨i⟩ := h; ⟨i, bot_le⟩⟩⟩
 
 namespace OpensLeCover

85d6221d

chore: exactly 4 spaces in subsequent lines for def (#7321)

Co-authored-by: Moritz Firsching <firsching@google.com>

11dbfb2b

Diff

@@ -121,7 +121,7 @@ variable {Y : Opens X} (hY : Y = iSup U)
     category of opens contained in some `U i`. -/
 @[simps]
 def generateEquivalenceOpensLe_functor' :
-  (FullSubcategory fun f : Over Y => (Sieve.generate (presieveOfCoveringAux U Y)).arrows f.hom) ⥤
+    (FullSubcategory fun f : Over Y => (Sieve.generate (presieveOfCoveringAux U Y)).arrows f.hom) ⥤
     OpensLeCover U :=
 { obj := fun f =>
     ⟨f.1.left,

85d6221d

chore: replace ConeMorphism.Hom by ConeMorphism.hom (#7176)

3e44bb07

Diff

@@ -181,13 +181,13 @@ def whiskerIsoMapGenerateCocone :
     (F.mapCone (opensLeCoverCocone U).op).whisker (generateEquivalenceOpensLe U hY).op.functor ≅
       F.mapCone (Sieve.generate (presieveOfCoveringAux U Y)).arrows.cocone.op where
   hom :=
-    { Hom := F.map (eqToHom (congr_arg op hY.symm))
+    { hom := F.map (eqToHom (congr_arg op hY.symm))
       w := fun j => by
         erw [← F.map_comp]
         dsimp
         congr 1 }
   inv :=
-    { Hom := F.map (eqToHom (congr_arg op hY))
+    { hom := F.map (eqToHom (congr_arg op hY))
       w := fun j => by
         erw [← F.map_comp]
         dsimp

85d6221d

chore: tidy various files (#7041)

4a238556

Diff

@@ -10,8 +10,8 @@ import Mathlib.Topology.Sheaves.SheafCondition.Sites
 /-!
 # Another version of the sheaf condition.
 
-Given a family of open sets `U : ι → opens X` we can form the subcategory
-`{ V : opens X // ∃ i, V ≤ U i }`, which has `iSup U` as a cocone.
+Given a family of open sets `U : ι → Opens X` we can form the subcategory
+`{ V : Opens X // ∃ i, V ≤ U i }`, which has `iSup U` as a cocone.
 
 The sheaf condition on a presheaf `F` is equivalent to
 `F` sending the opposite of this cocone to a limit cone in `C`, for every `U`.
@@ -24,7 +24,7 @@ or equivalently whether we're looking at the first or second object in an equali
 ## Main statement
 
 `TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover`: for a presheaf on a topological space,
-the sheaf condition in terms of Grothendieck topology is equivalent to the `opens_le_cover`
+the sheaf condition in terms of Grothendieck topology is equivalent to the `OpensLeCover`
 sheaf condition. This result will be used to further connect to other sheaf conditions on spaces,
 like `pairwise_intersections` and `equalizer_products`.
 
@@ -98,10 +98,10 @@ open SheafCondition
 
 /-- An equivalent formulation of the sheaf condition
 (which we prove equivalent to the usual one below as
-`is_sheaf_iff_is_sheaf_opens_le_cover`).
+`isSheaf_iff_isSheafOpensLeCover`).
 
-A presheaf is a sheaf if `F` sends the cone `(opens_le_cover_cocone U).op` to a limit cone.
-(Recall `opens_le_cover_cocone U`, has cone point `iSup U`,
+A presheaf is a sheaf if `F` sends the cone `(opensLeCoverCocone U).op` to a limit cone.
+(Recall `opensLeCoverCocone U`, has cone point `iSup U`,
 mapping down to any `V` which is contained in some `U i`.)
 -/
 def IsSheafOpensLeCover : Prop :=
@@ -117,7 +117,7 @@ variable {Y : Opens X} (hY : Y = iSup U)
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
-    in the sieve. This full subcategory is equivalent to `opens_le_cover U`, the (poset)
+    in the sieve. This full subcategory is equivalent to `OpensLeCover U`, the (poset)
     category of opens contained in some `U i`. -/
 @[simps]
 def generateEquivalenceOpensLe_functor' :
@@ -133,7 +133,7 @@ def generateEquivalenceOpensLe_functor' :
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
-    in the sieve. This full subcategory is equivalent to `opens_le_cover U`, the (poset)
+    in the sieve. This full subcategory is equivalent to `OpensLeCover U`, the (poset)
     category of opens contained in some `U i`. -/
 @[simps]
 def generateEquivalenceOpensLe_inverse' :
@@ -156,7 +156,7 @@ def generateEquivalenceOpensLe_inverse' :
 /-- Given a family of opens `U` and an open `Y` equal to the union of opens in `U`, we may
     take the presieve on `Y` associated to `U` and the sieve generated by it, and form the
     full subcategory (subposet) of opens contained in `Y` (`over Y`) consisting of arrows
-    in the sieve. This full subcategory is equivalent to `opens_le_cover U`, the (poset)
+    in the sieve. This full subcategory is equivalent to `OpensLeCover U`, the (poset)
     category of opens contained in some `U i`. -/
 @[simps]
 def generateEquivalenceOpensLe :
@@ -173,7 +173,7 @@ def generateEquivalenceOpensLe :
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.generate_equivalence_opens_le TopCat.Presheaf.generateEquivalenceOpensLe
 
-/-- Given a family of opens `opens_le_cover_cocone U` is essentially the natural cocone
+/-- Given a family of opens `opensLeCoverCocone U` is essentially the natural cocone
     associated to the sieve generated by the presieve associated to `U` with indexing
     category changed using the above equivalence. -/
 @[simps]
@@ -203,7 +203,7 @@ set_option linter.uppercaseLean3 false in
 
 /-- Given a presheaf `F` on the topological space `X` and a family of opens `U` of `X`,
     the natural cone associated to `F` and `U` used in the definition of
-    `F.is_sheaf_opens_le_cover` is a limit cone iff the natural cone associated to `F`
+    `F.IsSheafOpensLeCover` is a limit cone iff the natural cone associated to `F`
     and the sieve generated by the presieve associated to `U` is a limit cone. -/
 def isLimitOpensLeEquivGenerate₁ :
     IsLimit (F.mapCone (opensLeCoverCocone U).op) ≃
@@ -231,7 +231,7 @@ set_option linter.uppercaseLean3 false in
 #align Top.presheaf.is_limit_opens_le_equiv_generate₂ TopCat.Presheaf.isLimitOpensLeEquivGenerate₂
 
 /-- A presheaf `(opens X)ᵒᵖ ⥤ C` on a topological space `X` is a sheaf on the site `opens X` iff
-    it satisfies the `is_sheaf_opens_le_cover` sheaf condition. The latter is not the
+    it satisfies the `IsSheafOpensLeCover` sheaf condition. The latter is not the
     official definition of sheaves on spaces, but has the advantage that it does not
     require `has_products C`. -/
 theorem isSheaf_iff_isSheafOpensLeCover : F.IsSheaf ↔ F.IsSheafOpensLeCover := by

85d6221d

feat: make congr!'s typeEq plausibility heuristic consider binder info (#5900)

There are cases where we want convert/congr! to generate equalities between types, even if they don't pass the plausibility test. The examples involve types that are explicit arguments without forward dependencies, which seems like a reasonable rule to try out. We exclude forward dependencies because those lead to heterogenous equalities.

7bedbaeb

Diff

@@ -225,7 +225,7 @@ def isLimitOpensLeEquivGenerate₂ (R : Presieve Y)
     IsLimit (F.mapCone (opensLeCoverCocone (coveringOfPresieve Y R)).op) ≃
       IsLimit (F.mapCone (Sieve.generate R).arrows.cocone.op) := by
   convert isLimitOpensLeEquivGenerate₁ F (coveringOfPresieve Y R)
-      (coveringOfPresieve.iSup_eq_of_mem_grothendieck Y R hR).symm using 2
+      (coveringOfPresieve.iSup_eq_of_mem_grothendieck Y R hR).symm using 1
   rw [covering_presieve_eq_self R]
 set_option linter.uppercaseLean3 false in
 #align Top.presheaf.is_limit_opens_le_equiv_generate₂ TopCat.Presheaf.isLimitOpensLeEquivGenerate₂

85d6221d

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module topology.sheaves.sheaf_condition.opens_le_cover
-! leanprover-community/mathlib commit 85d6221d32c37e68f05b2e42cde6cee658dae5e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Sheaves.SheafCondition.Sites
 
+#align_import topology.sheaves.sheaf_condition.opens_le_cover from "leanprover-community/mathlib"@"85d6221d32c37e68f05b2e42cde6cee658dae5e9"
+
 /-!
 # Another version of the sheaf condition.

85d6221d

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -14,7 +14,7 @@ import Mathlib.Topology.Sheaves.SheafCondition.Sites
 # Another version of the sheaf condition.
 
 Given a family of open sets `U : ι → opens X` we can form the subcategory
-`{ V : opens X // ∃ i, V ≤ U i }`, which has `supr U` as a cocone.
+`{ V : opens X // ∃ i, V ≤ U i }`, which has `iSup U` as a cocone.
 
 The sheaf condition on a presheaf `F` is equivalent to
 `F` sending the opposite of this cocone to a limit cone in `C`, for every `U`.
@@ -26,7 +26,7 @@ or equivalently whether we're looking at the first or second object in an equali
 
 ## Main statement
 
-`Top.presheaf.is_sheaf_iff_is_sheaf_opens_le_cover`: for a presheaf on a topological space,
+`TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover`: for a presheaf on a topological space,
 the sheaf condition in terms of Grothendieck topology is equivalent to the `opens_le_cover`
 sheaf condition. This result will be used to further connect to other sheaf conditions on spaces,
 like `pairwise_intersections` and `equalizer_products`.
@@ -85,7 +85,7 @@ set_option linter.uppercaseLean3 false in
 
 end OpensLeCover
 
-/-- `supr U` as a cocone over the opens sets contained in some element of the cover.
+/-- `iSup U` as a cocone over the opens sets contained in some element of the cover.
 
 (In fact this is a colimit cocone.)
 -/
@@ -104,7 +104,7 @@ open SheafCondition
 `is_sheaf_iff_is_sheaf_opens_le_cover`).
 
 A presheaf is a sheaf if `F` sends the cone `(opens_le_cover_cocone U).op` to a limit cone.
-(Recall `opens_le_cover_cocone U`, has cone point `supr U`,
+(Recall `opens_le_cover_cocone U`, has cone point `iSup U`,
 mapping down to any `V` which is contained in some `U i`.)
 -/
 def IsSheafOpensLeCover : Prop :=

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feat: port Topology.Sheaves.SheafCondition.OpensLeCover (#4273)

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`topology.sheaves.sheaf_condition.opens_le_cover` ⟷ `Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 452

topology.sheaves.sheaf_condition.opens_le_cover ⟷ Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 452

`topology.sheaves.sheaf_condition.opens_le_cover` ⟷ `Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover`