topology.category.Profinite.as_limit ⟷ Mathlib.Topology.Category.Profinite.AsLimit

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

@@ -76,7 +76,7 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
     (by
       refine' ⟨fun a b h => _, fun a => _⟩
       · refine' DiscreteQuotient.eq_of_forall_proj_eq fun S => _
-        apply_fun fun f : (limit_cone X.diagram).pt => f.val S at h 
+        apply_fun fun f : (limit_cone X.diagram).pt => f.val S at h
         exact h
       · obtain ⟨b, hb⟩ :=
           DiscreteQuotient.exists_of_compat (fun S => a.val S) fun _ _ h => a.prop (hom_of_le h)

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Calle Sönne, Adam Topaz
 -/
-import Mathbin.Topology.Category.Profinite.Basic
-import Mathbin.Topology.DiscreteQuotient
+import Topology.Category.Profinite.Basic
+import Topology.DiscreteQuotient
 
 #align_import topology.category.Profinite.as_limit from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Calle Sönne, Adam Topaz
-
-! This file was ported from Lean 3 source module topology.category.Profinite.as_limit
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Category.Profinite.Basic
 import Mathbin.Topology.DiscreteQuotient
 
+#align_import topology.category.Profinite.as_limit from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
+
 /-!
 # Profinite sets as limits of finite sets.
 

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

@@ -47,6 +47,7 @@ universe u
 
 variable (X : Profinite.{u})
 
+#print Profinite.fintypeDiagram /-
 /-- The functor `discrete_quotient X ⥤ Fintype` whose limit is isomorphic to `X`. -/
 def fintypeDiagram : DiscreteQuotient X ⥤ FintypeCat
     where
@@ -55,18 +56,24 @@ def fintypeDiagram : DiscreteQuotient X ⥤ FintypeCat
     FintypeCat.of S
   map S T f := DiscreteQuotient.ofLE f.le
 #align Profinite.fintype_diagram Profinite.fintypeDiagram
+-/
 
+#print Profinite.diagram /-
 /-- An abbreviation for `X.fintype_diagram ⋙ Fintype_to_Profinite`. -/
 abbrev diagram : DiscreteQuotient X ⥤ Profinite :=
   X.fintypeDiagram ⋙ FintypeCat.toProfinite
 #align Profinite.diagram Profinite.diagram
+-/
 
+#print Profinite.asLimitCone /-
 /-- A cone over `X.diagram` whose cone point is `X`. -/
 def asLimitCone : CategoryTheory.Limits.Cone X.diagram :=
   { pt
     π := { app := fun S => ⟨S.proj, S.proj_isLocallyConstant.Continuous⟩ } }
 #align Profinite.as_limit_cone Profinite.asLimitCone
+-/
 
+#print Profinite.isIso_asLimitCone_lift /-
 instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asLimitCone) :=
   isIso_of_bijective _
     (by
@@ -80,30 +87,39 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
         ext S : 3
         apply hb)
 #align Profinite.is_iso_as_limit_cone_lift Profinite.isIso_asLimitCone_lift
+-/
 
+#print Profinite.isoAsLimitConeLift /-
 /-- The isomorphism between `X` and the explicit limit of `X.diagram`,
 induced by lifting `X.as_limit_cone`.
 -/
 def isoAsLimitConeLift : X ≅ (limitCone X.diagram).pt :=
   asIso <| (limitConeIsLimit _).lift X.asLimitCone
 #align Profinite.iso_as_limit_cone_lift Profinite.isoAsLimitConeLift
+-/
 
+#print Profinite.asLimitConeIso /-
 /-- The isomorphism of cones `X.as_limit_cone` and `Profinite.limit_cone X.diagram`.
 The underlying isomorphism is defeq to `X.iso_as_limit_cone_lift`.
 -/
 def asLimitConeIso : X.asLimitCone ≅ limitCone _ :=
   Limits.Cones.ext (isoAsLimitConeLift _) fun _ => rfl
 #align Profinite.as_limit_cone_iso Profinite.asLimitConeIso
+-/
 
+#print Profinite.asLimit /-
 /-- `X.as_limit_cone` is indeed a limit cone. -/
 def asLimit : CategoryTheory.Limits.IsLimit X.asLimitCone :=
   Limits.IsLimit.ofIsoLimit (limitConeIsLimit _) X.asLimitConeIso.symm
 #align Profinite.as_limit Profinite.asLimit
+-/
 
+#print Profinite.lim /-
 /-- A bundled version of `X.as_limit_cone` and `X.as_limit`. -/
 def lim : Limits.LimitCone X.diagram :=
   ⟨X.asLimitCone, X.asLimit⟩
 #align Profinite.lim Profinite.lim
+-/
 
 end Profinite
 

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

@@ -72,7 +72,7 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
     (by
       refine' ⟨fun a b h => _, fun a => _⟩
       · refine' DiscreteQuotient.eq_of_forall_proj_eq fun S => _
-        apply_fun fun f : (limit_cone X.diagram).pt => f.val S  at h 
+        apply_fun fun f : (limit_cone X.diagram).pt => f.val S at h 
         exact h
       · obtain ⟨b, hb⟩ :=
           DiscreteQuotient.exists_of_compat (fun S => a.val S) fun _ _ h => a.prop (hom_of_le h)

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

@@ -72,7 +72,7 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
     (by
       refine' ⟨fun a b h => _, fun a => _⟩
       · refine' DiscreteQuotient.eq_of_forall_proj_eq fun S => _
-        apply_fun fun f : (limit_cone X.diagram).pt => f.val S  at h
+        apply_fun fun f : (limit_cone X.diagram).pt => f.val S  at h 
         exact h
       · obtain ⟨b, hb⟩ :=
           DiscreteQuotient.exists_of_compat (fun S => a.val S) fun _ _ h => a.prop (hom_of_le h)

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

@@ -47,12 +47,6 @@ universe u
 
 variable (X : Profinite.{u})
 
-/- warning: Profinite.fintype_diagram -> Profinite.fintypeDiagram is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) FintypeCat.{u1} FintypeCat.CategoryTheory.category.{u1}
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) FintypeCat.{u1} FintypeCat.instCategoryFintypeCat.{u1}
-Case conversion may be inaccurate. Consider using '#align Profinite.fintype_diagram Profinite.fintypeDiagramₓ'. -/
 /-- The functor `discrete_quotient X ⥤ Fintype` whose limit is isomorphic to `X`. -/
 def fintypeDiagram : DiscreteQuotient X ⥤ FintypeCat
     where
@@ -62,32 +56,17 @@ def fintypeDiagram : DiscreteQuotient X ⥤ FintypeCat
   map S T f := DiscreteQuotient.ofLE f.le
 #align Profinite.fintype_diagram Profinite.fintypeDiagram
 
-/- warning: Profinite.diagram -> Profinite.diagram is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1}
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1}
-Case conversion may be inaccurate. Consider using '#align Profinite.diagram Profinite.diagramₓ'. -/
 /-- An abbreviation for `X.fintype_diagram ⋙ Fintype_to_Profinite`. -/
 abbrev diagram : DiscreteQuotient X ⥤ Profinite :=
   X.fintypeDiagram ⋙ FintypeCat.toProfinite
 #align Profinite.diagram Profinite.diagram
 
-/- warning: Profinite.as_limit_cone -> Profinite.asLimitCone is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
-Case conversion may be inaccurate. Consider using '#align Profinite.as_limit_cone Profinite.asLimitConeₓ'. -/
 /-- A cone over `X.diagram` whose cone point is `X`. -/
 def asLimitCone : CategoryTheory.Limits.Cone X.diagram :=
   { pt
     π := { app := fun S => ⟨S.proj, S.proj_isLocallyConstant.Continuous⟩ } }
 #align Profinite.as_limit_cone Profinite.asLimitCone
 
-/- warning: Profinite.is_iso_as_limit_cone_lift -> Profinite.isIso_asLimitCone_lift is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Profinite.is_iso_as_limit_cone_lift Profinite.isIso_asLimitCone_liftₓ'. -/
 instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asLimitCone) :=
   isIso_of_bijective _
     (by
@@ -102,12 +81,6 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
         apply hb)
 #align Profinite.is_iso_as_limit_cone_lift Profinite.isIso_asLimitCone_lift
 
-/- warning: Profinite.iso_as_limit_cone_lift -> Profinite.isoAsLimitConeLift is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} X (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)))
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} X (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)))
-Case conversion may be inaccurate. Consider using '#align Profinite.iso_as_limit_cone_lift Profinite.isoAsLimitConeLiftₓ'. -/
 /-- The isomorphism between `X` and the explicit limit of `X.diagram`,
 induced by lifting `X.as_limit_cone`.
 -/
@@ -115,12 +88,6 @@ def isoAsLimitConeLift : X ≅ (limitCone X.diagram).pt :=
   asIso <| (limitConeIsLimit _).lift X.asLimitCone
 #align Profinite.iso_as_limit_cone_lift Profinite.isoAsLimitConeLift
 
-/- warning: Profinite.as_limit_cone_iso -> Profinite.asLimitConeIso is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} (CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (CategoryTheory.Limits.Cone.category.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} (CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (CategoryTheory.Limits.Cone.category.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))
-Case conversion may be inaccurate. Consider using '#align Profinite.as_limit_cone_iso Profinite.asLimitConeIsoₓ'. -/
 /-- The isomorphism of cones `X.as_limit_cone` and `Profinite.limit_cone X.diagram`.
 The underlying isomorphism is defeq to `X.iso_as_limit_cone_lift`.
 -/
@@ -128,23 +95,11 @@ def asLimitConeIso : X.asLimitCone ≅ limitCone _ :=
   Limits.Cones.ext (isoAsLimitConeLift _) fun _ => rfl
 #align Profinite.as_limit_cone_iso Profinite.asLimitConeIso
 
-/- warning: Profinite.as_limit -> Profinite.asLimit is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.Limits.IsLimit.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.Limits.IsLimit.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)
-Case conversion may be inaccurate. Consider using '#align Profinite.as_limit Profinite.asLimitₓ'. -/
 /-- `X.as_limit_cone` is indeed a limit cone. -/
 def asLimit : CategoryTheory.Limits.IsLimit X.asLimitCone :=
   Limits.IsLimit.ofIsoLimit (limitConeIsLimit _) X.asLimitConeIso.symm
 #align Profinite.as_limit Profinite.asLimit
 
-/- warning: Profinite.lim -> Profinite.lim is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.Limits.LimitCone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.Limits.LimitCone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
-Case conversion may be inaccurate. Consider using '#align Profinite.lim Profinite.limₓ'. -/
 /-- A bundled version of `X.as_limit_cone` and `X.as_limit`. -/
 def lim : Limits.LimitCone X.diagram :=
   ⟨X.asLimitCone, X.asLimit⟩

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

@@ -86,10 +86,7 @@ def asLimitCone : CategoryTheory.Limits.Cone X.diagram :=
 #align Profinite.as_limit_cone Profinite.asLimitCone
 
 /- warning: Profinite.is_iso_as_limit_cone_lift -> Profinite.isIso_asLimitCone_lift is a dubious translation:
-lean 3 declaration is
-  forall (X : Profinite.{u1}), CategoryTheory.IsIso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)) (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))) (CategoryTheory.Limits.IsLimit.lift.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.limitConeIsLimit.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X))
-but is expected to have type
-  forall (X : Profinite.{u1}), CategoryTheory.IsIso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)) (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))) (CategoryTheory.Limits.IsLimit.lift.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.limitConeIsLimit.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X))
+<too large>
 Case conversion may be inaccurate. Consider using '#align Profinite.is_iso_as_limit_cone_lift Profinite.isIso_asLimitCone_liftₓ'. -/
 instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asLimitCone) :=
   isIso_of_bijective _

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Calle Sönne, Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.category.Profinite.as_limit
-! leanprover-community/mathlib commit d101e93197bb5f6ea89bd7ba386b7f7dff1f3903
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.DiscreteQuotient
 /-!
 # Profinite sets as limits of finite sets.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We show that any profinite set is isomorphic to the limit of its
 discrete (hence finite) quotients.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Calle Sönne, Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.category.Profinite.as_limit
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
+! leanprover-community/mathlib commit d101e93197bb5f6ea89bd7ba386b7f7dff1f3903
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,9 +14,6 @@ import Mathbin.Topology.DiscreteQuotient
 /-!
 # Profinite sets as limits of finite sets.
 
-> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.
-
 We show that any profinite set is isomorphic to the limit of its
 discrete (hence finite) quotients.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Calle Sönne, Adam Topaz
 
 ! This file was ported from Lean 3 source module topology.category.Profinite.as_limit
-! leanprover-community/mathlib commit d101e93197bb5f6ea89bd7ba386b7f7dff1f3903
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.DiscreteQuotient
 /-!
 # Profinite sets as limits of finite sets.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We show that any profinite set is isomorphic to the limit of its
 discrete (hence finite) quotients.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -44,6 +44,12 @@ universe u
 
 variable (X : Profinite.{u})
 
+/- warning: Profinite.fintype_diagram -> Profinite.fintypeDiagram is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) FintypeCat.{u1} FintypeCat.CategoryTheory.category.{u1}
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) FintypeCat.{u1} FintypeCat.instCategoryFintypeCat.{u1}
+Case conversion may be inaccurate. Consider using '#align Profinite.fintype_diagram Profinite.fintypeDiagramₓ'. -/
 /-- The functor `discrete_quotient X ⥤ Fintype` whose limit is isomorphic to `X`. -/
 def fintypeDiagram : DiscreteQuotient X ⥤ FintypeCat
     where
@@ -53,17 +59,35 @@ def fintypeDiagram : DiscreteQuotient X ⥤ FintypeCat
   map S T f := DiscreteQuotient.ofLE f.le
 #align Profinite.fintype_diagram Profinite.fintypeDiagram
 
+/- warning: Profinite.diagram -> Profinite.diagram is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1}
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.Functor.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1}
+Case conversion may be inaccurate. Consider using '#align Profinite.diagram Profinite.diagramₓ'. -/
 /-- An abbreviation for `X.fintype_diagram ⋙ Fintype_to_Profinite`. -/
 abbrev diagram : DiscreteQuotient X ⥤ Profinite :=
   X.fintypeDiagram ⋙ FintypeCat.toProfinite
 #align Profinite.diagram Profinite.diagram
 
+/- warning: Profinite.as_limit_cone -> Profinite.asLimitCone is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
+Case conversion may be inaccurate. Consider using '#align Profinite.as_limit_cone Profinite.asLimitConeₓ'. -/
 /-- A cone over `X.diagram` whose cone point is `X`. -/
 def asLimitCone : CategoryTheory.Limits.Cone X.diagram :=
   { pt
     π := { app := fun S => ⟨S.proj, S.proj_isLocallyConstant.Continuous⟩ } }
 #align Profinite.as_limit_cone Profinite.asLimitCone
 
+/- warning: Profinite.is_iso_as_limit_cone_lift -> Profinite.isIso_asLimitCone_lift is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.IsIso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)) (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))) (CategoryTheory.Limits.IsLimit.lift.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.limitConeIsLimit.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X))
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.IsIso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)) (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))) (CategoryTheory.Limits.IsLimit.lift.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.limitConeIsLimit.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X))
+Case conversion may be inaccurate. Consider using '#align Profinite.is_iso_as_limit_cone_lift Profinite.isIso_asLimitCone_liftₓ'. -/
 instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asLimitCone) :=
   isIso_of_bijective _
     (by
@@ -78,6 +102,12 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
         apply hb)
 #align Profinite.is_iso_as_limit_cone_lift Profinite.isIso_asLimitCone_lift
 
+/- warning: Profinite.iso_as_limit_cone_lift -> Profinite.isoAsLimitConeLift is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} X (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)))
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} Profinite.{u1} Profinite.category.{u1} X (CategoryTheory.Limits.Cone.pt.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X)))
+Case conversion may be inaccurate. Consider using '#align Profinite.iso_as_limit_cone_lift Profinite.isoAsLimitConeLiftₓ'. -/
 /-- The isomorphism between `X` and the explicit limit of `X.diagram`,
 induced by lifting `X.as_limit_cone`.
 -/
@@ -85,6 +115,12 @@ def isoAsLimitConeLift : X ≅ (limitCone X.diagram).pt :=
   asIso <| (limitConeIsLimit _).lift X.asLimitCone
 #align Profinite.iso_as_limit_cone_lift Profinite.isoAsLimitConeLift
 
+/- warning: Profinite.as_limit_cone_iso -> Profinite.asLimitConeIso is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} (CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (CategoryTheory.Limits.Cone.category.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.Iso.{u1, succ u1} (CategoryTheory.Limits.Cone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (CategoryTheory.Limits.Cone.category.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)) (Profinite.asLimitCone.{u1} X) (Profinite.limitCone.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) (Profinite.diagram.{u1} X))
+Case conversion may be inaccurate. Consider using '#align Profinite.as_limit_cone_iso Profinite.asLimitConeIsoₓ'. -/
 /-- The isomorphism of cones `X.as_limit_cone` and `Profinite.limit_cone X.diagram`.
 The underlying isomorphism is defeq to `X.iso_as_limit_cone_lift`.
 -/
@@ -92,11 +128,23 @@ def asLimitConeIso : X.asLimitCone ≅ limitCone _ :=
   Limits.Cones.ext (isoAsLimitConeLift _) fun _ => rfl
 #align Profinite.as_limit_cone_iso Profinite.asLimitConeIso
 
+/- warning: Profinite.as_limit -> Profinite.asLimit is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.Limits.IsLimit.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.Limits.IsLimit.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X) (Profinite.asLimitCone.{u1} X)
+Case conversion may be inaccurate. Consider using '#align Profinite.as_limit Profinite.asLimitₓ'. -/
 /-- `X.as_limit_cone` is indeed a limit cone. -/
 def asLimit : CategoryTheory.Limits.IsLimit X.asLimitCone :=
   Limits.IsLimit.ofIsoLimit (limitConeIsLimit _) X.asLimitConeIso.symm
 #align Profinite.as_limit Profinite.asLimit
 
+/- warning: Profinite.lim -> Profinite.lim is a dubious translation:
+lean 3 declaration is
+  forall (X : Profinite.{u1}), CategoryTheory.Limits.LimitCone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.semilatticeInf.{u1} (coeSort.{succ (succ u1), succ (succ u1)} Profinite.{u1} Type.{u1} Profinite.hasCoeToSort.{u1} X) (TopCat.topologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
+but is expected to have type
+  forall (X : Profinite.{u1}), CategoryTheory.Limits.LimitCone.{u1, u1, u1, succ u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (Preorder.smallCategory.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X)))) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} (CategoryTheory.Bundled.α.{u1, u1} TopologicalSpace.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))) (TopCat.topologicalSpace_coe.{u1} (CompHaus.toTop.{u1} (Profinite.toCompHaus.{u1} X))))))) Profinite.{u1} Profinite.category.{u1} (Profinite.diagram.{u1} X)
+Case conversion may be inaccurate. Consider using '#align Profinite.lim Profinite.limₓ'. -/
 /-- A bundled version of `X.as_limit_cone` and `X.as_limit`. -/
 def lim : Limits.LimitCone X.diagram :=
   ⟨X.asLimitCone, X.asLimit⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

@@ -50,7 +50,7 @@ def fintypeDiagram : DiscreteQuotient X ⥤ FintypeCat
   obj S :=
     haveI := Fintype.ofFinite S
     FintypeCat.of S
-  map S T f := DiscreteQuotient.ofLe f.le
+  map S T f := DiscreteQuotient.ofLE f.le
 #align Profinite.fintype_diagram Profinite.fintypeDiagram
 
 /-- An abbreviation for `X.fintype_diagram ⋙ Fintype_to_Profinite`. -/

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

@@ -60,7 +60,7 @@ abbrev diagram : DiscreteQuotient X ⥤ Profinite :=
 
 /-- A cone over `X.diagram` whose cone point is `X`. -/
 def asLimitCone : CategoryTheory.Limits.Cone X.diagram :=
-  { x
+  { pt
     π := { app := fun S => ⟨S.proj, S.proj_isLocallyConstant.Continuous⟩ } }
 #align Profinite.as_limit_cone Profinite.asLimitCone
 
@@ -69,7 +69,7 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
     (by
       refine' ⟨fun a b h => _, fun a => _⟩
       · refine' DiscreteQuotient.eq_of_forall_proj_eq fun S => _
-        apply_fun fun f : (limit_cone X.diagram).x => f.val S  at h
+        apply_fun fun f : (limit_cone X.diagram).pt => f.val S  at h
         exact h
       · obtain ⟨b, hb⟩ :=
           DiscreteQuotient.exists_of_compat (fun S => a.val S) fun _ _ h => a.prop (hom_of_le h)
@@ -81,7 +81,7 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
 /-- The isomorphism between `X` and the explicit limit of `X.diagram`,
 induced by lifting `X.as_limit_cone`.
 -/
-def isoAsLimitConeLift : X ≅ (limitCone X.diagram).x :=
+def isoAsLimitConeLift : X ≅ (limitCone X.diagram).pt :=
   asIso <| (limitConeIsLimit _).lift X.asLimitCone
 #align Profinite.iso_as_limit_cone_lift Profinite.isoAsLimitConeLift
 

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

We allow the indexing category for the cofiltered limit in the result Profinite.exists_locallyConstant to live in a smaller universe than our profinite sets.

@@ -64,12 +64,12 @@ def asLimitCone : CategoryTheory.Limits.Cone X.diagram :=
 set_option linter.uppercaseLean3 false in
 #align Profinite.as_limit_cone Profinite.asLimitCone
 
-instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asLimitCone) :=
+instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit.{u, u} X.diagram).lift X.asLimitCone) :=
   isIso_of_bijective _
     (by
       refine' ⟨fun a b h => _, fun a => _⟩
       · refine' DiscreteQuotient.eq_of_forall_proj_eq fun S => _
-        apply_fun fun f : (limitCone X.diagram).pt => f.val S at h
+        apply_fun fun f : (limitCone.{u, u} X.diagram).pt => f.val S at h
         exact h
       · obtain ⟨b, hb⟩ :=
           DiscreteQuotient.exists_of_compat (fun S => a.val S) fun _ _ h => a.prop (homOfLE h)
@@ -87,15 +87,15 @@ set_option linter.uppercaseLean3 false in
 /-- The isomorphism between `X` and the explicit limit of `X.diagram`,
 induced by lifting `X.asLimitCone`.
 -/
-def isoAsLimitConeLift : X ≅ (limitCone X.diagram).pt :=
-  asIso <| (limitConeIsLimit _).lift X.asLimitCone
+def isoAsLimitConeLift : X ≅ (limitCone.{u, u} X.diagram).pt :=
+  asIso <| (limitConeIsLimit.{u, u} _).lift X.asLimitCone
 set_option linter.uppercaseLean3 false in
 #align Profinite.iso_as_limit_cone_lift Profinite.isoAsLimitConeLift
 
 /-- The isomorphism of cones `X.asLimitCone` and `Profinite.limitCone X.diagram`.
 The underlying isomorphism is defeq to `X.isoAsLimitConeLift`.
 -/
-def asLimitConeIso : X.asLimitCone ≅ limitCone _ :=
+def asLimitConeIso : X.asLimitCone ≅ limitCone.{u, u} _ :=
   Limits.Cones.ext (isoAsLimitConeLift _) fun _ => rfl
 set_option linter.uppercaseLean3 false in
 #align Profinite.as_limit_cone_iso Profinite.asLimitConeIso

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Calle Sönne, Adam Topaz
-
-! This file was ported from Lean 3 source module topology.category.Profinite.as_limit
-! leanprover-community/mathlib commit d101e93197bb5f6ea89bd7ba386b7f7dff1f3903
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Category.Profinite.Basic
 import Mathlib.Topology.DiscreteQuotient
 
+#align_import topology.category.Profinite.as_limit from "leanprover-community/mathlib"@"d101e93197bb5f6ea89bd7ba386b7f7dff1f3903"
+
 /-!
 # Profinite sets as limits of finite sets.
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -72,7 +72,7 @@ instance isIso_asLimitCone_lift : IsIso ((limitConeIsLimit X.diagram).lift X.asL
     (by
       refine' ⟨fun a b h => _, fun a => _⟩
       · refine' DiscreteQuotient.eq_of_forall_proj_eq fun S => _
-        apply_fun fun f : (limitCone X.diagram).pt => f.val S  at h
+        apply_fun fun f : (limitCone X.diagram).pt => f.val S at h
         exact h
       · obtain ⟨b, hb⟩ :=
           DiscreteQuotient.exists_of_compat (fun S => a.val S) fun _ _ h => a.prop (homOfLE h)

@@ -25,10 +25,10 @@ There are a handful of definitions in this file, given `X : Profinite`:
 2. `X.diagram` is an abbreviation for `X.fintypeDiagram ⋙ FintypeCat.toProfinite`.
 3. `X.asLimitCone` is the cone over `X.diagram` whose cone point is `X`.
 4. `X.isoAsLimitConeLift` is the isomorphism `X ≅ (Profinite.limitCone X.diagram).X` induced
-  by lifting `X.as_limit_cone`.
+  by lifting `X.asLimitCone`.
 5. `X.asLimitConeIso` is the isomorphism `X.asLimitCone ≅ (Profinite.limitCone X.diagram)`
   induced by `X.isoAsLimitConeLift`.
-6. `X.asLimit` is a term of type `is_limit X.asLimitCone`.
+6. `X.asLimit` is a term of type `IsLimit X.asLimitCone`.
 7. `X.lim : CategoryTheory.Limits.LimitCone X.asLimitCone` is a bundled combination of 3 and 6.
 
 -/

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>