topology.sheaves.local_predicate | Mathlib porting status

(last sync)

chore(topology/sheaves): revert universe generalizations from #19153 (#19230)

This reverts commit 13361559.

These are just too difficult to forward port as is because of the max u v =?= max u ?v issue https://github.com/leanprover/lean4/issues/2297.

We have another candidate approach to this, using a new UnivLE typeclass, and I would prefer if we investigated that without the pressure of the port at the same time.

This will delay @hrmacbeth's plans to define meromorphic functions, perhaps.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff

@@ -38,12 +38,12 @@ to the types in the ambient type family.
 We give conditions sufficient to show that this map is injective and/or surjective.
 -/
 
-universes v w
+universe v
 
 noncomputable theory
 
 variables {X : Top.{v}}
-variables (T : X → Type w)
+variables (T : X → Type v)
 
 open topological_space
 open opposite
@@ -69,12 +69,12 @@ variables (X)
 Continuity is a "prelocal" predicate on functions to a fixed topological space `T`.
 -/
 @[simps]
-def continuous_prelocal (T : Top.{w}) : prelocal_predicate (λ x : X, T) :=
+def continuous_prelocal (T : Top.{v}) : prelocal_predicate (λ x : X, T) :=
 { pred := λ U f, continuous f,
   res := λ U V i f h, continuous.comp h (opens.open_embedding_of_le i.le).continuous, }
 
 /-- Satisfying the inhabited linter. -/
-instance inhabited_prelocal_predicate (T : Top.{w}) : inhabited (prelocal_predicate (λ x : X, T)) :=
+instance inhabited_prelocal_predicate (T : Top.{v}) : inhabited (prelocal_predicate (λ x : X, T)) :=
 ⟨continuous_prelocal X T⟩
 
 variables {X}
@@ -150,7 +150,7 @@ lemma prelocal_predicate.sheafify_of {T : X → Type v} {P : prelocal_predicate
 The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
 -/
 @[simps]
-def subpresheaf_to_Types (P : prelocal_predicate T) : presheaf (Type (max v w)) X :=
+def subpresheaf_to_Types (P : prelocal_predicate T) : presheaf (Type v) X :=
 { obj := λ U, { f : Π x : unop U, T x // P.pred f },
   map := λ U V i f, ⟨λ x, f.1 (i.unop x), P.res i.unop f.1 f.2⟩ }.
 
@@ -211,27 +211,22 @@ end subpresheaf_to_Types
 The subsheaf of the sheaf of all dependently typed functions satisfying the local predicate `P`.
 -/
 @[simps]
-def subsheaf_to_Types (P : local_predicate T) : sheaf (Type max v w) X :=
+def subsheaf_to_Types (P : local_predicate T) : sheaf (Type v) X :=
 ⟨subpresheaf_to_Types P.to_prelocal_predicate, subpresheaf_to_Types.is_sheaf P⟩
 
--- TODO There is further universe generalization to do here,
--- but it depends on more difficult universe generalization in `topology.sheaves.stalks`.
--- The aim is to replace `T'` with the more general `T` below.
-variables {T' : X → Type v}
-
 /--
 There is a canonical map from the stalk to the original fiber, given by evaluating sections.
 -/
-def stalk_to_fiber (P : local_predicate T') (x : X) :
-  (subsheaf_to_Types P).presheaf.stalk x ⟶ T' x :=
+def stalk_to_fiber (P : local_predicate T) (x : X) :
+  (subsheaf_to_Types P).presheaf.stalk x ⟶ T x :=
 begin
   refine colimit.desc _
-    { X := T' x, ι := { app := λ U f, _, naturality' := _ } },
+    { X := T x, ι := { app := λ U f, _, naturality' := _ } },
   { exact f.1 ⟨x, (unop U).2⟩, },
   { tidy, }
 end
 
-@[simp] lemma stalk_to_fiber_germ (P : local_predicate T') (U : opens X) (x : U) (f) :
+@[simp] lemma stalk_to_fiber_germ (P : local_predicate T) (U : opens X) (x : U) (f) :
   stalk_to_fiber P x ((subsheaf_to_Types P).presheaf.germ x f) = f.1 x :=
 begin
   dsimp [presheaf.germ, stalk_to_fiber],
@@ -244,8 +239,8 @@ end
 The `stalk_to_fiber` map is surjective at `x` if
 every point in the fiber `T x` has an allowed section passing through it.
 -/
-lemma stalk_to_fiber_surjective (P : local_predicate T') (x : X)
-  (w : ∀ (t : T' x), ∃ (U : open_nhds x) (f : Π y : U.1, T' y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
+lemma stalk_to_fiber_surjective (P : local_predicate T) (x : X)
+  (w : ∀ (t : T x), ∃ (U : open_nhds x) (f : Π y : U.1, T y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
   function.surjective (stalk_to_fiber P x) :=
 λ t,
 begin
@@ -259,16 +254,16 @@ end
 The `stalk_to_fiber` map is injective at `x` if any two allowed sections which agree at `x`
 agree on some neighborhood of `x`.
 -/
-lemma stalk_to_fiber_injective (P : local_predicate T') (x : X)
-  (w : ∀ (U V : open_nhds x) (fU : Π y : U.1, T' y) (hU : P.pred fU)
-    (fV : Π y : V.1, T' y) (hV : P.pred fV) (e : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
+lemma stalk_to_fiber_injective (P : local_predicate T) (x : X)
+  (w : ∀ (U V : open_nhds x) (fU : Π y : U.1, T y) (hU : P.pred fU)
+    (fV : Π y : V.1, T y) (hV : P.pred fV) (e : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
     ∃ (W : open_nhds x) (iU : W ⟶ U) (iV : W ⟶ V), ∀ (w : W.1), fU (iU w : U.1) = fV (iV w : V.1)) :
   function.injective (stalk_to_fiber P x) :=
 λ tU tV h,
 begin
   -- We promise to provide all the ingredients of the proof later:
   let Q :
-    ∃ (W : (open_nhds x)ᵒᵖ) (s : Π w : (unop W).1, T' w) (hW : P.pred s),
+    ∃ (W : (open_nhds x)ᵒᵖ) (s : Π w : (unop W).1, T w) (hW : P.pred s),
       tU = (subsheaf_to_Types P).presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ ∧
       tV = (subsheaf_to_Types P).presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ := _,
   { choose W s hW e using Q,
@@ -288,9 +283,6 @@ begin
            colimit_sound iV.op (subtype.eq (funext w).symm)⟩, },
 end
 
--- TODO to continue generalizing universes here, we will need to deal with the issue noted
--- at `presheaf_to_Top` (universe generalization for the Yoneda embedding).
-
 /--
 Some repackaging:
 the presheaf of functions satisfying `continuous_prelocal` is just the same thing as

chore(topology/sheaves/*): universe generalizations (#19153)

Necessary but sadly insufficient for the request at https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/.2319146.20sheaves.20on.20manifolds

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff

@@ -38,12 +38,12 @@ to the types in the ambient type family.
 We give conditions sufficient to show that this map is injective and/or surjective.
 -/
 
-universe v
+universes v w
 
 noncomputable theory
 
 variables {X : Top.{v}}
-variables (T : X → Type v)
+variables (T : X → Type w)
 
 open topological_space
 open opposite
@@ -69,12 +69,12 @@ variables (X)
 Continuity is a "prelocal" predicate on functions to a fixed topological space `T`.
 -/
 @[simps]
-def continuous_prelocal (T : Top.{v}) : prelocal_predicate (λ x : X, T) :=
+def continuous_prelocal (T : Top.{w}) : prelocal_predicate (λ x : X, T) :=
 { pred := λ U f, continuous f,
   res := λ U V i f h, continuous.comp h (opens.open_embedding_of_le i.le).continuous, }
 
 /-- Satisfying the inhabited linter. -/
-instance inhabited_prelocal_predicate (T : Top.{v}) : inhabited (prelocal_predicate (λ x : X, T)) :=
+instance inhabited_prelocal_predicate (T : Top.{w}) : inhabited (prelocal_predicate (λ x : X, T)) :=
 ⟨continuous_prelocal X T⟩
 
 variables {X}
@@ -150,7 +150,7 @@ lemma prelocal_predicate.sheafify_of {T : X → Type v} {P : prelocal_predicate
 The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
 -/
 @[simps]
-def subpresheaf_to_Types (P : prelocal_predicate T) : presheaf (Type v) X :=
+def subpresheaf_to_Types (P : prelocal_predicate T) : presheaf (Type (max v w)) X :=
 { obj := λ U, { f : Π x : unop U, T x // P.pred f },
   map := λ U V i f, ⟨λ x, f.1 (i.unop x), P.res i.unop f.1 f.2⟩ }.
 
@@ -211,22 +211,27 @@ end subpresheaf_to_Types
 The subsheaf of the sheaf of all dependently typed functions satisfying the local predicate `P`.
 -/
 @[simps]
-def subsheaf_to_Types (P : local_predicate T) : sheaf (Type v) X :=
+def subsheaf_to_Types (P : local_predicate T) : sheaf (Type max v w) X :=
 ⟨subpresheaf_to_Types P.to_prelocal_predicate, subpresheaf_to_Types.is_sheaf P⟩
 
+-- TODO There is further universe generalization to do here,
+-- but it depends on more difficult universe generalization in `topology.sheaves.stalks`.
+-- The aim is to replace `T'` with the more general `T` below.
+variables {T' : X → Type v}
+
 /--
 There is a canonical map from the stalk to the original fiber, given by evaluating sections.
 -/
-def stalk_to_fiber (P : local_predicate T) (x : X) :
-  (subsheaf_to_Types P).presheaf.stalk x ⟶ T x :=
+def stalk_to_fiber (P : local_predicate T') (x : X) :
+  (subsheaf_to_Types P).presheaf.stalk x ⟶ T' x :=
 begin
   refine colimit.desc _
-    { X := T x, ι := { app := λ U f, _, naturality' := _ } },
+    { X := T' x, ι := { app := λ U f, _, naturality' := _ } },
   { exact f.1 ⟨x, (unop U).2⟩, },
   { tidy, }
 end
 
-@[simp] lemma stalk_to_fiber_germ (P : local_predicate T) (U : opens X) (x : U) (f) :
+@[simp] lemma stalk_to_fiber_germ (P : local_predicate T') (U : opens X) (x : U) (f) :
   stalk_to_fiber P x ((subsheaf_to_Types P).presheaf.germ x f) = f.1 x :=
 begin
   dsimp [presheaf.germ, stalk_to_fiber],
@@ -239,8 +244,8 @@ end
 The `stalk_to_fiber` map is surjective at `x` if
 every point in the fiber `T x` has an allowed section passing through it.
 -/
-lemma stalk_to_fiber_surjective (P : local_predicate T) (x : X)
-  (w : ∀ (t : T x), ∃ (U : open_nhds x) (f : Π y : U.1, T y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
+lemma stalk_to_fiber_surjective (P : local_predicate T') (x : X)
+  (w : ∀ (t : T' x), ∃ (U : open_nhds x) (f : Π y : U.1, T' y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
   function.surjective (stalk_to_fiber P x) :=
 λ t,
 begin
@@ -254,16 +259,16 @@ end
 The `stalk_to_fiber` map is injective at `x` if any two allowed sections which agree at `x`
 agree on some neighborhood of `x`.
 -/
-lemma stalk_to_fiber_injective (P : local_predicate T) (x : X)
-  (w : ∀ (U V : open_nhds x) (fU : Π y : U.1, T y) (hU : P.pred fU)
-    (fV : Π y : V.1, T y) (hV : P.pred fV) (e : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
+lemma stalk_to_fiber_injective (P : local_predicate T') (x : X)
+  (w : ∀ (U V : open_nhds x) (fU : Π y : U.1, T' y) (hU : P.pred fU)
+    (fV : Π y : V.1, T' y) (hV : P.pred fV) (e : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
     ∃ (W : open_nhds x) (iU : W ⟶ U) (iV : W ⟶ V), ∀ (w : W.1), fU (iU w : U.1) = fV (iV w : V.1)) :
   function.injective (stalk_to_fiber P x) :=
 λ tU tV h,
 begin
   -- We promise to provide all the ingredients of the proof later:
   let Q :
-    ∃ (W : (open_nhds x)ᵒᵖ) (s : Π w : (unop W).1, T w) (hW : P.pred s),
+    ∃ (W : (open_nhds x)ᵒᵖ) (s : Π w : (unop W).1, T' w) (hW : P.pred s),
       tU = (subsheaf_to_Types P).presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ ∧
       tV = (subsheaf_to_Types P).presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ := _,
   { choose W s hW e using Q,
@@ -283,6 +288,9 @@ begin
            colimit_sound iV.op (subtype.eq (funext w).symm)⟩, },
 end
 
+-- TODO to continue generalizing universes here, we will need to deal with the issue noted
+-- at `presheaf_to_Top` (universe generalization for the Yoneda embedding).
+
 /--
 Some repackaging:
 the presheaf of functions satisfying `continuous_prelocal` is just the same thing as

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -5,7 +5,7 @@ Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
 import Topology.Sheaves.SheafOfFunctions
 import Topology.Sheaves.Stalks
-import Topology.LocalHomeomorph
+import Topology.PartialHomeomorph
 import Topology.Sheaves.SheafCondition.UniqueGluing
 
 #align_import topology.sheaves.local_predicate from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -128,8 +128,8 @@ def continuousLocal (T : TopCat.{v}) : LocalPredicate fun x : X => T :=
       intro x
       specialize w x
       rcases w with ⟨V, m, i, w⟩
-      dsimp at w 
-      rw [continuous_iff_continuousAt] at w 
+      dsimp at w
+      rw [continuous_iff_continuousAt] at w
       specialize w ⟨x, m⟩
       simpa using (opens.open_embedding_of_le i.le).continuousAt_iff.1 w }
 #align Top.continuous_local TopCat.continuousLocal
@@ -315,7 +315,7 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
   obtain ⟨V, ⟨fV, hV⟩, rfl⟩ := jointly_surjective'.{v, v} tV
   · -- Decompose everything into its constituent parts:
     dsimp
-    simp only [stalk_to_fiber, types.colimit.ι_desc_apply'] at h 
+    simp only [stalk_to_fiber, types.colimit.ι_desc_apply'] at h
     specialize w (unop U) (unop V) fU hU fV hV h
     rcases w with ⟨W, iU, iV, w⟩
     -- and put it back together again in the correct order.

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
-import Mathbin.Topology.Sheaves.SheafOfFunctions
-import Mathbin.Topology.Sheaves.Stalks
-import Mathbin.Topology.LocalHomeomorph
-import Mathbin.Topology.Sheaves.SheafCondition.UniqueGluing
+import Topology.Sheaves.SheafOfFunctions
+import Topology.Sheaves.Stalks
+import Topology.LocalHomeomorph
+import Topology.Sheaves.SheafCondition.UniqueGluing
 
 #align_import topology.sheaves.local_predicate from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module topology.sheaves.local_predicate
-! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Sheaves.SheafOfFunctions
 import Mathbin.Topology.Sheaves.Stalks
 import Mathbin.Topology.LocalHomeomorph
 import Mathbin.Topology.Sheaves.SheafCondition.UniqueGluing
 
+#align_import topology.sheaves.local_predicate from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"
+
 /-!
 # Functions satisfying a local predicate form a sheaf.

bump to nightly-2023-07-05-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

3fd81375

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.sheaves.local_predicate
-! leanprover-community/mathlib commit 13361559d66b84f80b6d5a1c4a26aa5054766725
+! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -44,13 +44,13 @@ We give conditions sufficient to show that this map is injective and/or surjecti
 -/
 
 
-universe v w
+universe v
 
 noncomputable section
 
 variable {X : TopCat.{v}}
 
-variable (T : X → Type w)
+variable (T : X → Type v)
 
 open TopologicalSpace
 
@@ -64,6 +64,7 @@ open CategoryTheory.Limits.Types
 
 namespace TopCat
 
+#print TopCat.PrelocalPredicate /-
 /-- Given a topological space `X : Top` and a type family `T : X → Type`,
 a `P : prelocal_predicate T` consists of:
 * a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
@@ -73,7 +74,8 @@ a `P : prelocal_predicate T` consists of:
 structure PrelocalPredicate where
   pred : ∀ {U : Opens X}, (∀ x : U, T x) → Prop
   res : ∀ {U V : Opens X} (i : U ⟶ V) (f : ∀ x : V, T x) (h : pred f), pred fun x : U => f (i x)
-#align Top.prelocal_predicate TopCat.PrelocalPredicateₓ
+#align Top.prelocal_predicate TopCat.PrelocalPredicate
+-/
 
 variable (X)
 
@@ -81,7 +83,7 @@ variable (X)
 /-- Continuity is a "prelocal" predicate on functions to a fixed topological space `T`.
 -/
 @[simps]
-def continuousPrelocal (T : TopCat.{w}) : PrelocalPredicate fun x : X => T
+def continuousPrelocal (T : TopCat.{v}) : PrelocalPredicate fun x : X => T
     where
   pred U f := Continuous f
   res U V i f h := Continuous.comp h (Opens.openEmbedding_of_le i.le).Continuous
@@ -90,7 +92,7 @@ def continuousPrelocal (T : TopCat.{w}) : PrelocalPredicate fun x : X => T
 
 #print TopCat.inhabitedPrelocalPredicate /-
 /-- Satisfying the inhabited linter. -/
-instance inhabitedPrelocalPredicate (T : TopCat.{w}) :
+instance inhabitedPrelocalPredicate (T : TopCat.{v}) :
     Inhabited (PrelocalPredicate fun x : X => T) :=
   ⟨continuousPrelocal X T⟩
 #align Top.inhabited_prelocal_predicate TopCat.inhabitedPrelocalPredicate
@@ -98,6 +100,7 @@ instance inhabitedPrelocalPredicate (T : TopCat.{w}) :
 
 variable {X}
 
+#print TopCat.LocalPredicate /-
 /-- Given a topological space `X : Top` and a type family `T : X → Type`,
 a `P : local_predicate T` consists of:
 * a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
@@ -113,7 +116,8 @@ structure LocalPredicate extends PrelocalPredicate T where
     ∀ {U : Opens X} (f : ∀ x : U, T x)
       (w : ∀ x : U, ∃ (V : Opens X) (m : x.1 ∈ V) (i : V ⟶ U), pred fun x : V => f (i x : U)),
       pred f
-#align Top.local_predicate TopCat.LocalPredicateₓ
+#align Top.local_predicate TopCat.LocalPredicate
+-/
 
 variable (X)
 
@@ -175,7 +179,7 @@ theorem PrelocalPredicate.sheafifyOf {T : X → Type v} {P : PrelocalPredicate T
 /-- The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
 -/
 @[simps]
-def subpresheafToTypes (P : PrelocalPredicate T) : Presheaf (Type max v w) X
+def subpresheafToTypes (P : PrelocalPredicate T) : Presheaf (Type v) X
     where
   obj U := { f : ∀ x : unop U, T x // P.pred f }
   map U V i f := ⟨fun x => f.1 (i.unop x), P.res i.unop f.1 f.2⟩
@@ -241,24 +245,19 @@ end SubpresheafToTypes
 /-- The subsheaf of the sheaf of all dependently typed functions satisfying the local predicate `P`.
 -/
 @[simps]
-def subsheafToTypes (P : LocalPredicate T) : Sheaf (Type max v w) X :=
+def subsheafToTypes (P : LocalPredicate T) : Sheaf (Type v) X :=
   ⟨subpresheafToTypes P.toPrelocalPredicate, subpresheafToTypes.isSheaf P⟩
 #align Top.subsheaf_to_Types TopCat.subsheafToTypes
 -/
 
--- TODO There is further universe generalization to do here,
--- but it depends on more difficult universe generalization in `topology.sheaves.stalks`.
--- The aim is to replace `T'` with the more general `T` below.
-variable {T' : X → Type v}
-
 #print TopCat.stalkToFiber /-
 /-- There is a canonical map from the stalk to the original fiber, given by evaluating sections.
 -/
-def stalkToFiber (P : LocalPredicate T') (x : X) : (subsheafToTypes P).Presheaf.stalk x ⟶ T' x :=
+def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).Presheaf.stalk x ⟶ T x :=
   by
   refine'
     colimit.desc _
-      { pt := T' x
+      { pt := T x
         ι :=
           { app := fun U f => _
             naturality' := _ } }
@@ -269,7 +268,7 @@ def stalkToFiber (P : LocalPredicate T') (x : X) : (subsheafToTypes P).Presheaf.
 
 #print TopCat.stalkToFiber_germ /-
 @[simp]
-theorem stalkToFiber_germ (P : LocalPredicate T') (U : Opens X) (x : U) (f) :
+theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
     stalkToFiber P x ((subsheafToTypes P).Presheaf.germ x f) = f.1 x :=
   by
   dsimp [presheaf.germ, stalk_to_fiber]
@@ -283,8 +282,8 @@ theorem stalkToFiber_germ (P : LocalPredicate T') (U : Opens X) (x : U) (f) :
 /-- The `stalk_to_fiber` map is surjective at `x` if
 every point in the fiber `T x` has an allowed section passing through it.
 -/
-theorem stalkToFiber_surjective (P : LocalPredicate T') (x : X)
-    (w : ∀ t : T' x, ∃ (U : OpenNhds x) (f : ∀ y : U.1, T' y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
+theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
+    (w : ∀ t : T x, ∃ (U : OpenNhds x) (f : ∀ y : U.1, T y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
     Function.Surjective (stalkToFiber P x) := fun t =>
   by
   rcases w t with ⟨U, f, h, rfl⟩
@@ -298,9 +297,9 @@ theorem stalkToFiber_surjective (P : LocalPredicate T') (x : X)
 /-- The `stalk_to_fiber` map is injective at `x` if any two allowed sections which agree at `x`
 agree on some neighborhood of `x`.
 -/
-theorem stalkToFiber_injective (P : LocalPredicate T') (x : X)
+theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
     (w :
-      ∀ (U V : OpenNhds x) (fU : ∀ y : U.1, T' y) (hU : P.pred fU) (fV : ∀ y : V.1, T' y)
+      ∀ (U V : OpenNhds x) (fU : ∀ y : U.1, T y) (hU : P.pred fU) (fV : ∀ y : V.1, T y)
         (hV : P.pred fV) (e : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
         ∃ (W : OpenNhds x) (iU : W ⟶ U) (iV : W ⟶ V),
           ∀ w : W.1, fU (iU w : U.1) = fV (iV w : V.1)) :
@@ -308,7 +307,7 @@ theorem stalkToFiber_injective (P : LocalPredicate T') (x : X)
   by
   -- We promise to provide all the ingredients of the proof later:
   let Q :
-    ∃ (W : (open_nhds x)ᵒᵖ) (s : ∀ w : (unop W).1, T' w) (hW : P.pred s),
+    ∃ (W : (open_nhds x)ᵒᵖ) (s : ∀ w : (unop W).1, T w) (hW : P.pred s),
       tU = (subsheaf_to_Types P).Presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ ∧
         tV = (subsheaf_to_Types P).Presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ :=
     _
@@ -330,8 +329,6 @@ theorem stalkToFiber_injective (P : LocalPredicate T') (x : X)
 -/
 
 #print TopCat.subpresheafContinuousPrelocalIsoPresheafToTop /-
--- TODO to continue generalizing universes here, we will need to deal with the issue noted
--- at `presheaf_to_Top` (universe generalization for the Yoneda embedding).
 /-- Some repackaging:
 the presheaf of functions satisfying `continuous_prelocal` is just the same thing as
 the presheaf of continuous functions.

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -342,8 +342,8 @@ def subpresheafContinuousPrelocalIsoPresheafToTop (T : TopCat.{v}) :
     (fun X =>
       { Hom := by rintro ⟨f, c⟩; exact ⟨f, c⟩
         inv := by rintro ⟨f, c⟩; exact ⟨f, c⟩
-        hom_inv_id' := by ext (⟨f, p⟩x); rfl
-        inv_hom_id' := by ext (⟨f, p⟩x); rfl })
+        hom_inv_id' := by ext ⟨f, p⟩ x; rfl
+        inv_hom_id' := by ext ⟨f, p⟩ x; rfl })
     (by tidy)
 #align Top.subpresheaf_continuous_prelocal_iso_presheaf_to_Top TopCat.subpresheafContinuousPrelocalIsoPresheafToTop
 -/

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -77,6 +77,7 @@ structure PrelocalPredicate where
 
 variable (X)
 
+#print TopCat.continuousPrelocal /-
 /-- Continuity is a "prelocal" predicate on functions to a fixed topological space `T`.
 -/
 @[simps]
@@ -85,12 +86,15 @@ def continuousPrelocal (T : TopCat.{w}) : PrelocalPredicate fun x : X => T
   pred U f := Continuous f
   res U V i f h := Continuous.comp h (Opens.openEmbedding_of_le i.le).Continuous
 #align Top.continuous_prelocal TopCat.continuousPrelocal
+-/
 
+#print TopCat.inhabitedPrelocalPredicate /-
 /-- Satisfying the inhabited linter. -/
 instance inhabitedPrelocalPredicate (T : TopCat.{w}) :
     Inhabited (PrelocalPredicate fun x : X => T) :=
   ⟨continuousPrelocal X T⟩
 #align Top.inhabited_prelocal_predicate TopCat.inhabitedPrelocalPredicate
+-/
 
 variable {X}
 
@@ -167,6 +171,7 @@ theorem PrelocalPredicate.sheafifyOf {T : X → Type v} {P : PrelocalPredicate T
 #align Top.prelocal_predicate.sheafify_of TopCat.PrelocalPredicate.sheafifyOf
 -/
 
+#print TopCat.subpresheafToTypes /-
 /-- The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
 -/
 @[simps]
@@ -175,19 +180,23 @@ def subpresheafToTypes (P : PrelocalPredicate T) : Presheaf (Type max v w) X
   obj U := { f : ∀ x : unop U, T x // P.pred f }
   map U V i f := ⟨fun x => f.1 (i.unop x), P.res i.unop f.1 f.2⟩
 #align Top.subpresheaf_to_Types TopCat.subpresheafToTypes
+-/
 
 namespace SubpresheafToTypes
 
 variable (P : PrelocalPredicate T)
 
+#print TopCat.subpresheafToTypes.subtype /-
 /-- The natural transformation including the subpresheaf of functions satisfying a local predicate
 into the presheaf of all functions.
 -/
 def subtype : subpresheafToTypes P ⟶ presheafToTypes X T where app U f := f.1
 #align Top.subpresheaf_to_Types.subtype TopCat.subpresheafToTypes.subtype
+-/
 
 open TopCat.Presheaf
 
+#print TopCat.subpresheafToTypes.isSheaf /-
 /-- The functions satisfying a local predicate satisfy the sheaf condition.
 -/
 theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredicate).IsSheaf :=
@@ -224,15 +233,18 @@ theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredica
       ext1
       exact gl_uniq gl'.1 fun i => congr_arg Subtype.val (hgl' i)
 #align Top.subpresheaf_to_Types.is_sheaf TopCat.subpresheafToTypes.isSheaf
+-/
 
 end SubpresheafToTypes
 
+#print TopCat.subsheafToTypes /-
 /-- The subsheaf of the sheaf of all dependently typed functions satisfying the local predicate `P`.
 -/
 @[simps]
 def subsheafToTypes (P : LocalPredicate T) : Sheaf (Type max v w) X :=
   ⟨subpresheafToTypes P.toPrelocalPredicate, subpresheafToTypes.isSheaf P⟩
 #align Top.subsheaf_to_Types TopCat.subsheafToTypes
+-/
 
 -- TODO There is further universe generalization to do here,
 -- but it depends on more difficult universe generalization in `topology.sheaves.stalks`.
@@ -317,6 +329,7 @@ theorem stalkToFiber_injective (P : LocalPredicate T') (x : X)
 #align Top.stalk_to_fiber_injective TopCat.stalkToFiber_injective
 -/
 
+#print TopCat.subpresheafContinuousPrelocalIsoPresheafToTop /-
 -- TODO to continue generalizing universes here, we will need to deal with the issue noted
 -- at `presheaf_to_Top` (universe generalization for the Yoneda embedding).
 /-- Some repackaging:
@@ -333,6 +346,7 @@ def subpresheafContinuousPrelocalIsoPresheafToTop (T : TopCat.{v}) :
         inv_hom_id' := by ext (⟨f, p⟩x); rfl })
     (by tidy)
 #align Top.subpresheaf_continuous_prelocal_iso_presheaf_to_Top TopCat.subpresheafContinuousPrelocalIsoPresheafToTop
+-/
 
 #print TopCat.sheafToTop /-
 /-- The sheaf of continuous functions on `X` with values in a space `T`.

bump to nightly-2023-06-05-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

0a33716c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.sheaves.local_predicate
-! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
+! leanprover-community/mathlib commit 13361559d66b84f80b6d5a1c4a26aa5054766725
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -44,13 +44,13 @@ We give conditions sufficient to show that this map is injective and/or surjecti
 -/
 
 
-universe v
+universe v w
 
 noncomputable section
 
 variable {X : TopCat.{v}}
 
-variable (T : X → Type v)
+variable (T : X → Type w)
 
 open TopologicalSpace
 
@@ -64,7 +64,6 @@ open CategoryTheory.Limits.Types
 
 namespace TopCat
 
-#print TopCat.PrelocalPredicate /-
 /-- Given a topological space `X : Top` and a type family `T : X → Type`,
 a `P : prelocal_predicate T` consists of:
 * a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
@@ -74,33 +73,27 @@ a `P : prelocal_predicate T` consists of:
 structure PrelocalPredicate where
   pred : ∀ {U : Opens X}, (∀ x : U, T x) → Prop
   res : ∀ {U V : Opens X} (i : U ⟶ V) (f : ∀ x : V, T x) (h : pred f), pred fun x : U => f (i x)
-#align Top.prelocal_predicate TopCat.PrelocalPredicate
--/
+#align Top.prelocal_predicate TopCat.PrelocalPredicateₓ
 
 variable (X)
 
-#print TopCat.continuousPrelocal /-
 /-- Continuity is a "prelocal" predicate on functions to a fixed topological space `T`.
 -/
 @[simps]
-def continuousPrelocal (T : TopCat.{v}) : PrelocalPredicate fun x : X => T
+def continuousPrelocal (T : TopCat.{w}) : PrelocalPredicate fun x : X => T
     where
   pred U f := Continuous f
   res U V i f h := Continuous.comp h (Opens.openEmbedding_of_le i.le).Continuous
 #align Top.continuous_prelocal TopCat.continuousPrelocal
--/
 
-#print TopCat.inhabitedPrelocalPredicate /-
 /-- Satisfying the inhabited linter. -/
-instance inhabitedPrelocalPredicate (T : TopCat.{v}) :
+instance inhabitedPrelocalPredicate (T : TopCat.{w}) :
     Inhabited (PrelocalPredicate fun x : X => T) :=
   ⟨continuousPrelocal X T⟩
 #align Top.inhabited_prelocal_predicate TopCat.inhabitedPrelocalPredicate
--/
 
 variable {X}
 
-#print TopCat.LocalPredicate /-
 /-- Given a topological space `X : Top` and a type family `T : X → Type`,
 a `P : local_predicate T` consists of:
 * a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
@@ -116,8 +109,7 @@ structure LocalPredicate extends PrelocalPredicate T where
     ∀ {U : Opens X} (f : ∀ x : U, T x)
       (w : ∀ x : U, ∃ (V : Opens X) (m : x.1 ∈ V) (i : V ⟶ U), pred fun x : V => f (i x : U)),
       pred f
-#align Top.local_predicate TopCat.LocalPredicate
--/
+#align Top.local_predicate TopCat.LocalPredicateₓ
 
 variable (X)
 
@@ -175,16 +167,14 @@ theorem PrelocalPredicate.sheafifyOf {T : X → Type v} {P : PrelocalPredicate T
 #align Top.prelocal_predicate.sheafify_of TopCat.PrelocalPredicate.sheafifyOf
 -/
 
-#print TopCat.subpresheafToTypes /-
 /-- The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
 -/
 @[simps]
-def subpresheafToTypes (P : PrelocalPredicate T) : Presheaf (Type v) X
+def subpresheafToTypes (P : PrelocalPredicate T) : Presheaf (Type max v w) X
     where
   obj U := { f : ∀ x : unop U, T x // P.pred f }
   map U V i f := ⟨fun x => f.1 (i.unop x), P.res i.unop f.1 f.2⟩
 #align Top.subpresheaf_to_Types TopCat.subpresheafToTypes
--/
 
 namespace SubpresheafToTypes
 
@@ -198,7 +188,6 @@ def subtype : subpresheafToTypes P ⟶ presheafToTypes X T where app U f := f.1
 
 open TopCat.Presheaf
 
-#print TopCat.subpresheafToTypes.isSheaf /-
 /-- The functions satisfying a local predicate satisfy the sheaf condition.
 -/
 theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredicate).IsSheaf :=
@@ -235,27 +224,29 @@ theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredica
       ext1
       exact gl_uniq gl'.1 fun i => congr_arg Subtype.val (hgl' i)
 #align Top.subpresheaf_to_Types.is_sheaf TopCat.subpresheafToTypes.isSheaf
--/
 
 end SubpresheafToTypes
 
-#print TopCat.subsheafToTypes /-
 /-- The subsheaf of the sheaf of all dependently typed functions satisfying the local predicate `P`.
 -/
 @[simps]
-def subsheafToTypes (P : LocalPredicate T) : Sheaf (Type v) X :=
+def subsheafToTypes (P : LocalPredicate T) : Sheaf (Type max v w) X :=
   ⟨subpresheafToTypes P.toPrelocalPredicate, subpresheafToTypes.isSheaf P⟩
 #align Top.subsheaf_to_Types TopCat.subsheafToTypes
--/
+
+-- TODO There is further universe generalization to do here,
+-- but it depends on more difficult universe generalization in `topology.sheaves.stalks`.
+-- The aim is to replace `T'` with the more general `T` below.
+variable {T' : X → Type v}
 
 #print TopCat.stalkToFiber /-
 /-- There is a canonical map from the stalk to the original fiber, given by evaluating sections.
 -/
-def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).Presheaf.stalk x ⟶ T x :=
+def stalkToFiber (P : LocalPredicate T') (x : X) : (subsheafToTypes P).Presheaf.stalk x ⟶ T' x :=
   by
   refine'
     colimit.desc _
-      { pt := T x
+      { pt := T' x
         ι :=
           { app := fun U f => _
             naturality' := _ } }
@@ -264,8 +255,9 @@ def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).Presheaf.s
 #align Top.stalk_to_fiber TopCat.stalkToFiber
 -/
 
+#print TopCat.stalkToFiber_germ /-
 @[simp]
-theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
+theorem stalkToFiber_germ (P : LocalPredicate T') (U : Opens X) (x : U) (f) :
     stalkToFiber P x ((subsheafToTypes P).Presheaf.germ x f) = f.1 x :=
   by
   dsimp [presheaf.germ, stalk_to_fiber]
@@ -273,13 +265,14 @@ theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
   simp
   rfl
 #align Top.stalk_to_fiber_germ TopCat.stalkToFiber_germ
+-/
 
 #print TopCat.stalkToFiber_surjective /-
 /-- The `stalk_to_fiber` map is surjective at `x` if
 every point in the fiber `T x` has an allowed section passing through it.
 -/
-theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
-    (w : ∀ t : T x, ∃ (U : OpenNhds x) (f : ∀ y : U.1, T y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
+theorem stalkToFiber_surjective (P : LocalPredicate T') (x : X)
+    (w : ∀ t : T' x, ∃ (U : OpenNhds x) (f : ∀ y : U.1, T' y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
     Function.Surjective (stalkToFiber P x) := fun t =>
   by
   rcases w t with ⟨U, f, h, rfl⟩
@@ -293,9 +286,9 @@ theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
 /-- The `stalk_to_fiber` map is injective at `x` if any two allowed sections which agree at `x`
 agree on some neighborhood of `x`.
 -/
-theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
+theorem stalkToFiber_injective (P : LocalPredicate T') (x : X)
     (w :
-      ∀ (U V : OpenNhds x) (fU : ∀ y : U.1, T y) (hU : P.pred fU) (fV : ∀ y : V.1, T y)
+      ∀ (U V : OpenNhds x) (fU : ∀ y : U.1, T' y) (hU : P.pred fU) (fV : ∀ y : V.1, T' y)
         (hV : P.pred fV) (e : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
         ∃ (W : OpenNhds x) (iU : W ⟶ U) (iV : W ⟶ V),
           ∀ w : W.1, fU (iU w : U.1) = fV (iV w : V.1)) :
@@ -303,7 +296,7 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
   by
   -- We promise to provide all the ingredients of the proof later:
   let Q :
-    ∃ (W : (open_nhds x)ᵒᵖ) (s : ∀ w : (unop W).1, T w) (hW : P.pred s),
+    ∃ (W : (open_nhds x)ᵒᵖ) (s : ∀ w : (unop W).1, T' w) (hW : P.pred s),
       tU = (subsheaf_to_Types P).Presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ ∧
         tV = (subsheaf_to_Types P).Presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ :=
     _
@@ -324,6 +317,8 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
 #align Top.stalk_to_fiber_injective TopCat.stalkToFiber_injective
 -/
 
+-- TODO to continue generalizing universes here, we will need to deal with the issue noted
+-- at `presheaf_to_Top` (universe generalization for the Yoneda embedding).
 /-- Some repackaging:
 the presheaf of functions satisfying `continuous_prelocal` is just the same thing as
 the presheaf of continuous functions.

599fffe7

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -223,7 +223,7 @@ theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredica
       -- We claim that the predicate holds in `U i`
       use U i, hi, opens.le_supr U i
       -- This follows, since our original family `sf` satisfies the predicate
-      convert(sf i).property
+      convert (sf i).property
       exact gl_spec i
     -- It remains to show that the chosen lift is really a gluing for the subsheaf and
     -- that it is unique. Both of which follow immediately from the corresponding facts

599fffe7

bump to nightly-2023-06-02-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9

c039be4e

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.sheaves.local_predicate
-! leanprover-community/mathlib commit b8fb47c4f31648a8273c864e75f06c7b759e468c
+! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Sheaves.SheafCondition.UniqueGluing
 /-!
 # Functions satisfying a local predicate form a sheaf.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 At this stage, in `topology/sheaves/sheaf_of_functions.lean`
 we've proved that not-necessarily-continuous functions from a topological space
 into some type (or type family) form a sheaf.

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -111,7 +111,8 @@ a `P : local_predicate T` consists of:
 structure LocalPredicate extends PrelocalPredicate T where
   locality :
     ∀ {U : Opens X} (f : ∀ x : U, T x)
-      (w : ∀ x : U, ∃ (V : Opens X)(m : x.1 ∈ V)(i : V ⟶ U), pred fun x : V => f (i x : U)), pred f
+      (w : ∀ x : U, ∃ (V : Opens X) (m : x.1 ∈ V) (i : V ⟶ U), pred fun x : V => f (i x : U)),
+      pred f
 #align Top.local_predicate TopCat.LocalPredicate
 -/
 
@@ -127,8 +128,8 @@ def continuousLocal (T : TopCat.{v}) : LocalPredicate fun x : X => T :=
       intro x
       specialize w x
       rcases w with ⟨V, m, i, w⟩
-      dsimp at w
-      rw [continuous_iff_continuousAt] at w
+      dsimp at w 
+      rw [continuous_iff_continuousAt] at w 
       specialize w ⟨x, m⟩
       simpa using (opens.open_embedding_of_le i.le).continuousAt_iff.1 w }
 #align Top.continuous_local TopCat.continuousLocal
@@ -149,7 +150,7 @@ by asking that the condition from `P` holds locally near every point.
 -/
 def PrelocalPredicate.sheafify {T : X → Type v} (P : PrelocalPredicate T) : LocalPredicate T
     where
-  pred U f := ∀ x : U, ∃ (V : Opens X)(m : x.1 ∈ V)(i : V ⟶ U), P.pred fun x : V => f (i x : U)
+  pred U f := ∀ x : U, ∃ (V : Opens X) (m : x.1 ∈ V) (i : V ⟶ U), P.pred fun x : V => f (i x : U)
   res V U i f w x := by
     specialize w (i x)
     rcases w with ⟨V', m', i', p⟩
@@ -275,7 +276,7 @@ theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
 every point in the fiber `T x` has an allowed section passing through it.
 -/
 theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
-    (w : ∀ t : T x, ∃ (U : OpenNhds x)(f : ∀ y : U.1, T y)(h : P.pred f), f ⟨x, U.2⟩ = t) :
+    (w : ∀ t : T x, ∃ (U : OpenNhds x) (f : ∀ y : U.1, T y) (h : P.pred f), f ⟨x, U.2⟩ = t) :
     Function.Surjective (stalkToFiber P x) := fun t =>
   by
   rcases w t with ⟨U, f, h, rfl⟩
@@ -293,12 +294,13 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
     (w :
       ∀ (U V : OpenNhds x) (fU : ∀ y : U.1, T y) (hU : P.pred fU) (fV : ∀ y : V.1, T y)
         (hV : P.pred fV) (e : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
-        ∃ (W : OpenNhds x)(iU : W ⟶ U)(iV : W ⟶ V), ∀ w : W.1, fU (iU w : U.1) = fV (iV w : V.1)) :
+        ∃ (W : OpenNhds x) (iU : W ⟶ U) (iV : W ⟶ V),
+          ∀ w : W.1, fU (iU w : U.1) = fV (iV w : V.1)) :
     Function.Injective (stalkToFiber P x) := fun tU tV h =>
   by
   -- We promise to provide all the ingredients of the proof later:
   let Q :
-    ∃ (W : (open_nhds x)ᵒᵖ)(s : ∀ w : (unop W).1, T w)(hW : P.pred s),
+    ∃ (W : (open_nhds x)ᵒᵖ) (s : ∀ w : (unop W).1, T w) (hW : P.pred s),
       tU = (subsheaf_to_Types P).Presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ ∧
         tV = (subsheaf_to_Types P).Presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ :=
     _
@@ -309,7 +311,7 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
   obtain ⟨V, ⟨fV, hV⟩, rfl⟩ := jointly_surjective'.{v, v} tV
   · -- Decompose everything into its constituent parts:
     dsimp
-    simp only [stalk_to_fiber, types.colimit.ι_desc_apply'] at h
+    simp only [stalk_to_fiber, types.colimit.ι_desc_apply'] at h 
     specialize w (unop U) (unop V) fU hU fV hV h
     rcases w with ⟨W, iU, iV, w⟩
     -- and put it back together again in the correct order.

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -61,6 +61,7 @@ open CategoryTheory.Limits.Types
 
 namespace TopCat
 
+#print TopCat.PrelocalPredicate /-
 /-- Given a topological space `X : Top` and a type family `T : X → Type`,
 a `P : prelocal_predicate T` consists of:
 * a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
@@ -71,9 +72,11 @@ structure PrelocalPredicate where
   pred : ∀ {U : Opens X}, (∀ x : U, T x) → Prop
   res : ∀ {U V : Opens X} (i : U ⟶ V) (f : ∀ x : V, T x) (h : pred f), pred fun x : U => f (i x)
 #align Top.prelocal_predicate TopCat.PrelocalPredicate
+-/
 
 variable (X)
 
+#print TopCat.continuousPrelocal /-
 /-- Continuity is a "prelocal" predicate on functions to a fixed topological space `T`.
 -/
 @[simps]
@@ -82,15 +85,19 @@ def continuousPrelocal (T : TopCat.{v}) : PrelocalPredicate fun x : X => T
   pred U f := Continuous f
   res U V i f h := Continuous.comp h (Opens.openEmbedding_of_le i.le).Continuous
 #align Top.continuous_prelocal TopCat.continuousPrelocal
+-/
 
+#print TopCat.inhabitedPrelocalPredicate /-
 /-- Satisfying the inhabited linter. -/
 instance inhabitedPrelocalPredicate (T : TopCat.{v}) :
     Inhabited (PrelocalPredicate fun x : X => T) :=
   ⟨continuousPrelocal X T⟩
 #align Top.inhabited_prelocal_predicate TopCat.inhabitedPrelocalPredicate
+-/
 
 variable {X}
 
+#print TopCat.LocalPredicate /-
 /-- Given a topological space `X : Top` and a type family `T : X → Type`,
 a `P : local_predicate T` consists of:
 * a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
@@ -106,9 +113,11 @@ structure LocalPredicate extends PrelocalPredicate T where
     ∀ {U : Opens X} (f : ∀ x : U, T x)
       (w : ∀ x : U, ∃ (V : Opens X)(m : x.1 ∈ V)(i : V ⟶ U), pred fun x : V => f (i x : U)), pred f
 #align Top.local_predicate TopCat.LocalPredicate
+-/
 
 variable (X)
 
+#print TopCat.continuousLocal /-
 /-- Continuity is a "local" predicate on functions to a fixed topological space `T`.
 -/
 def continuousLocal (T : TopCat.{v}) : LocalPredicate fun x : X => T :=
@@ -123,14 +132,18 @@ def continuousLocal (T : TopCat.{v}) : LocalPredicate fun x : X => T :=
       specialize w ⟨x, m⟩
       simpa using (opens.open_embedding_of_le i.le).continuousAt_iff.1 w }
 #align Top.continuous_local TopCat.continuousLocal
+-/
 
+#print TopCat.inhabitedLocalPredicate /-
 /-- Satisfying the inhabited linter. -/
 instance inhabitedLocalPredicate (T : TopCat.{v}) : Inhabited (LocalPredicate _) :=
   ⟨continuousLocal X T⟩
 #align Top.inhabited_local_predicate TopCat.inhabitedLocalPredicate
+-/
 
 variable {X T}
 
+#print TopCat.PrelocalPredicate.sheafify /-
 /-- Given a `P : prelocal_predicate`, we can always construct a `local_predicate`
 by asking that the condition from `P` holds locally near every point.
 -/
@@ -149,12 +162,16 @@ def PrelocalPredicate.sheafify {T : X → Type v} (P : PrelocalPredicate T) : Lo
     rcases p with ⟨V', m', i', p'⟩
     exact ⟨V', m', i' ≫ i, p'⟩
 #align Top.prelocal_predicate.sheafify TopCat.PrelocalPredicate.sheafify
+-/
 
+#print TopCat.PrelocalPredicate.sheafifyOf /-
 theorem PrelocalPredicate.sheafifyOf {T : X → Type v} {P : PrelocalPredicate T} {U : Opens X}
     {f : ∀ x : U, T x} (h : P.pred f) : P.sheafify.pred f := fun x =>
   ⟨U, x.2, 𝟙 _, by convert h; ext ⟨y, w⟩; rfl⟩
 #align Top.prelocal_predicate.sheafify_of TopCat.PrelocalPredicate.sheafifyOf
+-/
 
+#print TopCat.subpresheafToTypes /-
 /-- The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
 -/
 @[simps]
@@ -163,6 +180,7 @@ def subpresheafToTypes (P : PrelocalPredicate T) : Presheaf (Type v) X
   obj U := { f : ∀ x : unop U, T x // P.pred f }
   map U V i f := ⟨fun x => f.1 (i.unop x), P.res i.unop f.1 f.2⟩
 #align Top.subpresheaf_to_Types TopCat.subpresheafToTypes
+-/
 
 namespace SubpresheafToTypes
 
@@ -176,6 +194,7 @@ def subtype : subpresheafToTypes P ⟶ presheafToTypes X T where app U f := f.1
 
 open TopCat.Presheaf
 
+#print TopCat.subpresheafToTypes.isSheaf /-
 /-- The functions satisfying a local predicate satisfy the sheaf condition.
 -/
 theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredicate).IsSheaf :=
@@ -212,16 +231,20 @@ theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredica
       ext1
       exact gl_uniq gl'.1 fun i => congr_arg Subtype.val (hgl' i)
 #align Top.subpresheaf_to_Types.is_sheaf TopCat.subpresheafToTypes.isSheaf
+-/
 
 end SubpresheafToTypes
 
+#print TopCat.subsheafToTypes /-
 /-- The subsheaf of the sheaf of all dependently typed functions satisfying the local predicate `P`.
 -/
 @[simps]
 def subsheafToTypes (P : LocalPredicate T) : Sheaf (Type v) X :=
   ⟨subpresheafToTypes P.toPrelocalPredicate, subpresheafToTypes.isSheaf P⟩
 #align Top.subsheaf_to_Types TopCat.subsheafToTypes
+-/
 
+#print TopCat.stalkToFiber /-
 /-- There is a canonical map from the stalk to the original fiber, given by evaluating sections.
 -/
 def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).Presheaf.stalk x ⟶ T x :=
@@ -235,6 +258,7 @@ def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).Presheaf.s
   · exact f.1 ⟨x, (unop U).2⟩
   · tidy
 #align Top.stalk_to_fiber TopCat.stalkToFiber
+-/
 
 @[simp]
 theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
@@ -246,6 +270,7 @@ theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
   rfl
 #align Top.stalk_to_fiber_germ TopCat.stalkToFiber_germ
 
+#print TopCat.stalkToFiber_surjective /-
 /-- The `stalk_to_fiber` map is surjective at `x` if
 every point in the fiber `T x` has an allowed section passing through it.
 -/
@@ -258,7 +283,9 @@ theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
   · exact (subsheaf_to_Types P).Presheaf.germ ⟨x, U.2⟩ ⟨f, h⟩
   · exact stalk_to_fiber_germ _ U.1 ⟨x, U.2⟩ ⟨f, h⟩
 #align Top.stalk_to_fiber_surjective TopCat.stalkToFiber_surjective
+-/
 
+#print TopCat.stalkToFiber_injective /-
 /-- The `stalk_to_fiber` map is injective at `x` if any two allowed sections which agree at `x`
 agree on some neighborhood of `x`.
 -/
@@ -290,6 +317,7 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
     rcases W with ⟨W, m⟩
     exact ⟨colimit_sound iU.op (Subtype.eq rfl), colimit_sound iV.op (Subtype.eq (funext w).symm)⟩
 #align Top.stalk_to_fiber_injective TopCat.stalkToFiber_injective
+-/
 
 /-- Some repackaging:
 the presheaf of functions satisfying `continuous_prelocal` is just the same thing as
@@ -306,6 +334,7 @@ def subpresheafContinuousPrelocalIsoPresheafToTop (T : TopCat.{v}) :
     (by tidy)
 #align Top.subpresheaf_continuous_prelocal_iso_presheaf_to_Top TopCat.subpresheafContinuousPrelocalIsoPresheafToTop
 
+#print TopCat.sheafToTop /-
 /-- The sheaf of continuous functions on `X` with values in a space `T`.
 -/
 def sheafToTop (T : TopCat.{v}) : Sheaf (Type v) X :=
@@ -313,6 +342,7 @@ def sheafToTop (T : TopCat.{v}) : Sheaf (Type v) X :=
     Presheaf.isSheaf_of_iso (subpresheafContinuousPrelocalIsoPresheafToTop T)
       (subpresheafToTypes.isSheaf (continuousLocal X T))⟩
 #align Top.sheaf_to_Top TopCat.sheafToTop
+-/
 
 end TopCat

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -152,10 +152,7 @@ def PrelocalPredicate.sheafify {T : X → Type v} (P : PrelocalPredicate T) : Lo
 
 theorem PrelocalPredicate.sheafifyOf {T : X → Type v} {P : PrelocalPredicate T} {U : Opens X}
     {f : ∀ x : U, T x} (h : P.pred f) : P.sheafify.pred f := fun x =>
-  ⟨U, x.2, 𝟙 _, by
-    convert h
-    ext ⟨y, w⟩
-    rfl⟩
+  ⟨U, x.2, 𝟙 _, by convert h; ext ⟨y, w⟩; rfl⟩
 #align Top.prelocal_predicate.sheafify_of TopCat.PrelocalPredicate.sheafifyOf
 
 /-- The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
@@ -302,18 +299,10 @@ def subpresheafContinuousPrelocalIsoPresheafToTop (T : TopCat.{v}) :
     subpresheafToTypes (continuousPrelocal X T) ≅ presheafToTop X T :=
   NatIso.ofComponents
     (fun X =>
-      { Hom := by
-          rintro ⟨f, c⟩
-          exact ⟨f, c⟩
-        inv := by
-          rintro ⟨f, c⟩
-          exact ⟨f, c⟩
-        hom_inv_id' := by
-          ext (⟨f, p⟩x)
-          rfl
-        inv_hom_id' := by
-          ext (⟨f, p⟩x)
-          rfl })
+      { Hom := by rintro ⟨f, c⟩; exact ⟨f, c⟩
+        inv := by rintro ⟨f, c⟩; exact ⟨f, c⟩
+        hom_inv_id' := by ext (⟨f, p⟩x); rfl
+        inv_hom_id' := by ext (⟨f, p⟩x); rfl })
     (by tidy)
 #align Top.subpresheaf_continuous_prelocal_iso_presheaf_to_Top TopCat.subpresheafContinuousPrelocalIsoPresheafToTop

bump to nightly-2023-04-27-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

8f775de7

Diff

@@ -150,13 +150,13 @@ def PrelocalPredicate.sheafify {T : X → Type v} (P : PrelocalPredicate T) : Lo
     exact ⟨V', m', i' ≫ i, p'⟩
 #align Top.prelocal_predicate.sheafify TopCat.PrelocalPredicate.sheafify
 
-theorem PrelocalPredicate.sheafify_of {T : X → Type v} {P : PrelocalPredicate T} {U : Opens X}
+theorem PrelocalPredicate.sheafifyOf {T : X → Type v} {P : PrelocalPredicate T} {U : Opens X}
     {f : ∀ x : U, T x} (h : P.pred f) : P.sheafify.pred f := fun x =>
   ⟨U, x.2, 𝟙 _, by
     convert h
     ext ⟨y, w⟩
     rfl⟩
-#align Top.prelocal_predicate.sheafify_of TopCat.PrelocalPredicate.sheafify_of
+#align Top.prelocal_predicate.sheafify_of TopCat.PrelocalPredicate.sheafifyOf
 
 /-- The subpresheaf of dependent functions on `X` satisfying the "pre-local" predicate `P`.
 -/

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -203,7 +203,7 @@ theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredica
       -- We claim that the predicate holds in `U i`
       use U i, hi, opens.le_supr U i
       -- This follows, since our original family `sf` satisfies the predicate
-      convert (sf i).property
+      convert(sf i).property
       exact gl_spec i
     -- It remains to show that the chosen lift is really a gluing for the subsheaf and
     -- that it is unique. Both of which follow immediately from the corresponding facts

bump to nightly-2023-02-28-22

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

1fb1623f

Diff

@@ -231,7 +231,7 @@ def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).Presheaf.s
   by
   refine'
     colimit.desc _
-      { x := T x
+      { pt := T x
         ι :=
           { app := fun U f => _
             naturality' := _ } }

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

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 @@ universe v
 noncomputable section
 
 variable {X : TopCat.{v}}
-
 variable (T : X → Type v)
 
 open TopologicalSpace

chore: classify @[simp] removed porting notes (#11184)

Classifying by adding issue number #11119 to porting notes claiming anything semantically equivalent to:

"@[simp] removed [...]"
"@[simp] removed [...]"
"removed simp attribute"

28527d30

Diff

@@ -244,7 +244,8 @@ def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).presheaf.s
 set_option linter.uppercaseLean3 false in
 #align Top.stalk_to_fiber TopCat.stalkToFiber
 
--- Porting note: removed `simp` attribute, due to left hand side is not in simple normal form.
+-- Porting note (#11119): removed `simp` attribute,
+-- due to left hand side is not in simple normal form.
 theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
     stalkToFiber P x ((subsheafToTypes P).presheaf.germ x f) = f.1 x := by
   dsimp [Presheaf.germ, stalkToFiber]

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

@@ -244,7 +244,7 @@ def stalkToFiber (P : LocalPredicate T) (x : X) : (subsheafToTypes P).presheaf.s
 set_option linter.uppercaseLean3 false in
 #align Top.stalk_to_fiber TopCat.stalkToFiber
 
--- Porting note : removed `simp` attribute, due to left hand side is not in simple normal form.
+-- Porting note: removed `simp` attribute, due to left hand side is not in simple normal form.
 theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
     stalkToFiber P x ((subsheafToTypes P).presheaf.germ x f) = f.1 x := by
   dsimp [Presheaf.germ, stalkToFiber]

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -5,7 +5,6 @@ Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
 import Mathlib.Topology.Sheaves.SheafOfFunctions
 import Mathlib.Topology.Sheaves.Stalks
-import Mathlib.Topology.PartialHomeomorph
 import Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing
 
 #align_import topology.sheaves.local_predicate from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"

chore: rename LocalHomeomorph to PartialHomeomorph (#8982)

LocalHomeomorph evokes a "local homeomorphism": this is not what this means. Instead, this is a homeomorphism on an open set of the domain (extended to the whole space, by the junk value pattern). Hence, partial homeomorphism is more appropriate, and avoids confusion with IsLocallyHomeomorph.

A future PR will rename LocalEquiv to PartialEquiv.

Zulip discussion

bbc6e56d

Diff

@@ -5,7 +5,7 @@ Authors: Johan Commelin, Scott Morrison, Adam Topaz
 -/
 import Mathlib.Topology.Sheaves.SheafOfFunctions
 import Mathlib.Topology.Sheaves.Stalks
-import Mathlib.Topology.LocalHomeomorph
+import Mathlib.Topology.PartialHomeomorph
 import Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing
 
 #align_import topology.sheaves.local_predicate from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"

chore: tidy various files (#6534)

595af3d0

Diff

@@ -29,9 +29,9 @@ any collection of dependent functions on a topological space
 satisfying a "local predicate".
 
 As an application, we check that continuity is a local predicate in this sense, and provide
-* `Top.sheaf_to_Top`: continuous functions into a topological space form a sheaf
+* `TopCat.sheafToTop`: continuous functions into a topological space form a sheaf
 
-A sheaf constructed in this way has a natural map `stalk_to_fiber` from the stalks
+A sheaf constructed in this way has a natural map `stalkToFiber` from the stalks
 to the types in the ambient type family.
 
 We give conditions sufficient to show that this map is injective and/or surjective.
@@ -58,10 +58,10 @@ open CategoryTheory.Limits.Types
 
 namespace TopCat
 
-/-- Given a topological space `X : Top` and a type family `T : X → Type`,
-a `P : prelocal_predicate T` consists of:
-* a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
-* a proof that if `f : Π x : V, T x` satisfies the predicate on `V : opens X`, then
+/-- Given a topological space `X : TopCat` and a type family `T : X → Type`,
+a `P : PrelocalPredicate T` consists of:
+* a family of predicates `P.pred`, one for each `U : Opens X`, of the form `(Π x : U, T x) → Prop`
+* a proof that if `f : Π x : V, T x` satisfies the predicate on `V : Opens X`, then
   the restriction of `f` to any open subset `U` also satisfies the predicate.
 -/
 structure PrelocalPredicate where
@@ -92,10 +92,10 @@ set_option linter.uppercaseLean3 false in
 
 variable {X}
 
-/-- Given a topological space `X : Top` and a type family `T : X → Type`,
-a `P : local_predicate T` consists of:
-* a family of predicates `P.pred`, one for each `U : opens X`, of the form `(Π x : U, T x) → Prop`
-* a proof that if `f : Π x : V, T x` satisfies the predicate on `V : opens X`, then
+/-- Given a topological space `X : TopCat` and a type family `T : X → Type`,
+a `P : LocalPredicate T` consists of:
+* a family of predicates `P.pred`, one for each `U : Opens X`, of the form `(Π x : U, T x) → Prop`
+* a proof that if `f : Π x : V, T x` satisfies the predicate on `V : Opens X`, then
   the restriction of `f` to any open subset `U` also satisfies the predicate, and
 * a proof that given some `f : Π x : U, T x`,
   if for every `x : U` we can find an open set `x ∈ V ≤ U`
@@ -138,7 +138,7 @@ set_option linter.uppercaseLean3 false in
 
 variable {X T}
 
-/-- Given a `P : prelocal_predicate`, we can always construct a `local_predicate`
+/-- Given a `P : PrelocalPredicate`, we can always construct a `LocalPredicate`
 by asking that the condition from `P` holds locally near every point.
 -/
 def PrelocalPredicate.sheafify {T : X → Type v} (P : PrelocalPredicate T) : LocalPredicate T where
@@ -254,7 +254,7 @@ theorem stalkToFiber_germ (P : LocalPredicate T) (U : Opens X) (x : U) (f) :
 set_option linter.uppercaseLean3 false in
 #align Top.stalk_to_fiber_germ TopCat.stalkToFiber_germ
 
-/-- The `stalk_to_fiber` map is surjective at `x` if
+/-- The `stalkToFiber` map is surjective at `x` if
 every point in the fiber `T x` has an allowed section passing through it.
 -/
 theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
@@ -267,7 +267,7 @@ theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
 set_option linter.uppercaseLean3 false in
 #align Top.stalk_to_fiber_surjective TopCat.stalkToFiber_surjective
 
-/-- The `stalk_to_fiber` map is injective at `x` if any two allowed sections which agree at `x`
+/-- The `stalkToFiber` map is injective at `x` if any two allowed sections which agree at `x`
 agree on some neighborhood of `x`.
 -/
 theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
@@ -302,7 +302,7 @@ set_option linter.uppercaseLean3 false in
 #align Top.stalk_to_fiber_injective TopCat.stalkToFiber_injective
 
 /-- Some repackaging:
-the presheaf of functions satisfying `continuous_prelocal` is just the same thing as
+the presheaf of functions satisfying `continuousPrelocal` is just the same thing as
 the presheaf of continuous functions.
 -/
 def subpresheafContinuousPrelocalIsoPresheafToTop (T : TopCat.{v}) :

chore: tidy various files (#6393)

3697da16

Diff

@@ -13,7 +13,7 @@ import Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing
 /-!
 # Functions satisfying a local predicate form a sheaf.
 
-At this stage, in `topology/sheaves/sheaf_of_functions.lean`
+At this stage, in `Mathlib/Topology/Sheaves/SheafOfFunctions.lean`
 we've proved that not-necessarily-continuous functions from a topological space
 into some type (or type family) form a sheaf.

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module topology.sheaves.local_predicate
-! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Sheaves.SheafOfFunctions
 import Mathlib.Topology.Sheaves.Stalks
 import Mathlib.Topology.LocalHomeomorph
 import Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing
 
+#align_import topology.sheaves.local_predicate from "leanprover-community/mathlib"@"5dc6092d09e5e489106865241986f7f2ad28d4c8"
+
 /-!
 # Functions satisfying a local predicate form a sheaf.

feat: using UnivLE to generalize universes in UniqueGluing (#5726)

This is a test of the UnivLE proposal. The UniqueGluing file was one place where we couldn't forward port the universe generalisations made in mathlib3 in https://github.com/leanprover-community/mathlib/pull/19153.

Diff relative to #5724 is https://github.com/leanprover-community/mathlib4/compare/UnivLE_types...UnivLE_UniqueGluing.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Matthew Robert Ballard <matt@mrb.email> Co-authored-by: Bulhwi Cha <chabulhwi@semmalgil.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Oliver Nash <github@olivernash.org> Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com> Co-authored-by: Tobias Grosser <tobias@grosser.es> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Moritz Firsching <moritz.firsching@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com>

0f6207a5

Diff

@@ -191,7 +191,7 @@ open TopCat.Presheaf
 /-- The functions satisfying a local predicate satisfy the sheaf condition.
 -/
 theorem isSheaf (P : LocalPredicate T) : (subpresheafToTypes P.toPrelocalPredicate).IsSheaf :=
-  Presheaf.isSheaf_of_isSheafUniqueGluing_types _ fun ι U sf sf_comp => by
+  Presheaf.isSheaf_of_isSheafUniqueGluing_types.{v} _ fun ι U sf sf_comp => by
     -- We show the sheaf condition in terms of unique gluing.
     -- First we obtain a family of sections for the underlying sheaf of functions,
     -- by forgetting that the predicate holds

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -299,8 +299,8 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
     -- and put it back together again in the correct order.
     refine' ⟨op W, fun w => fU (iU w : (unop U).1), P.res _ _ hU, _⟩
     rcases W with ⟨W, m⟩
-    . exact iU
-    . exact ⟨colimit_sound iU.op (Subtype.eq rfl), colimit_sound iV.op (Subtype.eq (funext w).symm)⟩
+    · exact iU
+    · exact ⟨colimit_sound iU.op (Subtype.eq rfl), colimit_sound iV.op (Subtype.eq (funext w).symm)⟩
 set_option linter.uppercaseLean3 false in
 #align Top.stalk_to_fiber_injective TopCat.stalkToFiber_injective

chore: update SHAs after #19153 was reverted (#5712)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

6c35041e

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Scott Morrison, Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.sheaves.local_predicate
-! leanprover-community/mathlib commit b8fb47c4f31648a8273c864e75f06c7b759e468c
+! leanprover-community/mathlib commit 5dc6092d09e5e489106865241986f7f2ad28d4c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -261,7 +261,7 @@ set_option linter.uppercaseLean3 false in
 every point in the fiber `T x` has an allowed section passing through it.
 -/
 theorem stalkToFiber_surjective (P : LocalPredicate T) (x : X)
-    (w : ∀ t : T x, ∃ (U : OpenNhds x)(f : ∀ y : U.1, T y) (_ : P.pred f), f ⟨x, U.2⟩ = t) :
+    (w : ∀ t : T x, ∃ (U : OpenNhds x) (f : ∀ y : U.1, T y) (_ : P.pred f), f ⟨x, U.2⟩ = t) :
     Function.Surjective (stalkToFiber P x) := fun t => by
   rcases w t with ⟨U, f, h, rfl⟩
   fconstructor
@@ -277,11 +277,12 @@ theorem stalkToFiber_injective (P : LocalPredicate T) (x : X)
     (w :
       ∀ (U V : OpenNhds x) (fU : ∀ y : U.1, T y) (_ : P.pred fU) (fV : ∀ y : V.1, T y)
         (_ : P.pred fV) (_ : fU ⟨x, U.2⟩ = fV ⟨x, V.2⟩),
-        ∃ (W : OpenNhds x)(iU : W ⟶ U)(iV : W ⟶ V), ∀ w : W.1, fU (iU w : U.1) = fV (iV w : V.1)) :
+        ∃ (W : OpenNhds x) (iU : W ⟶ U) (iV : W ⟶ V), ∀ w : W.1,
+          fU (iU w : U.1) = fV (iV w : V.1)) :
     Function.Injective (stalkToFiber P x) := fun tU tV h => by
   -- We promise to provide all the ingredients of the proof later:
   let Q :
-    ∃ (W : (OpenNhds x)ᵒᵖ)(s : ∀ w : (unop W).1, T w)(hW : P.pred s),
+    ∃ (W : (OpenNhds x)ᵒᵖ) (s : ∀ w : (unop W).1, T w) (hW : P.pred s),
       tU = (subsheafToTypes P).presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ ∧
         tV = (subsheafToTypes P).presheaf.germ ⟨x, (unop W).2⟩ ⟨s, hW⟩ :=
     ?_

chore: review of automation in category theory (#4793)

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

5b958613

Diff

@@ -309,13 +309,9 @@ the presheaf of continuous functions.
 -/
 def subpresheafContinuousPrelocalIsoPresheafToTop (T : TopCat.{v}) :
     subpresheafToTypes (continuousPrelocal X T) ≅ presheafToTop X T :=
-  NatIso.ofComponents
-    (fun X =>
-      { hom := by rintro ⟨f, c⟩; exact ⟨f, c⟩
-        inv := by rintro ⟨f, c⟩; exact ⟨f, c⟩
-        hom_inv_id := by ext ⟨f, p⟩; rfl
-        inv_hom_id := by ext ⟨f, p⟩; rfl })
-    (by aesop_cat)
+  NatIso.ofComponents fun X =>
+    { hom := by rintro ⟨f, c⟩; exact ⟨f, c⟩
+      inv := by rintro ⟨f, c⟩; exact ⟨f, c⟩ }
 set_option linter.uppercaseLean3 false in
 #align Top.subpresheaf_continuous_prelocal_iso_presheaf_to_Top TopCat.subpresheafContinuousPrelocalIsoPresheafToTop

chore: bump to nightly-2023-05-31 (#4530)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com>

01da6a3c

Diff

@@ -313,8 +313,8 @@ def subpresheafContinuousPrelocalIsoPresheafToTop (T : TopCat.{v}) :
     (fun X =>
       { hom := by rintro ⟨f, c⟩; exact ⟨f, c⟩
         inv := by rintro ⟨f, c⟩; exact ⟨f, c⟩
-        hom_inv_id := by ext (⟨f, p⟩x); rfl
-        inv_hom_id := by ext (⟨f, p⟩x); rfl })
+        hom_inv_id := by ext ⟨f, p⟩; rfl
+        inv_hom_id := by ext ⟨f, p⟩; rfl })
     (by aesop_cat)
 set_option linter.uppercaseLean3 false in
 #align Top.subpresheaf_continuous_prelocal_iso_presheaf_to_Top TopCat.subpresheafContinuousPrelocalIsoPresheafToTop