topology.discrete_quotient ⟷ Mathlib.Topology.DiscreteQuotient

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

@@ -493,7 +493,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
 instance [CompactSpace X] : Finite S :=
   by
   have : CompactSpace S := Quotient.compactSpace
-  rwa [← isCompact_univ_iff, isCompact_iff_finite, finite_univ_iff] at this 
+  rwa [← isCompact_univ_iff, isCompact_iff_finite, finite_univ_iff] at this
 
 end DiscreteQuotient
 

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

@@ -479,7 +479,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
     ∃ x : X, ∀ Q : DiscreteQuotient X, Q.proj x = Qs _ :=
   by
   obtain ⟨x, hx⟩ : (⋂ Q, proj Q ⁻¹' {Qs Q}).Nonempty :=
-    IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed
+    IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed
       (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_isDirected_ge fun A B h => _)
       (fun Q => (singleton_nonempty _).Preimage Q.proj_surjective)
       (fun i => (is_closed_preimage _ _).IsCompact) fun i => is_closed_preimage _ _

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

@@ -82,14 +82,14 @@ namespace DiscreteQuotient
 
 variable (S : DiscreteQuotient X)
 
-#print DiscreteQuotient.ofClopen /-
+#print DiscreteQuotient.ofIsClopen /-
 /-- Construct a discrete quotient from a clopen set. -/
-def ofClopen {A : Set X} (h : IsClopen A) : DiscreteQuotient X
+def ofIsClopen {A : Set X} (h : IsClopen A) : DiscreteQuotient X
     where
   toSetoid :=
     ⟨fun x y => x ∈ A ↔ y ∈ A, fun _ => Iff.rfl, fun _ _ => Iff.symm, fun _ _ _ => Iff.trans⟩
   isOpen_setOf_rel x := by by_cases hx : x ∈ A <;> simp [Setoid.Rel, hx, h.1, h.2, ← compl_set_of]
-#align discrete_quotient.of_clopen DiscreteQuotient.ofClopen
+#align discrete_quotient.of_clopen DiscreteQuotient.ofIsClopen
 -/
 
 #print DiscreteQuotient.refl /-
@@ -456,7 +456,7 @@ end Map
 theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconnectedSpace X]
     {x y : X} (h : ∀ Q : DiscreteQuotient X, Q.proj x = Q.proj y) : x = y :=
   by
-  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_iInter_clopen,
+  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_iInter_isClopen,
     mem_Inter]
   rintro ⟨U, hU1, hU2⟩
   exact (Quotient.exact' (h (of_clopen hU1))).mpr hU2

mathlib commit https://github.com/leanprover-community/mathlib/commit/3365b20c2ffa7c35e47e5209b89ba9abdddf3ffe

@@ -480,7 +480,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
   by
   obtain ⟨x, hx⟩ : (⋂ Q, proj Q ⁻¹' {Qs Q}).Nonempty :=
     IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed
-      (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_inf fun A B h => _)
+      (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_isDirected_ge fun A B h => _)
       (fun Q => (singleton_nonempty _).Preimage Q.proj_surjective)
       (fun i => (is_closed_preimage _ _).IsCompact) fun i => is_closed_preimage _ _
   · refine' ⟨x, fun Q => _⟩

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

@@ -3,9 +3,9 @@ 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.Separation
-import Mathbin.Topology.SubsetProperties
-import Mathbin.Topology.LocallyConstant.Basic
+import Topology.Separation
+import Topology.SubsetProperties
+import Topology.LocallyConstant.Basic
 
 #align_import topology.discrete_quotient from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
 

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

@@ -2,16 +2,13 @@
 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.discrete_quotient
-! leanprover-community/mathlib commit 34ee86e6a59d911a8e4f89b68793ee7577ae79c7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Separation
 import Mathbin.Topology.SubsetProperties
 import Mathbin.Topology.LocallyConstant.Basic
 
+#align_import topology.discrete_quotient from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
+
 /-!
 
 # Discrete quotients of a topological space.

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

@@ -230,14 +230,18 @@ theorem comap_id : S.comap (ContinuousMap.id X) = S := by ext; rfl
 #align discrete_quotient.comap_id DiscreteQuotient.comap_id
 -/
 
+#print DiscreteQuotient.comap_comp /-
 @[simp]
 theorem comap_comp (S : DiscreteQuotient Z) : S.comap (g.comp f) = (S.comap g).comap f :=
   rfl
 #align discrete_quotient.comap_comp DiscreteQuotient.comap_comp
+-/
 
+#print DiscreteQuotient.comap_mono /-
 @[mono]
 theorem comap_mono {A B : DiscreteQuotient Y} (h : A ≤ B) : A.comap f ≤ B.comap f := by tauto
 #align discrete_quotient.comap_mono DiscreteQuotient.comap_mono
+-/
 
 end Comap
 
@@ -245,10 +249,12 @@ section OfLe
 
 variable {A B C : DiscreteQuotient X}
 
+#print DiscreteQuotient.ofLE /-
 /-- The map induced by a refinement of a discrete quotient. -/
 def ofLE (h : A ≤ B) : A → B :=
   Quotient.map' (fun x => x) h
 #align discrete_quotient.of_le DiscreteQuotient.ofLE
+-/
 
 #print DiscreteQuotient.ofLE_refl /-
 @[simp]
@@ -261,29 +267,39 @@ theorem ofLE_refl_apply (a : A) : ofLE (le_refl A) a = a := by simp
 #align discrete_quotient.of_le_refl_apply DiscreteQuotient.ofLE_refl_apply
 -/
 
+#print DiscreteQuotient.ofLE_ofLE /-
 @[simp]
 theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLE h₂ (ofLE h₁ x) = ofLE (h₁.trans h₂) x :=
   by rcases x with ⟨⟩; rfl
 #align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLE
+-/
 
+#print DiscreteQuotient.ofLE_comp_ofLE /-
 @[simp]
 theorem ofLE_comp_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) : ofLE h₂ ∘ ofLE h₁ = ofLE (le_trans h₁ h₂) :=
   funext <| ofLE_ofLE _ _
 #align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLE_comp_ofLE
+-/
 
+#print DiscreteQuotient.ofLE_continuous /-
 theorem ofLE_continuous (h : A ≤ B) : Continuous (ofLE h) :=
   continuous_of_discreteTopology
 #align discrete_quotient.of_le_continuous DiscreteQuotient.ofLE_continuous
+-/
 
+#print DiscreteQuotient.ofLE_proj /-
 @[simp]
 theorem ofLE_proj (h : A ≤ B) (x : X) : ofLE h (A.proj x) = B.proj x :=
   Quotient.sound' (B.refl _)
 #align discrete_quotient.of_le_proj DiscreteQuotient.ofLE_proj
+-/
 
+#print DiscreteQuotient.ofLE_comp_proj /-
 @[simp]
 theorem ofLE_comp_proj (h : A ≤ B) : ofLE h ∘ A.proj = B.proj :=
   funext <| ofLE_proj _
 #align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLE_comp_proj
+-/
 
 end OfLe
 
@@ -305,22 +321,30 @@ instance [LocallyConnectedSpace X] : OrderBot (DiscreteQuotient X)
   bot_le S x y (h : connectedComponent x = connectedComponent y) :=
     (S.isClopen_setOf_rel x).connectedComponent_subset (S.refl _) <| h.symm ▸ mem_connectedComponent
 
+#print DiscreteQuotient.proj_bot_eq /-
 @[simp]
 theorem proj_bot_eq [LocallyConnectedSpace X] {x y : X} :
     proj ⊥ x = proj ⊥ y ↔ connectedComponent x = connectedComponent y :=
   Quotient.eq''
 #align discrete_quotient.proj_bot_eq DiscreteQuotient.proj_bot_eq
+-/
 
+#print DiscreteQuotient.proj_bot_inj /-
 theorem proj_bot_inj [DiscreteTopology X] {x y : X} : proj ⊥ x = proj ⊥ y ↔ x = y := by simp
 #align discrete_quotient.proj_bot_inj DiscreteQuotient.proj_bot_inj
+-/
 
+#print DiscreteQuotient.proj_bot_injective /-
 theorem proj_bot_injective [DiscreteTopology X] : Injective (⊥ : DiscreteQuotient X).proj :=
   fun _ _ => proj_bot_inj.1
 #align discrete_quotient.proj_bot_injective DiscreteQuotient.proj_bot_injective
+-/
 
+#print DiscreteQuotient.proj_bot_bijective /-
 theorem proj_bot_bijective [DiscreteTopology X] : Bijective (⊥ : DiscreteQuotient X).proj :=
   ⟨proj_bot_injective, proj_surjective _⟩
 #align discrete_quotient.proj_bot_bijective DiscreteQuotient.proj_bot_bijective
+-/
 
 section Map
 
@@ -341,17 +365,23 @@ theorem leComap_id : LEComap (ContinuousMap.id X) A A := fun _ _ => id
 
 variable {A A' B B'} {f} {g : C(Y, Z)} {C : DiscreteQuotient Z}
 
+#print DiscreteQuotient.leComap_id_iff /-
 @[simp]
 theorem leComap_id_iff : LEComap (ContinuousMap.id X) A A' ↔ A ≤ A' :=
   Iff.rfl
 #align discrete_quotient.le_comap_id_iff DiscreteQuotient.leComap_id_iff
+-/
 
+#print DiscreteQuotient.LEComap.comp /-
 theorem LEComap.comp : LEComap g B C → LEComap f A B → LEComap (g.comp f) A C := by tauto
 #align discrete_quotient.le_comap.comp DiscreteQuotient.LEComap.comp
+-/
 
+#print DiscreteQuotient.LEComap.mono /-
 theorem LEComap.mono (h : LEComap f A B) (hA : A' ≤ A) (hB : B ≤ B') : LEComap f A' B' :=
   hA.trans <| le_trans h <| comap_mono _ hB
 #align discrete_quotient.le_comap.mono DiscreteQuotient.LEComap.mono
+-/
 
 #print DiscreteQuotient.map /-
 /-- Map a discrete quotient along a continuous map. -/
@@ -360,19 +390,25 @@ def map (f : C(X, Y)) (cond : LEComap f A B) : A → B :=
 #align discrete_quotient.map DiscreteQuotient.map
 -/
 
+#print DiscreteQuotient.map_continuous /-
 theorem map_continuous (cond : LEComap f A B) : Continuous (map f cond) :=
   continuous_of_discreteTopology
 #align discrete_quotient.map_continuous DiscreteQuotient.map_continuous
+-/
 
+#print DiscreteQuotient.map_comp_proj /-
 @[simp]
 theorem map_comp_proj (cond : LEComap f A B) : map f cond ∘ A.proj = B.proj ∘ f :=
   rfl
 #align discrete_quotient.map_comp_proj DiscreteQuotient.map_comp_proj
+-/
 
+#print DiscreteQuotient.map_proj /-
 @[simp]
 theorem map_proj (cond : LEComap f A B) (x : X) : map f cond (A.proj x) = B.proj (f x) :=
   rfl
 #align discrete_quotient.map_proj DiscreteQuotient.map_proj
+-/
 
 #print DiscreteQuotient.map_id /-
 @[simp]
@@ -380,32 +416,42 @@ theorem map_id : map _ (leComap_id A) = id := by ext ⟨⟩ <;> rfl
 #align discrete_quotient.map_id DiscreteQuotient.map_id
 -/
 
+#print DiscreteQuotient.map_comp /-
 @[simp]
 theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
     map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 := by ext ⟨⟩; rfl
 #align discrete_quotient.map_comp DiscreteQuotient.map_comp
+-/
 
+#print DiscreteQuotient.ofLE_map /-
 @[simp]
 theorem ofLE_map (cond : LEComap f A B) (h : B ≤ B') (a : A) :
     ofLE h (map f cond a) = map f (cond.mono le_rfl h) a := by rcases a with ⟨⟩; rfl
 #align discrete_quotient.of_le_map DiscreteQuotient.ofLE_map
+-/
 
+#print DiscreteQuotient.ofLE_comp_map /-
 @[simp]
 theorem ofLE_comp_map (cond : LEComap f A B) (h : B ≤ B') :
     ofLE h ∘ map f cond = map f (cond.mono le_rfl h) :=
   funext <| ofLE_map cond h
 #align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLE_comp_map
+-/
 
+#print DiscreteQuotient.map_ofLE /-
 @[simp]
 theorem map_ofLE (cond : LEComap f A B) (h : A' ≤ A) (c : A') :
     map f cond (ofLE h c) = map f (cond.mono h le_rfl) c := by rcases c with ⟨⟩; rfl
 #align discrete_quotient.map_of_le DiscreteQuotient.map_ofLE
+-/
 
+#print DiscreteQuotient.map_comp_ofLE /-
 @[simp]
 theorem map_comp_ofLE (cond : LEComap f A B) (h : A' ≤ A) :
     map f cond ∘ ofLE h = map f (cond.mono h le_rfl) :=
   funext <| map_ofLE cond h
 #align discrete_quotient.map_comp_of_le DiscreteQuotient.map_comp_ofLE
+-/
 
 end Map
 
@@ -420,6 +466,7 @@ theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconn
 #align discrete_quotient.eq_of_forall_proj_eq DiscreteQuotient.eq_of_forall_proj_eq
 -/
 
+#print DiscreteQuotient.fiber_subset_ofLE /-
 theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
     A.proj ⁻¹' {a} ⊆ B.proj ⁻¹' {ofLE h a} :=
   by
@@ -427,7 +474,9 @@ theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
   rw [fiber_eq, of_le_proj, fiber_eq]
   exact fun _ h' => h h'
 #align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLE
+-/
 
+#print DiscreteQuotient.exists_of_compat /-
 theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
     (compat : ∀ (A B : DiscreteQuotient X) (h : A ≤ B), ofLE h (Qs _) = Qs _) :
     ∃ x : X, ∀ Q : DiscreteQuotient X, Q.proj x = Qs _ :=
@@ -442,6 +491,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
   · rw [← compat _ _ h]
     exact fiber_subset_of_le _ _
 #align discrete_quotient.exists_of_compat DiscreteQuotient.exists_of_compat
+-/
 
 instance [CompactSpace X] : Finite S :=
   by
@@ -471,9 +521,11 @@ def lift : LocallyConstant f.DiscreteQuotient α :=
 #align locally_constant.lift LocallyConstant.lift
 -/
 
+#print LocallyConstant.lift_comp_proj /-
 @[simp]
 theorem lift_comp_proj : f.lift ∘ f.DiscreteQuotient.proj = f := by ext; rfl
 #align locally_constant.lift_comp_proj LocallyConstant.lift_comp_proj
+-/
 
 end LocallyConstant
 

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

@@ -296,7 +296,7 @@ instance [LocallyConnectedSpace X] : OrderBot (DiscreteQuotient X)
     { toSetoid := connectedComponentSetoid X
       isOpen_setOf_rel := fun x =>
         by
-        have : connectedComponent x = { y | (connectedComponentSetoid X).Rel x y } :=
+        have : connectedComponent x = {y | (connectedComponentSetoid X).Rel x y} :=
           by
           ext y
           simpa only [connectedComponentSetoid, ← connectedComponent_eq_iff_mem] using eq_comm

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

@@ -446,7 +446,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
 instance [CompactSpace X] : Finite S :=
   by
   have : CompactSpace S := Quotient.compactSpace
-  rwa [← isCompact_univ_iff, isCompact_iff_finite, finite_univ_iff] at this
+  rwa [← isCompact_univ_iff, isCompact_iff_finite, finite_univ_iff] at this 
 
 end DiscreteQuotient
 

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

@@ -230,23 +230,11 @@ theorem comap_id : S.comap (ContinuousMap.id X) = S := by ext; rfl
 #align discrete_quotient.comap_id DiscreteQuotient.comap_id
 -/
 
-/- warning: discrete_quotient.comap_comp -> DiscreteQuotient.comap_comp is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : TopologicalSpace.{u3} Z] (g : ContinuousMap.{u2, u3} Y Z _inst_2 _inst_3) (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) (S : DiscreteQuotient.{u3} Z _inst_3), Eq.{succ u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.comap.{u1, u3} X Z _inst_1 _inst_3 (ContinuousMap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 g f) S) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f (DiscreteQuotient.comap.{u2, u3} Y Z _inst_2 _inst_3 g S))
-but is expected to have type
-  forall {X : Type.{u2}} {Y : Type.{u1}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] [_inst_3 : TopologicalSpace.{u3} Z] (g : ContinuousMap.{u1, u3} Y Z _inst_2 _inst_3) (f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2) (S : DiscreteQuotient.{u3} Z _inst_3), Eq.{succ u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.comap.{u2, u3} X Z _inst_1 _inst_3 (ContinuousMap.comp.{u2, u1, u3} X Y Z _inst_1 _inst_2 _inst_3 g f) S) (DiscreteQuotient.comap.{u2, u1} X Y _inst_1 _inst_2 f (DiscreteQuotient.comap.{u1, u3} Y Z _inst_2 _inst_3 g S))
-Case conversion may be inaccurate. Consider using '#align discrete_quotient.comap_comp DiscreteQuotient.comap_compₓ'. -/
 @[simp]
 theorem comap_comp (S : DiscreteQuotient Z) : S.comap (g.comp f) = (S.comap g).comap f :=
   rfl
 #align discrete_quotient.comap_comp DiscreteQuotient.comap_comp
 
-/- warning: discrete_quotient.comap_mono -> DiscreteQuotient.comap_mono is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) {A : DiscreteQuotient.{u2} Y _inst_2} {B : DiscreteQuotient.{u2} Y _inst_2}, (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toHasLe.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f A) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f B))
-but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) {A : DiscreteQuotient.{u2} Y _inst_2} {B : DiscreteQuotient.{u2} Y _inst_2}, (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} Y _inst_2)))) A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f A) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f B))
-Case conversion may be inaccurate. Consider using '#align discrete_quotient.comap_mono DiscreteQuotient.comap_monoₓ'. -/
 @[mono]
 theorem comap_mono {A B : DiscreteQuotient Y} (h : A ≤ B) : A.comap f ≤ B.comap f := by tauto
 #align discrete_quotient.comap_mono DiscreteQuotient.comap_mono
@@ -257,12 +245,6 @@ section OfLe
 
 variable {A B C : DiscreteQuotient X}
 
-/- warning: discrete_quotient.of_le -> DiscreteQuotient.ofLE is a dubious translation:
-lean 3 declaration is
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 /-- The map induced by a refinement of a discrete quotient. -/
 def ofLE (h : A ≤ B) : A → B :=
   Quotient.map' (fun x => x) h
@@ -279,55 +261,25 @@ theorem ofLE_refl_apply (a : A) : ofLE (le_refl A) a = a := by simp
 #align discrete_quotient.of_le_refl_apply DiscreteQuotient.ofLE_refl_apply
 -/
 
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 @[simp]
 theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLE h₂ (ofLE h₁ x) = ofLE (h₁.trans h₂) x :=
   by rcases x with ⟨⟩; rfl
 #align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLE
 
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 @[simp]
 theorem ofLE_comp_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) : ofLE h₂ ∘ ofLE h₁ = ofLE (le_trans h₁ h₂) :=
   funext <| ofLE_ofLE _ _
 #align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLE_comp_ofLE
 
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 theorem ofLE_continuous (h : A ≤ B) : Continuous (ofLE h) :=
   continuous_of_discreteTopology
 #align discrete_quotient.of_le_continuous DiscreteQuotient.ofLE_continuous
 
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 @[simp]
 theorem ofLE_proj (h : A ≤ B) (x : X) : ofLE h (A.proj x) = B.proj x :=
   Quotient.sound' (B.refl _)
 #align discrete_quotient.of_le_proj DiscreteQuotient.ofLE_proj
 
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 @[simp]
 theorem ofLE_comp_proj (h : A ≤ B) : ofLE h ∘ A.proj = B.proj :=
   funext <| ofLE_proj _
@@ -353,43 +305,19 @@ instance [LocallyConnectedSpace X] : OrderBot (DiscreteQuotient X)
   bot_le S x y (h : connectedComponent x = connectedComponent y) :=
     (S.isClopen_setOf_rel x).connectedComponent_subset (S.refl _) <| h.symm ▸ mem_connectedComponent
 
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 @[simp]
 theorem proj_bot_eq [LocallyConnectedSpace X] {x y : X} :
     proj ⊥ x = proj ⊥ y ↔ connectedComponent x = connectedComponent y :=
   Quotient.eq''
 #align discrete_quotient.proj_bot_eq DiscreteQuotient.proj_bot_eq
 
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 theorem proj_bot_inj [DiscreteTopology X] {x y : X} : proj ⊥ x = proj ⊥ y ↔ x = y := by simp
 #align discrete_quotient.proj_bot_inj DiscreteQuotient.proj_bot_inj
 
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 theorem proj_bot_injective [DiscreteTopology X] : Injective (⊥ : DiscreteQuotient X).proj :=
   fun _ _ => proj_bot_inj.1
 #align discrete_quotient.proj_bot_injective DiscreteQuotient.proj_bot_injective
 
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 theorem proj_bot_bijective [DiscreteTopology X] : Bijective (⊥ : DiscreteQuotient X).proj :=
   ⟨proj_bot_injective, proj_surjective _⟩
 #align discrete_quotient.proj_bot_bijective DiscreteQuotient.proj_bot_bijective
@@ -413,32 +341,14 @@ theorem leComap_id : LEComap (ContinuousMap.id X) A A := fun _ _ => id
 
 variable {A A' B B'} {f} {g : C(Y, Z)} {C : DiscreteQuotient Z}
 
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 @[simp]
 theorem leComap_id_iff : LEComap (ContinuousMap.id X) A A' ↔ A ≤ A' :=
   Iff.rfl
 #align discrete_quotient.le_comap_id_iff DiscreteQuotient.leComap_id_iff
 
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 theorem LEComap.comp : LEComap g B C → LEComap f A B → LEComap (g.comp f) A C := by tauto
 #align discrete_quotient.le_comap.comp DiscreteQuotient.LEComap.comp
 
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 theorem LEComap.mono (h : LEComap f A B) (hA : A' ≤ A) (hB : B ≤ B') : LEComap f A' B' :=
   hA.trans <| le_trans h <| comap_mono _ hB
 #align discrete_quotient.le_comap.mono DiscreteQuotient.LEComap.mono
@@ -450,33 +360,15 @@ def map (f : C(X, Y)) (cond : LEComap f A B) : A → B :=
 #align discrete_quotient.map DiscreteQuotient.map
 -/
 
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 theorem map_continuous (cond : LEComap f A B) : Continuous (map f cond) :=
   continuous_of_discreteTopology
 #align discrete_quotient.map_continuous DiscreteQuotient.map_continuous
 
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 @[simp]
 theorem map_comp_proj (cond : LEComap f A B) : map f cond ∘ A.proj = B.proj ∘ f :=
   rfl
 #align discrete_quotient.map_comp_proj DiscreteQuotient.map_comp_proj
 
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 @[simp]
 theorem map_proj (cond : LEComap f A B) (x : X) : map f cond (A.proj x) = B.proj (f x) :=
   rfl
@@ -488,57 +380,27 @@ theorem map_id : map _ (leComap_id A) = id := by ext ⟨⟩ <;> rfl
 #align discrete_quotient.map_id DiscreteQuotient.map_id
 -/
 
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 @[simp]
 theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
     map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 := by ext ⟨⟩; rfl
 #align discrete_quotient.map_comp DiscreteQuotient.map_comp
 
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 @[simp]
 theorem ofLE_map (cond : LEComap f A B) (h : B ≤ B') (a : A) :
     ofLE h (map f cond a) = map f (cond.mono le_rfl h) a := by rcases a with ⟨⟩; rfl
 #align discrete_quotient.of_le_map DiscreteQuotient.ofLE_map
 
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 @[simp]
 theorem ofLE_comp_map (cond : LEComap f A B) (h : B ≤ B') :
     ofLE h ∘ map f cond = map f (cond.mono le_rfl h) :=
   funext <| ofLE_map cond h
 #align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLE_comp_map
 
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 @[simp]
 theorem map_ofLE (cond : LEComap f A B) (h : A' ≤ A) (c : A') :
     map f cond (ofLE h c) = map f (cond.mono h le_rfl) c := by rcases c with ⟨⟩; rfl
 #align discrete_quotient.map_of_le DiscreteQuotient.map_ofLE
 
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 @[simp]
 theorem map_comp_ofLE (cond : LEComap f A B) (h : A' ≤ A) :
     map f cond ∘ ofLE h = map f (cond.mono h le_rfl) :=
@@ -558,12 +420,6 @@ theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconn
 #align discrete_quotient.eq_of_forall_proj_eq DiscreteQuotient.eq_of_forall_proj_eq
 -/
 
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 theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
     A.proj ⁻¹' {a} ⊆ B.proj ⁻¹' {ofLE h a} :=
   by
@@ -572,12 +428,6 @@ theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
   exact fun _ h' => h h'
 #align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLE
 
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 theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
     (compat : ∀ (A B : DiscreteQuotient X) (h : A ≤ B), ofLE h (Qs _) = Qs _) :
     ∃ x : X, ∀ Q : DiscreteQuotient X, Q.proj x = Qs _ :=
@@ -621,12 +471,6 @@ def lift : LocallyConstant f.DiscreteQuotient α :=
 #align locally_constant.lift LocallyConstant.lift
 -/
 
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 @[simp]
 theorem lift_comp_proj : f.lift ∘ f.DiscreteQuotient.proj = f := by ext; rfl
 #align locally_constant.lift_comp_proj LocallyConstant.lift_comp_proj

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

@@ -155,9 +155,7 @@ theorem proj_continuous : Continuous S.proj :=
 
 instance : DiscreteTopology S :=
   singletons_open_iff_discrete.1 <|
-    S.proj_surjective.forall.2 fun x =>
-      by
-      rw [← S.proj_quotient_map.is_open_preimage, fiber_eq]
+    S.proj_surjective.forall.2 fun x => by rw [← S.proj_quotient_map.is_open_preimage, fiber_eq];
       exact S.is_open_set_of_rel _
 
 #print DiscreteQuotient.proj_isLocallyConstant /-
@@ -185,9 +183,7 @@ theorem isClosed_preimage (A : Set S) : IsClosed (S.proj ⁻¹' A) :=
 -/
 
 #print DiscreteQuotient.isClopen_setOf_rel /-
-theorem isClopen_setOf_rel (x : X) : IsClopen (setOf (S.Rel x)) :=
-  by
-  rw [← fiber_eq]
+theorem isClopen_setOf_rel (x : X) : IsClopen (setOf (S.Rel x)) := by rw [← fiber_eq];
   apply is_clopen_preimage
 #align discrete_quotient.is_clopen_set_of_rel DiscreteQuotient.isClopen_setOf_rel
 -/
@@ -230,10 +226,7 @@ def comap (S : DiscreteQuotient Y) : DiscreteQuotient X
 
 #print DiscreteQuotient.comap_id /-
 @[simp]
-theorem comap_id : S.comap (ContinuousMap.id X) = S :=
-  by
-  ext
-  rfl
+theorem comap_id : S.comap (ContinuousMap.id X) = S := by ext; rfl
 #align discrete_quotient.comap_id DiscreteQuotient.comap_id
 -/
 
@@ -277,9 +270,7 @@ def ofLE (h : A ≤ B) : A → B :=
 
 #print DiscreteQuotient.ofLE_refl /-
 @[simp]
-theorem ofLE_refl : ofLE (le_refl A) = id := by
-  ext ⟨⟩
-  rfl
+theorem ofLE_refl : ofLE (le_refl A) = id := by ext ⟨⟩; rfl
 #align discrete_quotient.of_le_refl DiscreteQuotient.ofLE_refl
 -/
 
@@ -296,9 +287,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLEₓ'. -/
 @[simp]
 theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLE h₂ (ofLE h₁ x) = ofLE (h₁.trans h₂) x :=
-  by
-  rcases x with ⟨⟩
-  rfl
+  by rcases x with ⟨⟩; rfl
 #align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLE
 
 /- warning: discrete_quotient.of_le_comp_of_le -> DiscreteQuotient.ofLE_comp_ofLE is a dubious translation:
@@ -507,10 +496,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_comp DiscreteQuotient.map_compₓ'. -/
 @[simp]
 theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
-    map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 :=
-  by
-  ext ⟨⟩
-  rfl
+    map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 := by ext ⟨⟩; rfl
 #align discrete_quotient.map_comp DiscreteQuotient.map_comp
 
 /- warning: discrete_quotient.of_le_map -> DiscreteQuotient.ofLE_map is a dubious translation:
@@ -521,10 +507,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_map DiscreteQuotient.ofLE_mapₓ'. -/
 @[simp]
 theorem ofLE_map (cond : LEComap f A B) (h : B ≤ B') (a : A) :
-    ofLE h (map f cond a) = map f (cond.mono le_rfl h) a :=
-  by
-  rcases a with ⟨⟩
-  rfl
+    ofLE h (map f cond a) = map f (cond.mono le_rfl h) a := by rcases a with ⟨⟩; rfl
 #align discrete_quotient.of_le_map DiscreteQuotient.ofLE_map
 
 /- warning: discrete_quotient.of_le_comp_map -> DiscreteQuotient.ofLE_comp_map is a dubious translation:
@@ -547,10 +530,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLEₓ'. -/
 @[simp]
 theorem map_ofLE (cond : LEComap f A B) (h : A' ≤ A) (c : A') :
-    map f cond (ofLE h c) = map f (cond.mono h le_rfl) c :=
-  by
-  rcases c with ⟨⟩
-  rfl
+    map f cond (ofLE h c) = map f (cond.mono h le_rfl) c := by rcases c with ⟨⟩; rfl
 #align discrete_quotient.map_of_le DiscreteQuotient.map_ofLE
 
 /- warning: discrete_quotient.map_comp_of_le -> DiscreteQuotient.map_comp_ofLE is a dubious translation:
@@ -648,10 +628,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align locally_constant.lift_comp_proj LocallyConstant.lift_comp_projₓ'. -/
 @[simp]
-theorem lift_comp_proj : f.lift ∘ f.DiscreteQuotient.proj = f :=
-  by
-  ext
-  rfl
+theorem lift_comp_proj : f.lift ∘ f.DiscreteQuotient.proj = f := by ext; rfl
 #align locally_constant.lift_comp_proj LocallyConstant.lift_comp_proj
 
 end LocallyConstant

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -250,7 +250,7 @@ theorem comap_comp (S : DiscreteQuotient Z) : S.comap (g.comp f) = (S.comap g).c
 
 /- warning: discrete_quotient.comap_mono -> DiscreteQuotient.comap_mono is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) {A : DiscreteQuotient.{u2} Y _inst_2} {B : DiscreteQuotient.{u2} Y _inst_2}, (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toHasLe.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f A) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f B))
 but is expected to have type
   forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] (f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) {A : DiscreteQuotient.{u2} Y _inst_2} {B : DiscreteQuotient.{u2} Y _inst_2}, (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} Y _inst_2)))) A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f A) (DiscreteQuotient.comap.{u1, u2} X Y _inst_1 _inst_2 f B))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.comap_mono DiscreteQuotient.comap_monoₓ'. -/
@@ -266,7 +266,7 @@ variable {A B C : DiscreteQuotient X}
 
 /- warning: discrete_quotient.of_le -> DiscreteQuotient.ofLE is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1}, (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1}, (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le DiscreteQuotient.ofLEₓ'. -/
@@ -290,7 +290,7 @@ theorem ofLE_refl_apply (a : A) : ofLE (le_refl A) a = a := by simp
 
 /- warning: discrete_quotient.of_le_of_le -> DiscreteQuotient.ofLE_ofLE is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) B C) (x : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂ (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁ x)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (LE.le.trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A B C h₁ h₂) x)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) B C) (x : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂ (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁ x)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (LE.le.trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A B C h₁ h₂) x)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) B C) (x : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 C)) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂ (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁ x)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (LE.le.trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1))) A B C h₁ h₂) x)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLEₓ'. -/
@@ -303,7 +303,7 @@ theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLE h₂ (ofLE h
 
 /- warning: discrete_quotient.of_le_comp_of_le -> DiscreteQuotient.ofLE_comp_ofLE is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) B C), Eq.{succ u1} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C)) (Function.comp.{succ u1, succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (le_trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A B C h₁ h₂))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) B C), Eq.{succ u1} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C)) (Function.comp.{succ u1, succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (le_trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A B C h₁ h₂))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) B C), Eq.{succ u1} ((Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 C))) (Function.comp.{succ u1, succ u1, succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 C)) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (le_trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1))) A B C h₁ h₂))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLE_comp_ofLEₓ'. -/
@@ -314,7 +314,7 @@ theorem ofLE_comp_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) : ofLE h₂ ∘ ofLE h
 
 /- warning: discrete_quotient.of_le_continuous -> DiscreteQuotient.ofLE_continuous is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Continuous.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 A) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Continuous.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 A) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Continuous.{u1, u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 A) (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_continuous DiscreteQuotient.ofLE_continuousₓ'. -/
@@ -324,7 +324,7 @@ theorem ofLE_continuous (h : A ≤ B) : Continuous (ofLE h) :=
 
 /- warning: discrete_quotient.of_le_proj -> DiscreteQuotient.ofLE_proj is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (x : X), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} X _inst_1 B x)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (x : X), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} X _inst_1 B x)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (x : X), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} X _inst_1 B x)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_proj DiscreteQuotient.ofLE_projₓ'. -/
@@ -335,7 +335,7 @@ theorem ofLE_proj (h : A ≤ B) (x : X) : ofLE h (A.proj x) = B.proj x :=
 
 /- warning: discrete_quotient.of_le_comp_proj -> DiscreteQuotient.ofLE_comp_proj is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Eq.{succ u1} (X -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (Function.comp.{succ u1, succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 B)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Eq.{succ u1} (X -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (Function.comp.{succ u1, succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 B)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Eq.{succ u1} (X -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))) (Function.comp.{succ u1, succ u1, succ u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 B)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLE_comp_projₓ'. -/
@@ -366,7 +366,7 @@ instance [LocallyConnectedSpace X] : OrderBot (DiscreteQuotient X)
 
 /- warning: discrete_quotient.proj_bot_eq -> DiscreteQuotient.proj_bot_eq is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : LocallyConnectedSpace.{u1} X _inst_1] {x : X} {y : X}, Iff (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 _inst_4)))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 _inst_4))) x) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 _inst_4))) y)) (Eq.{succ u1} (Set.{u1} X) (connectedComponent.{u1} X _inst_1 x) (connectedComponent.{u1} X _inst_1 y))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : LocallyConnectedSpace.{u1} X _inst_1] {x : X} {y : X}, Iff (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 _inst_4)))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 _inst_4))) x) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 _inst_4))) y)) (Eq.{succ u1} (Set.{u1} X) (connectedComponent.{u1} X _inst_1 x) (connectedComponent.{u1} X _inst_1 y))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : LocallyConnectedSpace.{u1} X _inst_1] {x : X} {y : X}, Iff (Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 _inst_4))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 _inst_4))) x) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 _inst_4))) y)) (Eq.{succ u1} (Set.{u1} X) (connectedComponent.{u1} X _inst_1 x) (connectedComponent.{u1} X _inst_1 y))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.proj_bot_eq DiscreteQuotient.proj_bot_eqₓ'. -/
@@ -378,7 +378,7 @@ theorem proj_bot_eq [LocallyConnectedSpace X] {x y : X} :
 
 /- warning: discrete_quotient.proj_bot_inj -> DiscreteQuotient.proj_bot_inj is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1] {x : X} {y : X}, Iff (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))) x) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))) y)) (Eq.{succ u1} X x y)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1] {x : X} {y : X}, Iff (Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))) x) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))) y)) (Eq.{succ u1} X x y)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1] {x : X} {y : X}, Iff (Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))) x) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))) y)) (Eq.{succ u1} X x y)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.proj_bot_inj DiscreteQuotient.proj_bot_injₓ'. -/
@@ -387,7 +387,7 @@ theorem proj_bot_inj [DiscreteTopology X] {x y : X} : proj ⊥ x = proj ⊥ y 
 
 /- warning: discrete_quotient.proj_bot_injective -> DiscreteQuotient.proj_bot_injective is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1], Function.Injective.{succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1], Function.Injective.{succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1], Function.Injective.{succ u1, succ u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.proj_bot_injective DiscreteQuotient.proj_bot_injectiveₓ'. -/
@@ -397,7 +397,7 @@ theorem proj_bot_injective [DiscreteTopology X] : Injective (⊥ : DiscreteQuoti
 
 /- warning: discrete_quotient.proj_bot_bijective -> DiscreteQuotient.proj_bot_bijective is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1], Function.Bijective.{succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1], Function.Bijective.{succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toHasBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) (DiscreteQuotient.orderBot.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : DiscreteTopology.{u1} X _inst_1], Function.Bijective.{succ u1, succ u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))) (DiscreteQuotient.proj.{u1} X _inst_1 (Bot.bot.{u1} (DiscreteQuotient.{u1} X _inst_1) (OrderBot.toBot.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) (DiscreteQuotient.instOrderBotDiscreteQuotientToLEToPreorderToPartialOrderInstSemilatticeInfDiscreteQuotient.{u1} X _inst_1 (DiscreteTopology.toLocallyConnectedSpace.{u1} X _inst_1 _inst_4)))))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.proj_bot_bijective DiscreteQuotient.proj_bot_bijectiveₓ'. -/
@@ -426,7 +426,7 @@ variable {A A' B B'} {f} {g : C(Y, Z)} {C : DiscreteQuotient Z}
 
 /- warning: discrete_quotient.le_comap_id_iff -> DiscreteQuotient.leComap_id_iff is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1}, Iff (DiscreteQuotient.LEComap.{u1, u1} X X _inst_1 _inst_1 (ContinuousMap.id.{u1} X _inst_1) A A') (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A A')
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1}, Iff (DiscreteQuotient.LEComap.{u1, u1} X X _inst_1 _inst_1 (ContinuousMap.id.{u1} X _inst_1) A A') (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A A')
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1}, Iff (DiscreteQuotient.LEComap.{u1, u1} X X _inst_1 _inst_1 (ContinuousMap.id.{u1} X _inst_1) A A') (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A A')
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.le_comap_id_iff DiscreteQuotient.leComap_id_iffₓ'. -/
@@ -446,7 +446,7 @@ theorem LEComap.comp : LEComap g B C → LEComap f A B → LEComap (g.comp f) A
 
 /- warning: discrete_quotient.le_comap.mono -> DiscreteQuotient.LEComap.mono is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2}, (DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A) -> (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B') -> (DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A' B')
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2}, (DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A) -> (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toHasLe.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B') -> (DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A' B')
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {A' : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} {B' : DiscreteQuotient.{u1} Y _inst_2}, (DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) -> (LE.le.{u2} (DiscreteQuotient.{u2} X _inst_1) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1)))) A' A) -> (LE.le.{u1} (DiscreteQuotient.{u1} Y _inst_2) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2)))) B B') -> (DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A' B')
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.le_comap.mono DiscreteQuotient.LEComap.monoₓ'. -/
@@ -515,7 +515,7 @@ theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
 
 /- warning: discrete_quotient.of_le_map -> DiscreteQuotient.ofLE_map is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B') (a : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B') (DiscreteQuotient.ofLE.{u2} Y _inst_2 B B' h (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond a)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A) h) a)
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toHasLe.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B') (a : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B') (DiscreteQuotient.ofLE.{u2} Y _inst_2 B B' h (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond a)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A) h) a)
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} {B' : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} Y _inst_2) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2)))) B B') (a : Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)), Eq.{succ u1} (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B')) (DiscreteQuotient.ofLE.{u1} Y _inst_2 B B' h (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond a)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1))) A) h) a)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_map DiscreteQuotient.ofLE_mapₓ'. -/
@@ -529,7 +529,7 @@ theorem ofLE_map (cond : LEComap f A B) (h : B ≤ B') (a : A) :
 
 /- warning: discrete_quotient.of_le_comp_map -> DiscreteQuotient.ofLE_comp_map is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B'), Eq.{max (succ u1) (succ u2)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B')) (Function.comp.{succ u1, succ u2, succ u2} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B') (DiscreteQuotient.ofLE.{u2} Y _inst_2 B B' h) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A) h))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toHasLe.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B'), Eq.{max (succ u1) (succ u2)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B')) (Function.comp.{succ u1, succ u2, succ u2} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B') (DiscreteQuotient.ofLE.{u2} Y _inst_2 B B' h) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A) h))
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} {B' : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} Y _inst_2) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2)))) B B'), Eq.{max (succ u2) (succ u1)} ((Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) -> (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B'))) (Function.comp.{succ u2, succ u1, succ u1} (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B')) (DiscreteQuotient.ofLE.{u1} Y _inst_2 B B' h) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1))) A) h))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLE_comp_mapₓ'. -/
@@ -541,7 +541,7 @@ theorem ofLE_comp_map (cond : LEComap f A B) (h : B ≤ B') :
 
 /- warning: discrete_quotient.map_of_le -> DiscreteQuotient.map_ofLE is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A) (c : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A'), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond (DiscreteQuotient.ofLE.{u1} X _inst_1 A' A h c)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2))) B)) c)
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A) (c : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A'), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond (DiscreteQuotient.ofLE.{u1} X _inst_1 A' A h c)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2))) B)) c)
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {A' : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} X _inst_1) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1)))) A' A) (c : Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A')), Eq.{succ u1} (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond (DiscreteQuotient.ofLE.{u2} X _inst_1 A' A h c)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2))) B)) c)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLEₓ'. -/
@@ -555,7 +555,7 @@ theorem map_ofLE (cond : LEComap f A B) (h : A' ≤ A) (c : A') :
 
 /- warning: discrete_quotient.map_comp_of_le -> DiscreteQuotient.map_comp_ofLE is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A), Eq.{max (succ u1) (succ u2)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A') -> (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B)) (Function.comp.{succ u1, succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A') (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond) (DiscreteQuotient.ofLE.{u1} X _inst_1 A' A h)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2))) B)))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A), Eq.{max (succ u1) (succ u2)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A') -> (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B)) (Function.comp.{succ u1, succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A') (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond) (DiscreteQuotient.ofLE.{u1} X _inst_1 A' A h)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2))) B)))
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {A' : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} X _inst_1) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1)))) A' A), Eq.{max (succ u2) (succ u1)} ((Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A')) -> (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B))) (Function.comp.{succ u2, succ u2, succ u1} (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A')) (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond) (DiscreteQuotient.ofLE.{u2} X _inst_1 A' A h)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2))) B)))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_comp_of_le DiscreteQuotient.map_comp_ofLEₓ'. -/
@@ -580,7 +580,7 @@ theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconn
 
 /- warning: discrete_quotient.fiber_subset_of_le -> DiscreteQuotient.fiber_subset_ofLE is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (a : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) (Set.preimage.{u1, u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (DiscreteQuotient.proj.{u1} X _inst_1 A) (Singleton.singleton.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (Set.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A)) (Set.hasSingleton.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A)) a)) (Set.preimage.{u1, u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.proj.{u1} X _inst_1 B) (Singleton.singleton.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (Set.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (Set.hasSingleton.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h a)))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (a : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) (Set.preimage.{u1, u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (DiscreteQuotient.proj.{u1} X _inst_1 A) (Singleton.singleton.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (Set.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A)) (Set.hasSingleton.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A)) a)) (Set.preimage.{u1, u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.proj.{u1} X _inst_1 B) (Singleton.singleton.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (Set.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (Set.hasSingleton.{u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h a)))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (a : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)), HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) (Set.preimage.{u1, u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 A) (Singleton.singleton.{u1, u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Set.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A))) (Set.instSingletonSet.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A))) a)) (Set.preimage.{u1, u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.proj.{u1} X _inst_1 B) (Singleton.singleton.{u1, u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (Set.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))) (Set.instSingletonSet.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h a)))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLEₓ'. -/
@@ -594,7 +594,7 @@ theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
 
 /- warning: discrete_quotient.exists_of_compat -> DiscreteQuotient.exists_of_compat is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : CompactSpace.{u1} X _inst_1] (Qs : forall (Q : DiscreteQuotient.{u1} X _inst_1), coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) Q), (forall (A : DiscreteQuotient.{u1} X _inst_1) (B : DiscreteQuotient.{u1} X _inst_1) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (Qs A)) (Qs B)) -> (Exists.{succ u1} X (fun (x : X) => forall (Q : DiscreteQuotient.{u1} X _inst_1), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) Q) (DiscreteQuotient.proj.{u1} X _inst_1 Q x) (Qs Q)))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : CompactSpace.{u1} X _inst_1] (Qs : forall (Q : DiscreteQuotient.{u1} X _inst_1), coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) Q), (forall (A : DiscreteQuotient.{u1} X _inst_1) (B : DiscreteQuotient.{u1} X _inst_1) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toHasLe.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (Qs A)) (Qs B)) -> (Exists.{succ u1} X (fun (x : X) => forall (Q : DiscreteQuotient.{u1} X _inst_1), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) Q) (DiscreteQuotient.proj.{u1} X _inst_1 Q x) (Qs Q)))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : CompactSpace.{u1} X _inst_1] (Qs : forall (Q : DiscreteQuotient.{u1} X _inst_1), Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 Q)), (forall (A : DiscreteQuotient.{u1} X _inst_1) (B : DiscreteQuotient.{u1} X _inst_1) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (Qs A)) (Qs B)) -> (Exists.{succ u1} X (fun (x : X) => forall (Q : DiscreteQuotient.{u1} X _inst_1), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 Q)) (DiscreteQuotient.proj.{u1} X _inst_1 Q x) (Qs Q)))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.exists_of_compat DiscreteQuotient.exists_of_compatₓ'. -/

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

@@ -571,7 +571,7 @@ end Map
 theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconnectedSpace X]
     {x y : X} (h : ∀ Q : DiscreteQuotient X, Q.proj x = Q.proj y) : x = y :=
   by
-  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_interᵢ_clopen,
+  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_iInter_clopen,
     mem_Inter]
   rintro ⟨U, hU1, hU2⟩
   exact (Quotient.exact' (h (of_clopen hU1))).mpr hU2
@@ -603,7 +603,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
     ∃ x : X, ∀ Q : DiscreteQuotient X, Q.proj x = Qs _ :=
   by
   obtain ⟨x, hx⟩ : (⋂ Q, proj Q ⁻¹' {Qs Q}).Nonempty :=
-    IsCompact.nonempty_interᵢ_of_directed_nonempty_compact_closed
+    IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed
       (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_inf fun A B h => _)
       (fun Q => (singleton_nonempty _).Preimage Q.proj_surjective)
       (fun i => (is_closed_preimage _ _).IsCompact) fun i => is_closed_preimage _ _

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

@@ -264,85 +264,85 @@ section OfLe
 
 variable {A B C : DiscreteQuotient X}
 
-/- warning: discrete_quotient.of_le -> DiscreteQuotient.ofLe is a dubious translation:
+/- warning: discrete_quotient.of_le -> DiscreteQuotient.ofLE is a dubious translation:
 lean 3 declaration is
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1}, (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1}, (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))
-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le DiscreteQuotient.ofLeₓ'. -/
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le DiscreteQuotient.ofLEₓ'. -/
 /-- The map induced by a refinement of a discrete quotient. -/
-def ofLe (h : A ≤ B) : A → B :=
+def ofLE (h : A ≤ B) : A → B :=
   Quotient.map' (fun x => x) h
-#align discrete_quotient.of_le DiscreteQuotient.ofLe
+#align discrete_quotient.of_le DiscreteQuotient.ofLE
 
-#print DiscreteQuotient.ofLe_refl /-
+#print DiscreteQuotient.ofLE_refl /-
 @[simp]
-theorem ofLe_refl : ofLe (le_refl A) = id := by
+theorem ofLE_refl : ofLE (le_refl A) = id := by
   ext ⟨⟩
   rfl
-#align discrete_quotient.of_le_refl DiscreteQuotient.ofLe_refl
+#align discrete_quotient.of_le_refl DiscreteQuotient.ofLE_refl
 -/
 
-#print DiscreteQuotient.ofLe_refl_apply /-
-theorem ofLe_refl_apply (a : A) : ofLe (le_refl A) a = a := by simp
-#align discrete_quotient.of_le_refl_apply DiscreteQuotient.ofLe_refl_apply
+#print DiscreteQuotient.ofLE_refl_apply /-
+theorem ofLE_refl_apply (a : A) : ofLE (le_refl A) a = a := by simp
+#align discrete_quotient.of_le_refl_apply DiscreteQuotient.ofLE_refl_apply
 -/
 
-/- warning: discrete_quotient.of_le_of_le -> DiscreteQuotient.ofLe_ofLe is a dubious translation:
+/- warning: discrete_quotient.of_le_of_le -> DiscreteQuotient.ofLE_ofLE is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) B C) (x : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C) (DiscreteQuotient.ofLe.{u1} X _inst_1 B C h₂ (DiscreteQuotient.ofLe.{u1} X _inst_1 A B h₁ x)) (DiscreteQuotient.ofLe.{u1} X _inst_1 A C (LE.le.trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A B C h₁ h₂) x)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) B C) (x : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂ (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁ x)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (LE.le.trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A B C h₁ h₂) x)
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLe_ofLeₓ'. -/
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) B C) (x : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 C)) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂ (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁ x)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (LE.le.trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1))) A B C h₁ h₂) x)
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLEₓ'. -/
 @[simp]
-theorem ofLe_ofLe (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLe h₂ (ofLe h₁ x) = ofLe (h₁.trans h₂) x :=
+theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLE h₂ (ofLE h₁ x) = ofLE (h₁.trans h₂) x :=
   by
   rcases x with ⟨⟩
   rfl
-#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLe_ofLe
+#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLE
 
-/- warning: discrete_quotient.of_le_comp_of_le -> DiscreteQuotient.ofLe_comp_ofLe is a dubious translation:
+/- warning: discrete_quotient.of_le_comp_of_le -> DiscreteQuotient.ofLE_comp_ofLE is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) B C), Eq.{succ u1} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C)) (Function.comp.{succ u1, succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) C) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (le_trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A B C h₁ h₂))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLe_comp_ofLeₓ'. -/
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} {C : DiscreteQuotient.{u1} X _inst_1} (h₁ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (h₂ : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) B C), Eq.{succ u1} ((Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 C))) (Function.comp.{succ u1, succ u1, succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 C)) (DiscreteQuotient.ofLE.{u1} X _inst_1 B C h₂) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h₁)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A C (le_trans.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1))) A B C h₁ h₂))
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLE_comp_ofLEₓ'. -/
 @[simp]
-theorem ofLe_comp_ofLe (h₁ : A ≤ B) (h₂ : B ≤ C) : ofLe h₂ ∘ ofLe h₁ = ofLe (le_trans h₁ h₂) :=
-  funext <| ofLe_ofLe _ _
-#align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLe_comp_ofLe
+theorem ofLE_comp_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) : ofLE h₂ ∘ ofLE h₁ = ofLE (le_trans h₁ h₂) :=
+  funext <| ofLE_ofLE _ _
+#align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLE_comp_ofLE
 
-/- warning: discrete_quotient.of_le_continuous -> DiscreteQuotient.ofLe_continuous is a dubious translation:
+/- warning: discrete_quotient.of_le_continuous -> DiscreteQuotient.ofLE_continuous is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Continuous.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 A) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 B) (DiscreteQuotient.ofLe.{u1} X _inst_1 A B h)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Continuous.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 A) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h)
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_continuous DiscreteQuotient.ofLe_continuousₓ'. -/
-theorem ofLe_continuous (h : A ≤ B) : Continuous (ofLe h) :=
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Continuous.{u1, u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 A) (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h)
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_continuous DiscreteQuotient.ofLE_continuousₓ'. -/
+theorem ofLE_continuous (h : A ≤ B) : Continuous (ofLE h) :=
   continuous_of_discreteTopology
-#align discrete_quotient.of_le_continuous DiscreteQuotient.ofLe_continuous
+#align discrete_quotient.of_le_continuous DiscreteQuotient.ofLE_continuous
 
-/- warning: discrete_quotient.of_le_proj -> DiscreteQuotient.ofLe_proj is a dubious translation:
+/- warning: discrete_quotient.of_le_proj -> DiscreteQuotient.ofLE_proj is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (x : X), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLe.{u1} X _inst_1 A B h (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} X _inst_1 B x)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B) (x : X), Eq.{succ u1} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} X _inst_1 B x)
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (x : X), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLe.{u1} X _inst_1 A B h (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} X _inst_1 B x)
-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_proj DiscreteQuotient.ofLe_projₓ'. -/
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (x : X), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} X _inst_1 B x)
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_proj DiscreteQuotient.ofLE_projₓ'. -/
 @[simp]
-theorem ofLe_proj (h : A ≤ B) (x : X) : ofLe h (A.proj x) = B.proj x :=
+theorem ofLE_proj (h : A ≤ B) (x : X) : ofLE h (A.proj x) = B.proj x :=
   Quotient.sound' (B.refl _)
-#align discrete_quotient.of_le_proj DiscreteQuotient.ofLe_proj
+#align discrete_quotient.of_le_proj DiscreteQuotient.ofLE_proj
 
-/- warning: discrete_quotient.of_le_comp_proj -> DiscreteQuotient.ofLe_comp_proj is a dubious translation:
+/- warning: discrete_quotient.of_le_comp_proj -> DiscreteQuotient.ofLE_comp_proj is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Eq.{succ u1} (X -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (Function.comp.{succ u1, succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLe.{u1} X _inst_1 A B h) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 B)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A B), Eq.{succ u1} (X -> (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B)) (Function.comp.{succ u1, succ u1, succ u1} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) B) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 B)
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Eq.{succ u1} (X -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))) (Function.comp.{succ u1, succ u1, succ u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLe.{u1} X _inst_1 A B h) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 B)
-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLe_comp_projₓ'. -/
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Eq.{succ u1} (X -> (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))) (Function.comp.{succ u1, succ u1, succ u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 B)
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLE_comp_projₓ'. -/
 @[simp]
-theorem ofLe_comp_proj (h : A ≤ B) : ofLe h ∘ A.proj = B.proj :=
-  funext <| ofLe_proj _
-#align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLe_comp_proj
+theorem ofLE_comp_proj (h : A ≤ B) : ofLE h ∘ A.proj = B.proj :=
+  funext <| ofLE_proj _
+#align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLE_comp_proj
 
 end OfLe
 
@@ -409,16 +409,16 @@ section Map
 
 variable (f : C(X, Y)) (A A' : DiscreteQuotient X) (B B' : DiscreteQuotient Y)
 
-#print DiscreteQuotient.LeComap /-
+#print DiscreteQuotient.LEComap /-
 /-- Given `f : C(X, Y)`, `le_comap cont A B` is defined as `A ≤ B.comap f`. Mathematically this
 means that `f` descends to a morphism `A → B`. -/
-def LeComap : Prop :=
+def LEComap : Prop :=
   A ≤ B.comap f
-#align discrete_quotient.le_comap DiscreteQuotient.LeComap
+#align discrete_quotient.le_comap DiscreteQuotient.LEComap
 -/
 
 #print DiscreteQuotient.leComap_id /-
-theorem leComap_id : LeComap (ContinuousMap.id X) A A := fun _ _ => id
+theorem leComap_id : LEComap (ContinuousMap.id X) A A := fun _ _ => id
 #align discrete_quotient.le_comap_id DiscreteQuotient.leComap_id
 -/
 
@@ -426,70 +426,70 @@ variable {A A' B B'} {f} {g : C(Y, Z)} {C : DiscreteQuotient Z}
 
 /- warning: discrete_quotient.le_comap_id_iff -> DiscreteQuotient.leComap_id_iff is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1}, Iff (DiscreteQuotient.LeComap.{u1, u1} X X _inst_1 _inst_1 (ContinuousMap.id.{u1} X _inst_1) A A') (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A A')
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1}, Iff (DiscreteQuotient.LEComap.{u1, u1} X X _inst_1 _inst_1 (ContinuousMap.id.{u1} X _inst_1) A A') (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A A')
 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1}, Iff (DiscreteQuotient.LeComap.{u1, u1} X X _inst_1 _inst_1 (ContinuousMap.id.{u1} X _inst_1) A A') (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A A')
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1}, Iff (DiscreteQuotient.LEComap.{u1, u1} X X _inst_1 _inst_1 (ContinuousMap.id.{u1} X _inst_1) A A') (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A A')
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.le_comap_id_iff DiscreteQuotient.leComap_id_iffₓ'. -/
 @[simp]
-theorem leComap_id_iff : LeComap (ContinuousMap.id X) A A' ↔ A ≤ A' :=
+theorem leComap_id_iff : LEComap (ContinuousMap.id X) A A' ↔ A ≤ A' :=
   Iff.rfl
 #align discrete_quotient.le_comap_id_iff DiscreteQuotient.leComap_id_iff
 
-/- warning: discrete_quotient.le_comap.comp -> DiscreteQuotient.LeComap.comp is a dubious translation:
+/- warning: discrete_quotient.le_comap.comp -> DiscreteQuotient.LEComap.comp is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : TopologicalSpace.{u3} Z] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {g : ContinuousMap.{u2, u3} Y Z _inst_2 _inst_3} {C : DiscreteQuotient.{u3} Z _inst_3}, (DiscreteQuotient.LeComap.{u2, u3} Y Z _inst_2 _inst_3 g B C) -> (DiscreteQuotient.LeComap.{u1, u2} X Y _inst_1 _inst_2 f A B) -> (DiscreteQuotient.LeComap.{u1, u3} X Z _inst_1 _inst_3 (ContinuousMap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 g f) A C)
+  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : TopologicalSpace.{u3} Z] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {g : ContinuousMap.{u2, u3} Y Z _inst_2 _inst_3} {C : DiscreteQuotient.{u3} Z _inst_3}, (DiscreteQuotient.LEComap.{u2, u3} Y Z _inst_2 _inst_3 g B C) -> (DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) -> (DiscreteQuotient.LEComap.{u1, u3} X Z _inst_1 _inst_3 (ContinuousMap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 g f) A C)
 but is expected to have type
-  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u3} Y] [_inst_3 : TopologicalSpace.{u2} Z] {f : ContinuousMap.{u1, u3} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u3} Y _inst_2} {g : ContinuousMap.{u3, u2} Y Z _inst_2 _inst_3} {C : DiscreteQuotient.{u2} Z _inst_3}, (DiscreteQuotient.LeComap.{u3, u2} Y Z _inst_2 _inst_3 g B C) -> (DiscreteQuotient.LeComap.{u1, u3} X Y _inst_1 _inst_2 f A B) -> (DiscreteQuotient.LeComap.{u1, u2} X Z _inst_1 _inst_3 (ContinuousMap.comp.{u1, u3, u2} X Y Z _inst_1 _inst_2 _inst_3 g f) A C)
-Case conversion may be inaccurate. Consider using '#align discrete_quotient.le_comap.comp DiscreteQuotient.LeComap.compₓ'. -/
-theorem LeComap.comp : LeComap g B C → LeComap f A B → LeComap (g.comp f) A C := by tauto
-#align discrete_quotient.le_comap.comp DiscreteQuotient.LeComap.comp
+  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u3} Y] [_inst_3 : TopologicalSpace.{u2} Z] {f : ContinuousMap.{u1, u3} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u3} Y _inst_2} {g : ContinuousMap.{u3, u2} Y Z _inst_2 _inst_3} {C : DiscreteQuotient.{u2} Z _inst_3}, (DiscreteQuotient.LEComap.{u3, u2} Y Z _inst_2 _inst_3 g B C) -> (DiscreteQuotient.LEComap.{u1, u3} X Y _inst_1 _inst_2 f A B) -> (DiscreteQuotient.LEComap.{u1, u2} X Z _inst_1 _inst_3 (ContinuousMap.comp.{u1, u3, u2} X Y Z _inst_1 _inst_2 _inst_3 g f) A C)
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.le_comap.comp DiscreteQuotient.LEComap.compₓ'. -/
+theorem LEComap.comp : LEComap g B C → LEComap f A B → LEComap (g.comp f) A C := by tauto
+#align discrete_quotient.le_comap.comp DiscreteQuotient.LEComap.comp
 
-/- warning: discrete_quotient.le_comap.mono -> DiscreteQuotient.LeComap.mono is a dubious translation:
+/- warning: discrete_quotient.le_comap.mono -> DiscreteQuotient.LEComap.mono is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2}, (DiscreteQuotient.LeComap.{u1, u2} X Y _inst_1 _inst_2 f A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A) -> (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B') -> (DiscreteQuotient.LeComap.{u1, u2} X Y _inst_1 _inst_2 f A' B')
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2}, (DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) -> (LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A) -> (LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B') -> (DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A' B')
 but is expected to have type
-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {A' : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} {B' : DiscreteQuotient.{u1} Y _inst_2}, (DiscreteQuotient.LeComap.{u2, u1} X Y _inst_1 _inst_2 f A B) -> (LE.le.{u2} (DiscreteQuotient.{u2} X _inst_1) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1)))) A' A) -> (LE.le.{u1} (DiscreteQuotient.{u1} Y _inst_2) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2)))) B B') -> (DiscreteQuotient.LeComap.{u2, u1} X Y _inst_1 _inst_2 f A' B')
-Case conversion may be inaccurate. Consider using '#align discrete_quotient.le_comap.mono DiscreteQuotient.LeComap.monoₓ'. -/
-theorem LeComap.mono (h : LeComap f A B) (hA : A' ≤ A) (hB : B ≤ B') : LeComap f A' B' :=
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {A' : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} {B' : DiscreteQuotient.{u1} Y _inst_2}, (DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) -> (LE.le.{u2} (DiscreteQuotient.{u2} X _inst_1) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1)))) A' A) -> (LE.le.{u1} (DiscreteQuotient.{u1} Y _inst_2) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2)))) B B') -> (DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A' B')
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.le_comap.mono DiscreteQuotient.LEComap.monoₓ'. -/
+theorem LEComap.mono (h : LEComap f A B) (hA : A' ≤ A) (hB : B ≤ B') : LEComap f A' B' :=
   hA.trans <| le_trans h <| comap_mono _ hB
-#align discrete_quotient.le_comap.mono DiscreteQuotient.LeComap.mono
+#align discrete_quotient.le_comap.mono DiscreteQuotient.LEComap.mono
 
 #print DiscreteQuotient.map /-
 /-- Map a discrete quotient along a continuous map. -/
-def map (f : C(X, Y)) (cond : LeComap f A B) : A → B :=
+def map (f : C(X, Y)) (cond : LEComap f A B) : A → B :=
   Quotient.map' f cond
 #align discrete_quotient.map DiscreteQuotient.map
 -/
 
 /- warning: discrete_quotient.map_continuous -> DiscreteQuotient.map_continuous is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B), Continuous.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.topologicalSpace.{u1} X _inst_1 A) (DiscreteQuotient.topologicalSpace.{u2} Y _inst_2 B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond)
 but is expected to have type
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+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B), Continuous.{u2, u1} (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u2} X _inst_1 A) (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} Y _inst_2 B) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond)
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_continuous DiscreteQuotient.map_continuousₓ'. -/
-theorem map_continuous (cond : LeComap f A B) : Continuous (map f cond) :=
+theorem map_continuous (cond : LEComap f A B) : Continuous (map f cond) :=
   continuous_of_discreteTopology
 #align discrete_quotient.map_continuous DiscreteQuotient.map_continuous
 
 /- warning: discrete_quotient.map_comp_proj -> DiscreteQuotient.map_comp_proj is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B), Eq.{max (succ u1) (succ u2)} (X -> (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B)) (Function.comp.{succ u1, succ u1, succ u2} X (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond) (DiscreteQuotient.proj.{u1} X _inst_1 A)) (Function.comp.{succ u1, succ u2, succ u2} X Y (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.proj.{u2} Y _inst_2 B) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) => X -> Y) (ContinuousMap.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2) f))
 but is expected to have type
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+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B), Eq.{max (succ u2) (succ u1)} (X -> (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B))) (Function.comp.{succ u2, succ u2, succ u1} X (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond) (DiscreteQuotient.proj.{u2} X _inst_1 A)) (Function.comp.{succ u2, succ u1, succ u1} X Y (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.proj.{u1} Y _inst_2 B) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} X Y _inst_1 _inst_2)) f))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_comp_proj DiscreteQuotient.map_comp_projₓ'. -/
 @[simp]
-theorem map_comp_proj (cond : LeComap f A B) : map f cond ∘ A.proj = B.proj ∘ f :=
+theorem map_comp_proj (cond : LEComap f A B) : map f cond ∘ A.proj = B.proj ∘ f :=
   rfl
 #align discrete_quotient.map_comp_proj DiscreteQuotient.map_comp_proj
 
 /- warning: discrete_quotient.map_proj -> DiscreteQuotient.map_proj is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (x : X), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond (DiscreteQuotient.proj.{u1} X _inst_1 A x)) (DiscreteQuotient.proj.{u2} Y _inst_2 B (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) (fun (_x : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2) => X -> Y) (ContinuousMap.hasCoeToFun.{u1, u2} X Y _inst_1 _inst_2) f x))
 but is expected to have type
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+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (x : X), Eq.{succ u1} (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond (DiscreteQuotient.proj.{u2} X _inst_1 A x)) (DiscreteQuotient.proj.{u1} Y _inst_2 B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousMap.{u2, u1} X Y _inst_1 _inst_2) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : X) => Y) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousMap.{u2, u1} X Y _inst_1 _inst_2) X Y _inst_1 _inst_2 (ContinuousMap.instContinuousMapClassContinuousMap.{u2, u1} X Y _inst_1 _inst_2)) f x))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_proj DiscreteQuotient.map_projₓ'. -/
 @[simp]
-theorem map_proj (cond : LeComap f A B) (x : X) : map f cond (A.proj x) = B.proj (f x) :=
+theorem map_proj (cond : LEComap f A B) (x : X) : map f cond (A.proj x) = B.proj (f x) :=
   rfl
 #align discrete_quotient.map_proj DiscreteQuotient.map_proj
 
@@ -501,69 +501,69 @@ theorem map_id : map _ (leComap_id A) = id := by ext ⟨⟩ <;> rfl
 
 /- warning: discrete_quotient.map_comp -> DiscreteQuotient.map_comp is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : TopologicalSpace.{u3} Z] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {g : ContinuousMap.{u2, u3} Y Z _inst_2 _inst_3} {C : DiscreteQuotient.{u3} Z _inst_3} (h1 : DiscreteQuotient.LeComap.{u2, u3} Y Z _inst_2 _inst_3 g B C) (h2 : DiscreteQuotient.LeComap.{u1, u2} X Y _inst_1 _inst_2 f A B), Eq.{max (succ u1) (succ u3)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u3, succ (succ u3)} (DiscreteQuotient.{u3} Z _inst_3) Type.{u3} (DiscreteQuotient.hasCoeToSort.{u3} Z _inst_3) C)) (DiscreteQuotient.map.{u1, u3} X Z _inst_1 _inst_3 A C (ContinuousMap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 g f) (DiscreteQuotient.LeComap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 f A B g C h1 h2)) (Function.comp.{succ u1, succ u2, succ u3} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (coeSort.{succ u3, succ (succ u3)} (DiscreteQuotient.{u3} Z _inst_3) Type.{u3} (DiscreteQuotient.hasCoeToSort.{u3} Z _inst_3) C) (DiscreteQuotient.map.{u2, u3} Y Z _inst_2 _inst_3 B C g h1) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f h2))
+  forall {X : Type.{u1}} {Y : Type.{u2}} {Z : Type.{u3}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : TopologicalSpace.{u3} Z] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {g : ContinuousMap.{u2, u3} Y Z _inst_2 _inst_3} {C : DiscreteQuotient.{u3} Z _inst_3} (h1 : DiscreteQuotient.LEComap.{u2, u3} Y Z _inst_2 _inst_3 g B C) (h2 : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B), Eq.{max (succ u1) (succ u3)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u3, succ (succ u3)} (DiscreteQuotient.{u3} Z _inst_3) Type.{u3} (DiscreteQuotient.hasCoeToSort.{u3} Z _inst_3) C)) (DiscreteQuotient.map.{u1, u3} X Z _inst_1 _inst_3 A C (ContinuousMap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 g f) (DiscreteQuotient.LEComap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 f A B g C h1 h2)) (Function.comp.{succ u1, succ u2, succ u3} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (coeSort.{succ u3, succ (succ u3)} (DiscreteQuotient.{u3} Z _inst_3) Type.{u3} (DiscreteQuotient.hasCoeToSort.{u3} Z _inst_3) C) (DiscreteQuotient.map.{u2, u3} Y Z _inst_2 _inst_3 B C g h1) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f h2))
 but is expected to have type
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+  forall {X : Type.{u1}} {Y : Type.{u3}} {Z : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u3} Y] [_inst_3 : TopologicalSpace.{u2} Z] {f : ContinuousMap.{u1, u3} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u3} Y _inst_2} {g : ContinuousMap.{u3, u2} Y Z _inst_2 _inst_3} {C : DiscreteQuotient.{u2} Z _inst_3} (h1 : DiscreteQuotient.LEComap.{u3, u2} Y Z _inst_2 _inst_3 g B C) (h2 : DiscreteQuotient.LEComap.{u1, u3} X Y _inst_1 _inst_2 f A B), Eq.{max (succ u1) (succ u2)} ((Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) -> (Quotient.{succ u2} Z (DiscreteQuotient.toSetoid.{u2} Z _inst_3 C))) (DiscreteQuotient.map.{u1, u2} X Z _inst_1 _inst_3 A C (ContinuousMap.comp.{u1, u3, u2} X Y Z _inst_1 _inst_2 _inst_3 g f) (DiscreteQuotient.LEComap.comp.{u1, u2, u3} X Y Z _inst_1 _inst_2 _inst_3 f A B g C h1 h2)) (Function.comp.{succ u1, succ u3, succ u2} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Quotient.{succ u3} Y (DiscreteQuotient.toSetoid.{u3} Y _inst_2 B)) (Quotient.{succ u2} Z (DiscreteQuotient.toSetoid.{u2} Z _inst_3 C)) (DiscreteQuotient.map.{u3, u2} Y Z _inst_2 _inst_3 B C g h1) (DiscreteQuotient.map.{u1, u3} X Y _inst_1 _inst_2 A B f h2))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_comp DiscreteQuotient.map_compₓ'. -/
 @[simp]
-theorem map_comp (h1 : LeComap g B C) (h2 : LeComap f A B) :
+theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
     map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 :=
   by
   ext ⟨⟩
   rfl
 #align discrete_quotient.map_comp DiscreteQuotient.map_comp
 
-/- warning: discrete_quotient.of_le_map -> DiscreteQuotient.ofLe_map is a dubious translation:
+/- warning: discrete_quotient.of_le_map -> DiscreteQuotient.ofLE_map is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B') (a : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B') (DiscreteQuotient.ofLE.{u2} Y _inst_2 B B' h (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond a)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A) h) a)
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_map DiscreteQuotient.ofLe_mapₓ'. -/
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} {B' : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} Y _inst_2) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2)))) B B') (a : Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)), Eq.{succ u1} (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B')) (DiscreteQuotient.ofLE.{u1} Y _inst_2 B B' h (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond a)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1))) A) h) a)
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_map DiscreteQuotient.ofLE_mapₓ'. -/
 @[simp]
-theorem ofLe_map (cond : LeComap f A B) (h : B ≤ B') (a : A) :
-    ofLe h (map f cond a) = map f (cond.mono le_rfl h) a :=
+theorem ofLE_map (cond : LEComap f A B) (h : B ≤ B') (a : A) :
+    ofLE h (map f cond a) = map f (cond.mono le_rfl h) a :=
   by
   rcases a with ⟨⟩
   rfl
-#align discrete_quotient.of_le_map DiscreteQuotient.ofLe_map
+#align discrete_quotient.of_le_map DiscreteQuotient.ofLE_map
 
-/- warning: discrete_quotient.of_le_comp_map -> DiscreteQuotient.ofLe_comp_map is a dubious translation:
+/- warning: discrete_quotient.of_le_comp_map -> DiscreteQuotient.ofLE_comp_map is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LeComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B'), Eq.{max (succ u1) (succ u2)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B')) (Function.comp.{succ u1, succ u2, succ u2} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B') (DiscreteQuotient.ofLe.{u2} Y _inst_2 B B' h) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LeComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A) h))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} {B' : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} Y _inst_2) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2)))) B B'), Eq.{max (succ u1) (succ u2)} ((coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) -> (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B')) (Function.comp.{succ u1, succ u2, succ u2} (coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B') (DiscreteQuotient.ofLE.{u2} Y _inst_2 B B' h) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1))) A) h))
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLe_comp_mapₓ'. -/
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} {B' : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} Y _inst_2) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2)))) B B'), Eq.{max (succ u2) (succ u1)} ((Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) -> (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B'))) (Function.comp.{succ u2, succ u1, succ u1} (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B')) (DiscreteQuotient.ofLE.{u1} Y _inst_2 B B' h) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B' f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A B B' cond (le_rfl.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1))) A) h))
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLE_comp_mapₓ'. -/
 @[simp]
-theorem ofLe_comp_map (cond : LeComap f A B) (h : B ≤ B') :
-    ofLe h ∘ map f cond = map f (cond.mono le_rfl h) :=
-  funext <| ofLe_map cond h
-#align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLe_comp_map
+theorem ofLE_comp_map (cond : LEComap f A B) (h : B ≤ B') :
+    ofLE h ∘ map f cond = map f (cond.mono le_rfl h) :=
+  funext <| ofLE_map cond h
+#align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLE_comp_map
 
-/- warning: discrete_quotient.map_of_le -> DiscreteQuotient.map_ofLe is a dubious translation:
+/- warning: discrete_quotient.map_of_le -> DiscreteQuotient.map_ofLE is a dubious translation:
 lean 3 declaration is
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+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : TopologicalSpace.{u2} Y] {f : ContinuousMap.{u1, u2} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u1} X _inst_1} {A' : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u2} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u1, u2} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.semilatticeInf.{u1} X _inst_1)))) A' A) (c : coeSort.{succ u1, succ (succ u1)} (DiscreteQuotient.{u1} X _inst_1) Type.{u1} (DiscreteQuotient.hasCoeToSort.{u1} X _inst_1) A'), Eq.{succ u2} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} Y _inst_2) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} Y _inst_2) B) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A B f cond (DiscreteQuotient.ofLE.{u1} X _inst_1 A' A h c)) (DiscreteQuotient.map.{u1, u2} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u2} (DiscreteQuotient.{u2} Y _inst_2) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} Y _inst_2) (DiscreteQuotient.semilatticeInf.{u2} Y _inst_2))) B)) c)
 but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLeₓ'. -/
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {A' : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} X _inst_1) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1)))) A' A) (c : Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A')), Eq.{succ u1} (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond (DiscreteQuotient.ofLE.{u2} X _inst_1 A' A h c)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2))) B)) c)
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLEₓ'. -/
 @[simp]
-theorem map_ofLe (cond : LeComap f A B) (h : A' ≤ A) (c : A') :
-    map f cond (ofLe h c) = map f (cond.mono h le_rfl) c :=
+theorem map_ofLE (cond : LEComap f A B) (h : A' ≤ A) (c : A') :
+    map f cond (ofLE h c) = map f (cond.mono h le_rfl) c :=
   by
   rcases c with ⟨⟩
   rfl
-#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLe
+#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLE
 
-/- warning: discrete_quotient.map_comp_of_le -> DiscreteQuotient.map_comp_ofLe is a dubious translation:
+/- warning: discrete_quotient.map_comp_of_le -> DiscreteQuotient.map_comp_ofLE is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : TopologicalSpace.{u1} Y] {f : ContinuousMap.{u2, u1} X Y _inst_1 _inst_2} {A : DiscreteQuotient.{u2} X _inst_1} {A' : DiscreteQuotient.{u2} X _inst_1} {B : DiscreteQuotient.{u1} Y _inst_2} (cond : DiscreteQuotient.LEComap.{u2, u1} X Y _inst_1 _inst_2 f A B) (h : LE.le.{u2} (DiscreteQuotient.{u2} X _inst_1) (Preorder.toLE.{u2} (DiscreteQuotient.{u2} X _inst_1) (PartialOrder.toPreorder.{u2} (DiscreteQuotient.{u2} X _inst_1) (SemilatticeInf.toPartialOrder.{u2} (DiscreteQuotient.{u2} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u2} X _inst_1)))) A' A), Eq.{max (succ u2) (succ u1)} ((Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A')) -> (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B))) (Function.comp.{succ u2, succ u2, succ u1} (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A')) (Quotient.{succ u2} X (DiscreteQuotient.toSetoid.{u2} X _inst_1 A)) (Quotient.{succ u1} Y (DiscreteQuotient.toSetoid.{u1} Y _inst_2 B)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A B f cond) (DiscreteQuotient.ofLE.{u2} X _inst_1 A' A h)) (DiscreteQuotient.map.{u2, u1} X Y _inst_1 _inst_2 A' B f (DiscreteQuotient.LEComap.mono.{u1, u2} X Y _inst_1 _inst_2 f A A' B B cond h (le_rfl.{u1} (DiscreteQuotient.{u1} Y _inst_2) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} Y _inst_2) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} Y _inst_2))) B)))
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.map_comp_of_le DiscreteQuotient.map_comp_ofLEₓ'. -/
 @[simp]
-theorem map_comp_ofLe (cond : LeComap f A B) (h : A' ≤ A) :
-    map f cond ∘ ofLe h = map f (cond.mono h le_rfl) :=
-  funext <| map_ofLe cond h
-#align discrete_quotient.map_comp_of_le DiscreteQuotient.map_comp_ofLe
+theorem map_comp_ofLE (cond : LEComap f A B) (h : A' ≤ A) :
+    map f cond ∘ ofLE h = map f (cond.mono h le_rfl) :=
+  funext <| map_ofLE cond h
+#align discrete_quotient.map_comp_of_le DiscreteQuotient.map_comp_ofLE
 
 end Map
 
@@ -578,28 +578,28 @@ theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconn
 #align discrete_quotient.eq_of_forall_proj_eq DiscreteQuotient.eq_of_forall_proj_eq
 -/
 
-/- warning: discrete_quotient.fiber_subset_of_le -> DiscreteQuotient.fiber_subset_ofLe is a dubious translation:
+/- warning: discrete_quotient.fiber_subset_of_le -> DiscreteQuotient.fiber_subset_ofLE is a dubious translation:
 lean 3 declaration is
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-theorem fiber_subset_ofLe {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
-    A.proj ⁻¹' {a} ⊆ B.proj ⁻¹' {ofLe h a} :=
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {A : DiscreteQuotient.{u1} X _inst_1} {B : DiscreteQuotient.{u1} X _inst_1} (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B) (a : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)), HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) (Set.preimage.{u1, u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (DiscreteQuotient.proj.{u1} X _inst_1 A) (Singleton.singleton.{u1, u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A)) (Set.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A))) (Set.instSingletonSet.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 A))) a)) (Set.preimage.{u1, u1} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.proj.{u1} X _inst_1 B) (Singleton.singleton.{u1, u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (Set.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))) (Set.instSingletonSet.{u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B))) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h a)))
+Case conversion may be inaccurate. Consider using '#align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLEₓ'. -/
+theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
+    A.proj ⁻¹' {a} ⊆ B.proj ⁻¹' {ofLE h a} :=
   by
   rcases A.proj_surjective a with ⟨a, rfl⟩
   rw [fiber_eq, of_le_proj, fiber_eq]
   exact fun _ h' => h h'
-#align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLe
+#align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLE
 
 /- warning: discrete_quotient.exists_of_compat -> DiscreteQuotient.exists_of_compat is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : CompactSpace.{u1} X _inst_1] (Qs : forall (Q : DiscreteQuotient.{u1} X _inst_1), Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 Q)), (forall (A : DiscreteQuotient.{u1} X _inst_1) (B : DiscreteQuotient.{u1} X _inst_1) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLe.{u1} X _inst_1 A B h (Qs A)) (Qs B)) -> (Exists.{succ u1} X (fun (x : X) => forall (Q : DiscreteQuotient.{u1} X _inst_1), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 Q)) (DiscreteQuotient.proj.{u1} X _inst_1 Q x) (Qs Q)))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_4 : CompactSpace.{u1} X _inst_1] (Qs : forall (Q : DiscreteQuotient.{u1} X _inst_1), Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 Q)), (forall (A : DiscreteQuotient.{u1} X _inst_1) (B : DiscreteQuotient.{u1} X _inst_1) (h : LE.le.{u1} (DiscreteQuotient.{u1} X _inst_1) (Preorder.toLE.{u1} (DiscreteQuotient.{u1} X _inst_1) (PartialOrder.toPreorder.{u1} (DiscreteQuotient.{u1} X _inst_1) (SemilatticeInf.toPartialOrder.{u1} (DiscreteQuotient.{u1} X _inst_1) (DiscreteQuotient.instSemilatticeInfDiscreteQuotient.{u1} X _inst_1)))) A B), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 B)) (DiscreteQuotient.ofLE.{u1} X _inst_1 A B h (Qs A)) (Qs B)) -> (Exists.{succ u1} X (fun (x : X) => forall (Q : DiscreteQuotient.{u1} X _inst_1), Eq.{succ u1} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 Q)) (DiscreteQuotient.proj.{u1} X _inst_1 Q x) (Qs Q)))
 Case conversion may be inaccurate. Consider using '#align discrete_quotient.exists_of_compat DiscreteQuotient.exists_of_compatₓ'. -/
 theorem exists_of_compat [CompactSpace X] (Qs : ∀ Q : DiscreteQuotient X, Q)
-    (compat : ∀ (A B : DiscreteQuotient X) (h : A ≤ B), ofLe h (Qs _) = Qs _) :
+    (compat : ∀ (A B : DiscreteQuotient X) (h : A ≤ B), ofLE h (Qs _) = Qs _) :
     ∃ x : X, ∀ Q : DiscreteQuotient X, Q.proj x = Qs _ :=
   by
   obtain ⟨x, hx⟩ : (⋂ Q, proj Q ⁻¹' {Qs Q}).Nonempty :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

@@ -645,7 +645,7 @@ def lift : LocallyConstant f.DiscreteQuotient α :=
 lean 3 declaration is
   forall {α : Type.{u1}} {X : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} X] (f : LocallyConstant.{u2, u1} X α _inst_1), Eq.{max (succ u2) (succ u1)} (X -> α) (Function.comp.{succ u2, succ u2, succ u1} X (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} X _inst_1) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} X _inst_1) (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f)) α (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LocallyConstant.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} X _inst_1) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} X _inst_1) (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f)) α (DiscreteQuotient.topologicalSpace.{u2} X _inst_1 (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f))) (fun (_x : LocallyConstant.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} X _inst_1) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} X _inst_1) (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f)) α (DiscreteQuotient.topologicalSpace.{u2} X _inst_1 (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f))) => (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} X _inst_1) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} X _inst_1) (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f)) -> α) (LocallyConstant.hasCoeToFun.{u2, u1} (coeSort.{succ u2, succ (succ u2)} (DiscreteQuotient.{u2} X _inst_1) Type.{u2} (DiscreteQuotient.hasCoeToSort.{u2} X _inst_1) (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f)) α (DiscreteQuotient.topologicalSpace.{u2} X _inst_1 (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f))) (LocallyConstant.lift.{u1, u2} α X _inst_1 f)) (DiscreteQuotient.proj.{u2} X _inst_1 (LocallyConstant.discreteQuotient.{u1, u2} α X _inst_1 f))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (LocallyConstant.{u2, u1} X α _inst_1) (fun (_x : LocallyConstant.{u2, u1} X α _inst_1) => X -> α) (LocallyConstant.hasCoeToFun.{u2, u1} X α _inst_1) f)
 but is expected to have type
-  forall {α : Type.{u2}} {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (f : LocallyConstant.{u1, u2} X α _inst_1), Eq.{max (succ u2) (succ u1)} (X -> α) (Function.comp.{succ u1, succ u1, succ u2} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LocallyConstant.{u1, u2} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) α (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (fun (_x : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) => (fun (x._@.Mathlib.Topology.LocallyConstant.Basic._hyg.2185 : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) => α) _x) (LocallyConstant.instFunLikeLocallyConstant.{u1, u2} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) α (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (LocallyConstant.lift.{u2, u1} α X _inst_1 f)) (DiscreteQuotient.proj.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LocallyConstant.{u1, u2} X α _inst_1) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.LocallyConstant.Basic._hyg.2185 : X) => α) _x) (LocallyConstant.instFunLikeLocallyConstant.{u1, u2} X α _inst_1) f)
+  forall {α : Type.{u2}} {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] (f : LocallyConstant.{u1, u2} X α _inst_1), Eq.{max (succ u2) (succ u1)} (X -> α) (Function.comp.{succ u1, succ u1, succ u2} X (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) α (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LocallyConstant.{u1, u2} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) α (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (fun (_x : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) => (fun (x._@.Mathlib.Topology.LocallyConstant.Basic._hyg.5691 : Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) => α) _x) (LocallyConstant.instFunLikeLocallyConstant.{u1, u2} (Quotient.{succ u1} X (DiscreteQuotient.toSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) α (DiscreteQuotient.instTopologicalSpaceQuotientToSetoid.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (LocallyConstant.lift.{u2, u1} α X _inst_1 f)) (DiscreteQuotient.proj.{u1} X _inst_1 (LocallyConstant.discreteQuotient.{u2, u1} α X _inst_1 f))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (LocallyConstant.{u1, u2} X α _inst_1) X (fun (_x : X) => (fun (x._@.Mathlib.Topology.LocallyConstant.Basic._hyg.5691 : X) => α) _x) (LocallyConstant.instFunLikeLocallyConstant.{u1, u2} X α _inst_1) f)
 Case conversion may be inaccurate. Consider using '#align locally_constant.lift_comp_proj LocallyConstant.lift_comp_projₓ'. -/
 @[simp]
 theorem lift_comp_proj : f.lift ∘ f.DiscreteQuotient.proj = f :=

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

@@ -192,7 +192,7 @@ theorem isClopen_setOf_rel (x : X) : IsClopen (setOf (S.Rel x)) :=
 #align discrete_quotient.is_clopen_set_of_rel DiscreteQuotient.isClopen_setOf_rel
 -/
 
-instance : HasInf (DiscreteQuotient X) :=
+instance : Inf (DiscreteQuotient X) :=
   ⟨fun S₁ S₂ => ⟨S₁.1 ⊓ S₂.1, fun x => (S₁.2 x).inter (S₂.2 x)⟩⟩
 
 instance : SemilatticeInf (DiscreteQuotient X) :=

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

This PR defines the class Profinite.IsLight which is the property of a profinite space to have countably many clopens. We prove that such a profinite space gives rise to a LightProfinite, and the underlying profinite space of a LightProfinite is light.

• depends on: #10390

@@ -3,6 +3,7 @@ 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 Mathlib.Data.Setoid.Partition
 import Mathlib.Topology.Separation
 import Mathlib.Topology.LocallyConstant.Basic
 
@@ -62,7 +63,7 @@ of finite discrete spaces.
 -/
 
 
-open Set Function
+open Set Function TopologicalSpace
 
 variable {α X Y Z : Type*} [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z]
 
@@ -394,6 +395,54 @@ instance [CompactSpace X] : Finite S := by
   have : CompactSpace S := Quotient.compactSpace
   rwa [← isCompact_univ_iff, isCompact_iff_finite, finite_univ_iff] at this
 
+variable (X)
+
+open Classical in
+/--
+If `X` is a compact space, then we associate to any discrete quotient on `X` a finite set of
+clopen subsets of `X`, given by the fibers of `proj`.
+
+TODO: prove that these form a partition of `X` 
+-/
+noncomputable def finsetClopens [CompactSpace X]
+    (d : DiscreteQuotient X) : Finset (Clopens X) := have : Fintype d := Fintype.ofFinite _
+  (Set.range (fun (x : d) ↦ ⟨_, d.isClopen_preimage {x}⟩) : Set (Clopens X)).toFinset
+
+/-- A helper lemma to prove that `finsetClopens X` is injective, see `finsetClopens_inj`. -/
+lemma comp_finsetClopens [CompactSpace X] :
+    (Set.image (fun (t : Clopens X) ↦ t.carrier) ∘ Finset.toSet) ∘
+      finsetClopens X = fun ⟨f, _⟩ ↦ f.classes := by
+  ext d
+  simp only [Setoid.classes, Setoid.Rel, Set.mem_setOf_eq, Function.comp_apply,
+    finsetClopens, Set.coe_toFinset, Set.mem_image, Set.mem_range,
+    exists_exists_eq_and]
+  constructor
+  · refine fun ⟨y, h⟩ ↦ ⟨Quotient.out (s := d.toSetoid) y, ?_⟩
+    ext
+    simpa [← h] using Quotient.mk_eq_iff_out (s := d.toSetoid)
+  · exact fun ⟨y, h⟩ ↦ ⟨d.proj y, by ext; simp [h, proj]⟩
+
+/-- `finsetClopens X` is injective. -/
+theorem finsetClopens_inj [CompactSpace X] :
+    (finsetClopens X).Injective := by
+  apply Function.Injective.of_comp (f := Set.image (fun (t : Clopens X) ↦ t.carrier) ∘ Finset.toSet)
+  rw [comp_finsetClopens]
+  intro ⟨_, _⟩ ⟨_, _⟩ h
+  congr
+  rw [Setoid.classes_inj]
+  exact h
+
+/--
+The discrete quotients of a compact space are in bijection with a subtype of the type of
+`Finset (Clopens X)`.
+
+TODO: show that this is precisely those finsets of clopens which form a partition of `X`.
+-/
+noncomputable
+def equivFinsetClopens [CompactSpace X] := Equiv.ofInjective _ (finsetClopens_inj X)
+
+variable {X}
+
 end DiscreteQuotient
 
 namespace LocallyConstant

@@ -69,7 +69,7 @@ variable {α X Y Z : Type*} [TopologicalSpace X] [TopologicalSpace Y] [Topologic
 /-- The type of discrete quotients of a topological space. -/
 @[ext] -- Porting note: in Lean 4, uses projection to `r` instead of `Setoid`.
 structure DiscreteQuotient (X : Type*) [TopologicalSpace X] extends Setoid X where
-  /-- For every point `x`, the set `{ y | Rel x y }` is a clopen set. -/
+  /-- For every point `x`, the set `{ y | Rel x y }` is an open set. -/
   protected isOpen_setOf_rel : ∀ x, IsOpen (setOf (toSetoid.Rel x))
 #align discrete_quotient DiscreteQuotient
 

Classifies by adding issue number #10756 to porting notes claiming anything semantically equivalent to:

• "new lemma"
• "added lemma"

@@ -77,7 +77,7 @@ namespace DiscreteQuotient
 
 variable (S : DiscreteQuotient X)
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 lemma toSetoid_injective : Function.Injective (@toSetoid X _)
   | ⟨_, _⟩, ⟨_, _⟩, _ => by congr
 
@@ -169,7 +169,7 @@ instance inhabitedQuotient [Inhabited X] : Inhabited S := ⟨S.proj default⟩
 -- Porting note (#11215): TODO: add instances about `Nonempty (Quot _)`/`Nonempty (Quotient _)`
 instance [Nonempty X] : Nonempty S := Nonempty.map S.proj ‹_›
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 /-- The quotient by `⊤ : DiscreteQuotient X` is a `Subsingleton`. -/
 instance : Subsingleton (⊤ : DiscreteQuotient X) where
   allEq := by rintro ⟨_⟩ ⟨_⟩; exact Quotient.sound trivial

Classifies by adding issue number #11215 to porting notes claiming "TODO".

@@ -166,7 +166,7 @@ instance : Inhabited (DiscreteQuotient X) := ⟨⊤⟩
 instance inhabitedQuotient [Inhabited X] : Inhabited S := ⟨S.proj default⟩
 #align discrete_quotient.inhabited_quotient DiscreteQuotient.inhabitedQuotient
 
--- Porting note: TODO: add instances about `Nonempty (Quot _)`/`Nonempty (Quotient _)`
+-- Porting note (#11215): TODO: add instances about `Nonempty (Quot _)`/`Nonempty (Quotient _)`
 instance [Nonempty X] : Nonempty S := Nonempty.map S.proj ‹_›
 
 -- Porting note: new lemma
@@ -325,7 +325,7 @@ theorem map_proj (cond : LEComap f A B) (x : X) : map f cond (A.proj x) = B.proj
 theorem map_id : map _ (leComap_id A) = id := by ext ⟨⟩; rfl
 #align discrete_quotient.map_id DiscreteQuotient.map_id
 
--- Porting note: todo: figure out why `simpNF` says this is a bad `@[simp]` lemma
+-- Porting note (#11215): TODO: figure out why `simpNF` says this is a bad `@[simp]` lemma
 theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
     map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 := by
   ext ⟨⟩

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -67,7 +67,7 @@ open Set Function
 variable {α X Y Z : Type*} [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z]
 
 /-- The type of discrete quotients of a topological space. -/
-@[ext] -- porting note: in Lean 4, uses projection to `r` instead of `Setoid`.
+@[ext] -- Porting note: in Lean 4, uses projection to `r` instead of `Setoid`.
 structure DiscreteQuotient (X : Type*) [TopologicalSpace X] extends Setoid X where
   /-- For every point `x`, the set `{ y | Rel x y }` is a clopen set. -/
   protected isOpen_setOf_rel : ∀ x, IsOpen (setOf (toSetoid.Rel x))
@@ -77,7 +77,7 @@ namespace DiscreteQuotient
 
 variable (S : DiscreteQuotient X)
 
--- porting note: new lemma
+-- Porting note: new lemma
 lemma toSetoid_injective : Function.Injective (@toSetoid X _)
   | ⟨_, _⟩, ⟨_, _⟩, _ => by congr
 
@@ -166,10 +166,10 @@ instance : Inhabited (DiscreteQuotient X) := ⟨⊤⟩
 instance inhabitedQuotient [Inhabited X] : Inhabited S := ⟨S.proj default⟩
 #align discrete_quotient.inhabited_quotient DiscreteQuotient.inhabitedQuotient
 
--- porting note: TODO: add instances about `Nonempty (Quot _)`/`Nonempty (Quotient _)`
+-- Porting note: TODO: add instances about `Nonempty (Quot _)`/`Nonempty (Quotient _)`
 instance [Nonempty X] : Nonempty S := Nonempty.map S.proj ‹_›
 
--- porting note: new lemma
+-- Porting note: new lemma
 /-- The quotient by `⊤ : DiscreteQuotient X` is a `Subsingleton`. -/
 instance : Subsingleton (⊤ : DiscreteQuotient X) where
   allEq := by rintro ⟨_⟩ ⟨_⟩; exact Quotient.sound trivial
@@ -325,7 +325,7 @@ theorem map_proj (cond : LEComap f A B) (x : X) : map f cond (A.proj x) = B.proj
 theorem map_id : map _ (leComap_id A) = id := by ext ⟨⟩; rfl
 #align discrete_quotient.map_id DiscreteQuotient.map_id
 
--- porting note: todo: figure out why `simpNF` says this is a bad `@[simp]` lemma
+-- Porting note: todo: figure out why `simpNF` says this is a bad `@[simp]` lemma
 theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
     map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 := by
   ext ⟨⟩

The iInter version of Cantor's intersection theorem is already present: IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed. The proof of the added sInter version takes advantage of the iInter version.

Much of the addition due to conversation with Sebastien Gouezel on Zulip.

@@ -382,7 +382,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : (Q : DiscreteQuotient X) → Q)
     rw [← compat _ _ h]
     exact fiber_subset_ofLE _ _
   obtain ⟨x, hx⟩ : Set.Nonempty (⋂ Q, proj Q ⁻¹' {Qs Q}) :=
-    IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed
+    IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosed
       (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_isDirected_ge H₁)
       (fun Q => (singleton_nonempty _).preimage Q.proj_surjective)
       (fun Q => (Q.isClosed_preimage {Qs _}).isCompact) fun Q => Q.isClosed_preimage _

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

@@ -139,11 +139,11 @@ theorem isClopen_preimage (A : Set S) : IsClopen (S.proj ⁻¹' A) :=
 #align discrete_quotient.is_clopen_preimage DiscreteQuotient.isClopen_preimage
 
 theorem isOpen_preimage (A : Set S) : IsOpen (S.proj ⁻¹' A) :=
-  (S.isClopen_preimage A).1
+  (S.isClopen_preimage A).2
 #align discrete_quotient.is_open_preimage DiscreteQuotient.isOpen_preimage
 
 theorem isClosed_preimage (A : Set S) : IsClosed (S.proj ⁻¹' A) :=
-  (S.isClopen_preimage A).2
+  (S.isClopen_preimage A).1
 #align discrete_quotient.is_closed_preimage DiscreteQuotient.isClosed_preimage
 
 theorem isClopen_setOf_rel (x : X) : IsClopen (setOf (S.Rel x)) := by

This PR renames the field Clopens.clopen' -> Clopens.isClopen', and the lemmas

• preimage_closed_of_closed -> ContinuousOn.preimage_isClosed_of_isClosed

as well as: ClopenUpperSet.clopen -> ClopenUpperSet.isClopen connectedComponent_eq_iInter_clopen -> connectedComponent_eq_iInter_isClopen connectedComponent_subset_iInter_clopen -> connectedComponent_subset_iInter_isClopen continuous_boolIndicator_iff_clopen -> continuous_boolIndicator_iff_isClopen continuousOn_boolIndicator_iff_clopen -> continuousOn_boolIndicator_iff_isClopen DiscreteQuotient.ofClopen -> DiscreteQuotient.ofIsClopen disjoint_or_subset_of_clopen -> disjoint_or_subset_of_isClopen exists_clopen_{lower,upper}of_not_le -> exists_isClopen{lower,upper}_of_not_le exists_clopen_of_cofiltered -> exists_isClopen_of_cofiltered exists_clopen_of_totally_separated -> exists_isClopen_of_totally_separated exists_clopen_upper_or_lower_of_ne -> exists_isClopen_upper_or_lower_of_ne IsPreconnected.subset_clopen -> IsPreconnected.subset_isClopen isTotallyDisconnected_of_clopen_set -> isTotallyDisconnected_of_isClopen_set LocallyConstant.ofClopen_fiber_one -> LocallyConstant.ofIsClopen_fiber_one LocallyConstant.ofClopen_fiber_zero -> LocallyConstant.ofIsClopen_fiber_zero LocallyConstant.ofClopen -> LocallyConstant.ofIsClopen preimage_clopen_of_clopen -> preimage_isClopen_of_isClopen TopologicalSpace.Clopens.clopen -> TopologicalSpace.Clopens.isClopen

@@ -82,10 +82,10 @@ lemma toSetoid_injective : Function.Injective (@toSetoid X _)
   | ⟨_, _⟩, ⟨_, _⟩, _ => by congr
 
 /-- Construct a discrete quotient from a clopen set. -/
-def ofClopen {A : Set X} (h : IsClopen A) : DiscreteQuotient X where
+def ofIsClopen {A : Set X} (h : IsClopen A) : DiscreteQuotient X where
   toSetoid := ⟨fun x y => x ∈ A ↔ y ∈ A, fun _ => Iff.rfl, Iff.symm, Iff.trans⟩
   isOpen_setOf_rel x := by by_cases hx : x ∈ A <;> simp [Setoid.Rel, hx, h.1, h.2, ← compl_setOf]
-#align discrete_quotient.of_clopen DiscreteQuotient.ofClopen
+#align discrete_quotient.of_clopen DiscreteQuotient.ofIsClopen
 
 theorem refl : ∀ x, S.Rel x x := S.refl'
 #align discrete_quotient.refl DiscreteQuotient.refl
@@ -362,10 +362,10 @@ end Map
 
 theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconnectedSpace X]
     {x y : X} (h : ∀ Q : DiscreteQuotient X, Q.proj x = Q.proj y) : x = y := by
-  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_iInter_clopen,
+  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_iInter_isClopen,
     mem_iInter]
   rintro ⟨U, hU1, hU2⟩
-  exact (Quotient.exact' (h (ofClopen hU1))).mpr hU2
+  exact (Quotient.exact' (h (ofIsClopen hU1))).mpr hU2
 #align discrete_quotient.eq_of_forall_proj_eq DiscreteQuotient.eq_of_forall_proj_eq
 
 theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :

New lemmas / instances

• An archimedean ordered semiring is directed upwards.
• Filter.hasAntitoneBasis_atTop;
• Filter.HasAntitoneBasis.iInf_principal;

Fix typos

• Docstrings: "if the agree" -> "if they agree".
• ProbabilityTheory.measure_eq_zero_or_one_of_indepSetCat_self -> ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self.

Weaken typeclass assumptions

From a semilattice to a directed type

• MeasureTheory.tendsto_measure_iUnion;
• MeasureTheory.tendsto_measure_iInter;
• Monotone.directed_le, Monotone.directed_ge;
• Antitone.directed_le, Antitone.directed_ge;
• directed_of_sup, renamed to directed_of_isDirected_le;
• directed_of_inf, renamed to directed_of_isDirected_ge;

From a strict ordered semiring to an ordered semiring

• tendsto_nat_cast_atTop_atTop;
• Filter.Eventually.nat_cast_atTop;
• atTop_hasAntitoneBasis_of_archimedean;

@@ -383,7 +383,7 @@ theorem exists_of_compat [CompactSpace X] (Qs : (Q : DiscreteQuotient X) → Q)
     exact fiber_subset_ofLE _ _
   obtain ⟨x, hx⟩ : Set.Nonempty (⋂ Q, proj Q ⁻¹' {Qs Q}) :=
     IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed
-      (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_inf H₁)
+      (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_isDirected_ge H₁)
       (fun Q => (singleton_nonempty _).preimage Q.proj_surjective)
       (fun Q => (Q.isClosed_preimage {Qs _}).isCompact) fun Q => Q.isClosed_preimage _
   exact ⟨x, mem_iInter.1 hx⟩

Split up the 2000-line Topology/SubsetProperties.lean into several smaller files. Not only is it too huge, but the name is very unhelpful, since actually about 90% of the file is about compactness; I've moved this material into various files inside a new subdirectory Topology/Compactness/.

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Calle Sönne, Adam Topaz
 -/
 import Mathlib.Topology.Separation
-import Mathlib.Topology.SubsetProperties
 import Mathlib.Topology.LocallyConstant.Basic
 
 #align_import topology.discrete_quotient from "leanprover-community/mathlib"@"d101e93197bb5f6ea89bd7ba386b7f7dff1f3903"

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -65,11 +65,11 @@ of finite discrete spaces.
 
 open Set Function
 
-variable {α X Y Z : Type _} [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z]
+variable {α X Y Z : Type*} [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z]
 
 /-- The type of discrete quotients of a topological space. -/
 @[ext] -- porting note: in Lean 4, uses projection to `r` instead of `Setoid`.
-structure DiscreteQuotient (X : Type _) [TopologicalSpace X] extends Setoid X where
+structure DiscreteQuotient (X : Type*) [TopologicalSpace X] extends Setoid X where
   /-- For every point `x`, the set `{ y | Rel x y }` is a clopen set. -/
   protected isOpen_setOf_rel : ∀ x, IsOpen (setOf (toSetoid.Rel x))
 #align discrete_quotient DiscreteQuotient

• depends on: #5966

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

@@ -2,16 +2,13 @@
 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.discrete_quotient
-! 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.Separation
 import Mathlib.Topology.SubsetProperties
 import Mathlib.Topology.LocallyConstant.Basic
 
+#align_import topology.discrete_quotient from "leanprover-community/mathlib"@"d101e93197bb5f6ea89bd7ba386b7f7dff1f3903"
+
 /-!
 
 # Discrete quotients of a topological space.

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -87,7 +87,7 @@ lemma toSetoid_injective : Function.Injective (@toSetoid X _)
 
 /-- Construct a discrete quotient from a clopen set. -/
 def ofClopen {A : Set X} (h : IsClopen A) : DiscreteQuotient X where
-  toSetoid := ⟨fun x y => x ∈ A ↔ y ∈ A, fun _ => Iff.rfl,  Iff.symm,  Iff.trans⟩
+  toSetoid := ⟨fun x y => x ∈ A ↔ y ∈ A, fun _ => Iff.rfl, Iff.symm, Iff.trans⟩
   isOpen_setOf_rel x := by by_cases hx : x ∈ A <;> simp [Setoid.Rel, hx, h.1, h.2, ← compl_setOf]
 #align discrete_quotient.of_clopen DiscreteQuotient.ofClopen
 

I wrote a script to find lines that contain an odd number of backticks

@@ -43,8 +43,8 @@ i.e., `x ~ y` means that `x` and `y` belong to the same connected component. In
 is a discrete topological space, then `x ~ y` is equivalent (propositionally, not definitionally) to
 `x = y`.
 
-Given `f : C(X, Y)`, we define a predicate `DiscreteQuotient.LEComap f A B` for `A :
-DiscreteQuotient X` and `B : DiscreteQuotient Y`, asserting that `f` descends to `A → B`.  If
+Given `f : C(X, Y)`, we define a predicate `DiscreteQuotient.LEComap f A B` for
+`A : DiscreteQuotient X` and `B : DiscreteQuotient Y`, asserting that `f` descends to `A → B`. If
 `cond : DiscreteQuotient.LEComap h A B`, the function `A → B` is obtained by
 `DiscreteQuotient.map f cond`.
 

Part 3 of #5001

@@ -38,7 +38,7 @@ The top element `⊤` is the trivial quotient, meaning that every element of `X`
 to a point. Given `h : A ≤ B`, the map `A → B` is `DiscreteQuotient.ofLE h`.
 
 Whenever `X` is a locally connected space, the type `DiscreteQuotient X` is also endowed with an
-instance of a `OrderBot`, where the bot element `⊥` is given by the `connectedComponentSetoid`,
+instance of an `OrderBot`, where the bot element `⊥` is given by the `connectedComponentSetoid`,
 i.e., `x ~ y` means that `x` and `y` belong to the same connected component. In particular, if `X`
 is a discrete topological space, then `x ~ y` is equivalent (propositionally, not definitionally) to
 `x = y`.

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -366,8 +366,8 @@ end Map
 
 theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconnectedSpace X]
     {x y : X} (h : ∀ Q : DiscreteQuotient X, Q.proj x = Q.proj y) : x = y := by
-  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_interᵢ_clopen,
-    mem_interᵢ]
+  rw [← mem_singleton_iff, ← connectedComponent_eq_singleton, connectedComponent_eq_iInter_clopen,
+    mem_iInter]
   rintro ⟨U, hU1, hU2⟩
   exact (Quotient.exact' (h (ofClopen hU1))).mpr hU2
 #align discrete_quotient.eq_of_forall_proj_eq DiscreteQuotient.eq_of_forall_proj_eq
@@ -386,11 +386,11 @@ theorem exists_of_compat [CompactSpace X] (Qs : (Q : DiscreteQuotient X) → Q)
     rw [← compat _ _ h]
     exact fiber_subset_ofLE _ _
   obtain ⟨x, hx⟩ : Set.Nonempty (⋂ Q, proj Q ⁻¹' {Qs Q}) :=
-    IsCompact.nonempty_interᵢ_of_directed_nonempty_compact_closed
+    IsCompact.nonempty_iInter_of_directed_nonempty_compact_closed
       (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_inf H₁)
       (fun Q => (singleton_nonempty _).preimage Q.proj_surjective)
       (fun Q => (Q.isClosed_preimage {Qs _}).isCompact) fun Q => Q.isClosed_preimage _
-  exact ⟨x, mem_interᵢ.1 hx⟩
+  exact ⟨x, mem_iInter.1 hx⟩
 #align discrete_quotient.exists_of_compat DiscreteQuotient.exists_of_compat
 
 /-- If `X` is a compact space, then any discrete quotient of `X` is finite. -/

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -222,8 +222,8 @@ theorem ofLE_refl_apply (a : A) : ofLE (le_refl A) a = a := by simp
 #align discrete_quotient.of_le_refl_apply DiscreteQuotient.ofLE_refl_apply
 
 @[simp]
-theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLE h₂ (ofLE h₁ x) = ofLE (h₁.trans h₂) x :=
-  by
+theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) :
+    ofLE h₂ (ofLE h₁ x) = ofLE (h₁.trans h₂) x := by
   rcases x with ⟨⟩
   rfl
 #align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLE

@@ -203,7 +203,7 @@ theorem comap_mono {A B : DiscreteQuotient Y} (h : A ≤ B) : A.comap f ≤ B.co
 
 end Comap
 
-section OfLe
+section OfLE
 
 variable {A B C : DiscreteQuotient X}
 
@@ -247,7 +247,7 @@ theorem ofLE_comp_proj (h : A ≤ B) : ofLE h ∘ A.proj = B.proj :=
   funext <| ofLE_proj _
 #align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLE_comp_proj
 
-end OfLe
+end OfLE
 
 /-- When `X` is a locally connected space, there is an `OrderBot` instance on
 `DiscreteQuotient X`. The bottom element is given by `connectedComponentSetoid X`

@@ -35,7 +35,7 @@ quotients as setoids whose equivalence classes are clopen.
 The type `DiscreteQuotient X` is endowed with an instance of a `SemilatticeInf` with `OrderTop`.
 The partial ordering `A ≤ B` mathematically means that `B.proj` factors through `A.proj`.
 The top element `⊤` is the trivial quotient, meaning that every element of `X` is collapsed
-to a point. Given `h : A ≤ B`, the map `A → B` is `DiscreteQuotient.ofLe h`.
+to a point. Given `h : A ≤ B`, the map `A → B` is `DiscreteQuotient.ofLE h`.
 
 Whenever `X` is a locally connected space, the type `DiscreteQuotient X` is also endowed with an
 instance of a `OrderBot`, where the bot element `⊥` is given by the `connectedComponentSetoid`,
@@ -43,9 +43,9 @@ i.e., `x ~ y` means that `x` and `y` belong to the same connected component. In
 is a discrete topological space, then `x ~ y` is equivalent (propositionally, not definitionally) to
 `x = y`.
 
-Given `f : C(X, Y)`, we define a predicate `DiscreteQuotient.LeComap f A B` for `A :
+Given `f : C(X, Y)`, we define a predicate `DiscreteQuotient.LEComap f A B` for `A :
 DiscreteQuotient X` and `B : DiscreteQuotient Y`, asserting that `f` descends to `A → B`.  If
-`cond : DiscreteQuotient.LeComap h A B`, the function `A → B` is obtained by
+`cond : DiscreteQuotient.LEComap h A B`, the function `A → B` is obtained by
 `DiscreteQuotient.map f cond`.
 
 ## Theorems
@@ -58,7 +58,7 @@ The two main results proved in this file are:
 
 2. `DiscreteQuotient.exists_of_compat` which states that when `X` is compact, then any
   system of elements of `Q` as `Q : DiscreteQuotient X` varies, which is compatible with
-  respect to `DiscreteQuotient.ofLe`, must arise from some element of `X`.
+  respect to `DiscreteQuotient.ofLE`, must arise from some element of `X`.
 
 ## Remarks
 The constructions in this file will be used to show that any profinite space is a limit
@@ -208,44 +208,44 @@ section OfLe
 variable {A B C : DiscreteQuotient X}
 
 /-- The map induced by a refinement of a discrete quotient. -/
-def ofLe (h : A ≤ B) : A → B :=
+def ofLE (h : A ≤ B) : A → B :=
   Quotient.map' (fun x => x) h
-#align discrete_quotient.of_le DiscreteQuotient.ofLe
+#align discrete_quotient.of_le DiscreteQuotient.ofLE
 
 @[simp]
-theorem ofLe_refl : ofLe (le_refl A) = id := by
+theorem ofLE_refl : ofLE (le_refl A) = id := by
   ext ⟨⟩
   rfl
-#align discrete_quotient.of_le_refl DiscreteQuotient.ofLe_refl
+#align discrete_quotient.of_le_refl DiscreteQuotient.ofLE_refl
 
-theorem ofLe_refl_apply (a : A) : ofLe (le_refl A) a = a := by simp
-#align discrete_quotient.of_le_refl_apply DiscreteQuotient.ofLe_refl_apply
+theorem ofLE_refl_apply (a : A) : ofLE (le_refl A) a = a := by simp
+#align discrete_quotient.of_le_refl_apply DiscreteQuotient.ofLE_refl_apply
 
 @[simp]
-theorem ofLe_ofLe (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLe h₂ (ofLe h₁ x) = ofLe (h₁.trans h₂) x :=
+theorem ofLE_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) (x : A) : ofLE h₂ (ofLE h₁ x) = ofLE (h₁.trans h₂) x :=
   by
   rcases x with ⟨⟩
   rfl
-#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLe_ofLe
+#align discrete_quotient.of_le_of_le DiscreteQuotient.ofLE_ofLE
 
 @[simp]
-theorem ofLe_comp_ofLe (h₁ : A ≤ B) (h₂ : B ≤ C) : ofLe h₂ ∘ ofLe h₁ = ofLe (le_trans h₁ h₂) :=
-  funext <| ofLe_ofLe _ _
-#align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLe_comp_ofLe
+theorem ofLE_comp_ofLE (h₁ : A ≤ B) (h₂ : B ≤ C) : ofLE h₂ ∘ ofLE h₁ = ofLE (le_trans h₁ h₂) :=
+  funext <| ofLE_ofLE _ _
+#align discrete_quotient.of_le_comp_of_le DiscreteQuotient.ofLE_comp_ofLE
 
-theorem ofLe_continuous (h : A ≤ B) : Continuous (ofLe h) :=
+theorem ofLE_continuous (h : A ≤ B) : Continuous (ofLE h) :=
   continuous_of_discreteTopology
-#align discrete_quotient.of_le_continuous DiscreteQuotient.ofLe_continuous
+#align discrete_quotient.of_le_continuous DiscreteQuotient.ofLE_continuous
 
 @[simp]
-theorem ofLe_proj (h : A ≤ B) (x : X) : ofLe h (A.proj x) = B.proj x :=
+theorem ofLE_proj (h : A ≤ B) (x : X) : ofLE h (A.proj x) = B.proj x :=
   Quotient.sound' (B.refl _)
-#align discrete_quotient.of_le_proj DiscreteQuotient.ofLe_proj
+#align discrete_quotient.of_le_proj DiscreteQuotient.ofLE_proj
 
 @[simp]
-theorem ofLe_comp_proj (h : A ≤ B) : ofLe h ∘ A.proj = B.proj :=
-  funext <| ofLe_proj _
-#align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLe_comp_proj
+theorem ofLE_comp_proj (h : A ≤ B) : ofLE h ∘ A.proj = B.proj :=
+  funext <| ofLE_proj _
+#align discrete_quotient.of_le_comp_proj DiscreteQuotient.ofLE_comp_proj
 
 end OfLe
 
@@ -283,45 +283,45 @@ section Map
 
 variable (f : C(X, Y)) (A A' : DiscreteQuotient X) (B B' : DiscreteQuotient Y)
 
-/-- Given `f : C(X, Y)`, `DiscreteQuotient.LeComap f A B` is defined as
+/-- Given `f : C(X, Y)`, `DiscreteQuotient.LEComap f A B` is defined as
 `A ≤ B.comap f`. Mathematically this means that `f` descends to a morphism `A → B`. -/
-def LeComap : Prop :=
+def LEComap : Prop :=
   A ≤ B.comap f
-#align discrete_quotient.le_comap DiscreteQuotient.LeComap
+#align discrete_quotient.le_comap DiscreteQuotient.LEComap
 
-theorem leComap_id : LeComap (.id X) A A := le_rfl
+theorem leComap_id : LEComap (.id X) A A := le_rfl
 #align discrete_quotient.le_comap_id DiscreteQuotient.leComap_id
 
 variable {A A' B B'} {f} {g : C(Y, Z)} {C : DiscreteQuotient Z}
 
 @[simp]
-theorem leComap_id_iff : LeComap (ContinuousMap.id X) A A' ↔ A ≤ A' :=
+theorem leComap_id_iff : LEComap (ContinuousMap.id X) A A' ↔ A ≤ A' :=
   Iff.rfl
 #align discrete_quotient.le_comap_id_iff DiscreteQuotient.leComap_id_iff
 
-theorem LeComap.comp : LeComap g B C → LeComap f A B → LeComap (g.comp f) A C := by tauto
-#align discrete_quotient.le_comap.comp DiscreteQuotient.LeComap.comp
+theorem LEComap.comp : LEComap g B C → LEComap f A B → LEComap (g.comp f) A C := by tauto
+#align discrete_quotient.le_comap.comp DiscreteQuotient.LEComap.comp
 
 @[mono]
-theorem LeComap.mono (h : LeComap f A B) (hA : A' ≤ A) (hB : B ≤ B') : LeComap f A' B' :=
+theorem LEComap.mono (h : LEComap f A B) (hA : A' ≤ A) (hB : B ≤ B') : LEComap f A' B' :=
   hA.trans <| h.trans <| comap_mono _ hB
-#align discrete_quotient.le_comap.mono DiscreteQuotient.LeComap.mono
+#align discrete_quotient.le_comap.mono DiscreteQuotient.LEComap.mono
 
 /-- Map a discrete quotient along a continuous map. -/
-def map (f : C(X, Y)) (cond : LeComap f A B) : A → B := Quotient.map' f cond
+def map (f : C(X, Y)) (cond : LEComap f A B) : A → B := Quotient.map' f cond
 #align discrete_quotient.map DiscreteQuotient.map
 
-theorem map_continuous (cond : LeComap f A B) : Continuous (map f cond) :=
+theorem map_continuous (cond : LEComap f A B) : Continuous (map f cond) :=
   continuous_of_discreteTopology
 #align discrete_quotient.map_continuous DiscreteQuotient.map_continuous
 
 @[simp]
-theorem map_comp_proj (cond : LeComap f A B) : map f cond ∘ A.proj = B.proj ∘ f :=
+theorem map_comp_proj (cond : LEComap f A B) : map f cond ∘ A.proj = B.proj ∘ f :=
   rfl
 #align discrete_quotient.map_comp_proj DiscreteQuotient.map_comp_proj
 
 @[simp]
-theorem map_proj (cond : LeComap f A B) (x : X) : map f cond (A.proj x) = B.proj (f x) :=
+theorem map_proj (cond : LEComap f A B) (x : X) : map f cond (A.proj x) = B.proj (f x) :=
   rfl
 #align discrete_quotient.map_proj DiscreteQuotient.map_proj
 
@@ -330,37 +330,37 @@ theorem map_id : map _ (leComap_id A) = id := by ext ⟨⟩; rfl
 #align discrete_quotient.map_id DiscreteQuotient.map_id
 
 -- porting note: todo: figure out why `simpNF` says this is a bad `@[simp]` lemma
-theorem map_comp (h1 : LeComap g B C) (h2 : LeComap f A B) :
+theorem map_comp (h1 : LEComap g B C) (h2 : LEComap f A B) :
     map (g.comp f) (h1.comp h2) = map g h1 ∘ map f h2 := by
   ext ⟨⟩
   rfl
 #align discrete_quotient.map_comp DiscreteQuotient.map_comp
 
 @[simp]
-theorem ofLe_map (cond : LeComap f A B) (h : B ≤ B') (a : A) :
-    ofLe h (map f cond a) = map f (cond.mono le_rfl h) a := by
+theorem ofLE_map (cond : LEComap f A B) (h : B ≤ B') (a : A) :
+    ofLE h (map f cond a) = map f (cond.mono le_rfl h) a := by
   rcases a with ⟨⟩
   rfl
-#align discrete_quotient.of_le_map DiscreteQuotient.ofLe_map
+#align discrete_quotient.of_le_map DiscreteQuotient.ofLE_map
 
 @[simp]
-theorem ofLe_comp_map (cond : LeComap f A B) (h : B ≤ B') :
-    ofLe h ∘ map f cond = map f (cond.mono le_rfl h) :=
-  funext <| ofLe_map cond h
-#align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLe_comp_map
+theorem ofLE_comp_map (cond : LEComap f A B) (h : B ≤ B') :
+    ofLE h ∘ map f cond = map f (cond.mono le_rfl h) :=
+  funext <| ofLE_map cond h
+#align discrete_quotient.of_le_comp_map DiscreteQuotient.ofLE_comp_map
 
 @[simp]
-theorem map_ofLe (cond : LeComap f A B) (h : A' ≤ A) (c : A') :
-    map f cond (ofLe h c) = map f (cond.mono h le_rfl) c := by
+theorem map_ofLE (cond : LEComap f A B) (h : A' ≤ A) (c : A') :
+    map f cond (ofLE h c) = map f (cond.mono h le_rfl) c := by
   rcases c with ⟨⟩
   rfl
-#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLe
+#align discrete_quotient.map_of_le DiscreteQuotient.map_ofLE
 
 @[simp]
-theorem map_comp_ofLe (cond : LeComap f A B) (h : A' ≤ A) :
-    map f cond ∘ ofLe h = map f (cond.mono h le_rfl) :=
-  funext <| map_ofLe cond h
-#align discrete_quotient.map_comp_of_le DiscreteQuotient.map_comp_ofLe
+theorem map_comp_ofLE (cond : LEComap f A B) (h : A' ≤ A) :
+    map f cond ∘ ofLE h = map f (cond.mono h le_rfl) :=
+  funext <| map_ofLE cond h
+#align discrete_quotient.map_comp_of_le DiscreteQuotient.map_comp_ofLE
 
 end Map
 
@@ -372,19 +372,19 @@ theorem eq_of_forall_proj_eq [T2Space X] [CompactSpace X] [disc : TotallyDisconn
   exact (Quotient.exact' (h (ofClopen hU1))).mpr hU2
 #align discrete_quotient.eq_of_forall_proj_eq DiscreteQuotient.eq_of_forall_proj_eq
 
-theorem fiber_subset_ofLe {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
-    A.proj ⁻¹' {a} ⊆ B.proj ⁻¹' {ofLe h a} := by
+theorem fiber_subset_ofLE {A B : DiscreteQuotient X} (h : A ≤ B) (a : A) :
+    A.proj ⁻¹' {a} ⊆ B.proj ⁻¹' {ofLE h a} := by
   rcases A.proj_surjective a with ⟨a, rfl⟩
-  rw [fiber_eq, ofLe_proj, fiber_eq]
+  rw [fiber_eq, ofLE_proj, fiber_eq]
   exact fun _ h' => h h'
-#align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLe
+#align discrete_quotient.fiber_subset_of_le DiscreteQuotient.fiber_subset_ofLE
 
 theorem exists_of_compat [CompactSpace X] (Qs : (Q : DiscreteQuotient X) → Q)
-    (compat : ∀ (A B : DiscreteQuotient X) (h : A ≤ B), ofLe h (Qs _) = Qs _) :
+    (compat : ∀ (A B : DiscreteQuotient X) (h : A ≤ B), ofLE h (Qs _) = Qs _) :
     ∃ x : X, ∀ Q : DiscreteQuotient X, Q.proj x = Qs _ := by
   have H₁ : ∀ Q₁ Q₂, Q₁ ≤ Q₂ → proj Q₁ ⁻¹' {Qs Q₁} ⊆ proj Q₂ ⁻¹' {Qs Q₂} := fun _ _ h => by
     rw [← compat _ _ h]
-    exact fiber_subset_ofLe _ _
+    exact fiber_subset_ofLE _ _
   obtain ⟨x, hx⟩ : Set.Nonempty (⋂ Q, proj Q ⁻¹' {Qs Q}) :=
     IsCompact.nonempty_interᵢ_of_directed_nonempty_compact_closed
       (fun Q : DiscreteQuotient X => Q.proj ⁻¹' {Qs _}) (directed_of_inf H₁)

Restore most of the mono attribute now that #1740 is merged.

I think I got all of the monos.

@@ -197,7 +197,7 @@ theorem comap_comp (S : DiscreteQuotient Z) : S.comap (g.comp f) = (S.comap g).c
   rfl
 #align discrete_quotient.comap_comp DiscreteQuotient.comap_comp
 
--- porting note: todo: add `@[mono]`
+@[mono]
 theorem comap_mono {A B : DiscreteQuotient Y} (h : A ≤ B) : A.comap f ≤ B.comap f := by tauto
 #align discrete_quotient.comap_mono DiscreteQuotient.comap_mono
 
@@ -302,7 +302,7 @@ theorem leComap_id_iff : LeComap (ContinuousMap.id X) A A' ↔ A ≤ A' :=
 theorem LeComap.comp : LeComap g B C → LeComap f A B → LeComap (g.comp f) A C := by tauto
 #align discrete_quotient.le_comap.comp DiscreteQuotient.LeComap.comp
 
--- porting note: todo: add `@[mono]`
+@[mono]
 theorem LeComap.mono (h : LeComap f A B) (hA : A' ≤ A) (hB : B ≤ B') : LeComap f A' B' :=
   hA.trans <| h.trans <| comap_mono _ hB
 #align discrete_quotient.le_comap.mono DiscreteQuotient.LeComap.mono

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -155,7 +155,7 @@ theorem isClopen_setOf_rel (x : X) : IsClopen (setOf (S.Rel x)) := by
   apply isClopen_preimage
 #align discrete_quotient.is_clopen_set_of_rel DiscreteQuotient.isClopen_setOf_rel
 
-instance : HasInf (DiscreteQuotient X) :=
+instance : Inf (DiscreteQuotient X) :=
   ⟨fun S₁ S₂ => ⟨S₁.1 ⊓ S₂.1, fun x => (S₁.2 x).inter (S₂.2 x)⟩⟩
 
 instance : SemilatticeInf (DiscreteQuotient X) :=

Also sync SHA in Topology.Connected. The changes in Mathlib 3 were backported from this branch, see

• topology.connected@92ca63f0fb391a9ca5f22d2409a6080e786d99f7..d101e93197bb5f6ea89bd7ba386b7f7dff1f3903