topology.semicontinuous ⟷ Mathlib.Topology.Semicontinuous

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Algebra.IndicatorFunction
+import Algebra.Function.Indicator
 import Topology.ContinuousOn
-import Topology.Instances.Ennreal
+import Topology.Instances.ENNReal
 
 #align_import topology.semicontinuous from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
 

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

@@ -246,7 +246,7 @@ theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
   intro x z hz
-  by_cases h : x ∈ s <;> simp [h] at hz 
+  by_cases h : x ∈ s <;> simp [h] at hz
   · filter_upwards [hs.mem_nhds h]
     simp (config := { contextual := true }) [hz]
   · apply Filter.eventually_of_forall fun x' => _
@@ -280,7 +280,7 @@ theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0)
     LowerSemicontinuous (indicator s fun x => y) :=
   by
   intro x z hz
-  by_cases h : x ∈ s <;> simp [h] at hz 
+  by_cases h : x ∈ s <;> simp [h] at hz
   · apply Filter.eventually_of_forall fun x' => _
     by_cases h' : x' ∈ s <;> simp [h', hz, hz.trans_le hy]
   · filter_upwards [hs.is_open_compl.mem_nhds h]
@@ -402,7 +402,7 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
     calc
       y < g (min (f x) (f a)) := hz (by simp [zlt, ha, le_refl])
       _ ≤ g (f a) := gmon (min_le_right _ _)
-  · simp only [not_exists, not_lt] at h 
+  · simp only [not_exists, not_lt] at h
     exact Filter.eventually_of_forall fun a => hy.trans_le (gmon (h (f a)))
 #align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAt
 -/
@@ -508,7 +508,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < min (f z) (f x) + min (g z) (g x) := h this
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (min_le_left _ _)
-    · simp only [not_exists, not_lt] at hx₂ 
+    · simp only [not_exists, not_lt] at hx₂
       filter_upwards [hf z₁ z₁lt] with z h₁z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
@@ -518,7 +518,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < min (f z) (f x) + g x := h this
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (hx₂ (g z))
-  · simp only [not_exists, not_lt] at hx₁ 
+  · simp only [not_exists, not_lt] at hx₁
     by_cases hx₂ : ∃ l, l < g x
     · obtain ⟨z₂, z₂lt, h₂⟩ : ∃ z₂ < g x, Ioc z₂ (g x) ⊆ v :=
         exists_Ioc_subset_of_mem_nhds (v_open.mem_nhds xv) hx₂
@@ -531,7 +531,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < f x + min (g z) (g x) := h this
         _ ≤ f z + g z := add_le_add (hx₁ (f z)) (min_le_left _ _)
-    · simp only [not_exists, not_lt] at hx₁ hx₂ 
+    · simp only [not_exists, not_lt] at hx₁ hx₂
       apply Filter.eventually_of_forall
       intro z
       have : (f x, g x) ∈ u ×ˢ v := ⟨xu, xv⟩
@@ -704,7 +704,7 @@ theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
   by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
-  rw [← nhdsWithin_univ] at bdd 
+  rw [← nhdsWithin_univ] at bdd
   exact lowerSemicontinuousWithinAt_ciSup bdd h
 #align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSup
 -/
@@ -1374,15 +1374,15 @@ theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ}
       cases' le_or_gt (f a) (f x) with h h
       · exact hl ⟨lfa, h⟩
       · exact hu ⟨le_of_lt h, fau⟩
-    · simp only [not_exists, not_lt] at Hu 
+    · simp only [not_exists, not_lt] at Hu
       filter_upwards [h₁ l lfx] with a lfa using hl ⟨lfa, Hu (f a)⟩
-  · simp only [not_exists, not_lt] at Hl 
+  · simp only [not_exists, not_lt] at Hl
     by_cases Hu : ∃ u, f x < u
     · rcases exists_Ico_subset_of_mem_nhds hv Hu with ⟨u, fxu, hu⟩
       filter_upwards [h₂ u fxu] with a lfa
       apply hu
       exact ⟨Hl (f a), lfa⟩
-    · simp only [not_exists, not_lt] at Hu 
+    · simp only [not_exists, not_lt] at Hu
       apply Filter.eventually_of_forall
       intro a
       have : f a = f x := le_antisymm (Hu _) (Hl _)

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

@@ -622,7 +622,14 @@ theorem LowerSemicontinuous.add {f g : α → γ} (hf : LowerSemicontinuous f)
 #print lowerSemicontinuousWithinAt_sum /-
 theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousWithinAt (f i) s x) :
-    LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by classical
+    LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by
+  classical
+  induction' a using Finset.induction_on with i a ia IH generalizing ha
+  · exact lowerSemicontinuousWithinAt_const
+  · simp only [ia, Finset.sum_insert, not_false_iff]
+    exact
+      LowerSemicontinuousWithinAt.add (ha _ (Finset.mem_insert_self i a))
+        (IH fun j ja => ha j (Finset.mem_insert_of_mem ja))
 #align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sum
 -/
 

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

@@ -622,14 +622,7 @@ theorem LowerSemicontinuous.add {f g : α → γ} (hf : LowerSemicontinuous f)
 #print lowerSemicontinuousWithinAt_sum /-
 theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousWithinAt (f i) s x) :
-    LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by
-  classical
-  induction' a using Finset.induction_on with i a ia IH generalizing ha
-  · exact lowerSemicontinuousWithinAt_const
-  · simp only [ia, Finset.sum_insert, not_false_iff]
-    exact
-      LowerSemicontinuousWithinAt.add (ha _ (Finset.mem_insert_self i a))
-        (IH fun j ja => ha j (Finset.mem_insert_of_mem ja))
+    LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by classical
 #align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sum
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Algebra.IndicatorFunction
-import Mathbin.Topology.ContinuousOn
-import Mathbin.Topology.Instances.Ennreal
+import Algebra.IndicatorFunction
+import Topology.ContinuousOn
+import Topology.Instances.Ennreal
 
 #align_import topology.semicontinuous from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.semicontinuous
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.IndicatorFunction
 import Mathbin.Topology.ContinuousOn
 import Mathbin.Topology.Instances.Ennreal
 
+#align_import topology.semicontinuous from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Semicontinuous maps
 

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

@@ -150,66 +150,92 @@ def UpperSemicontinuous (f : α → β) :=
 /-! #### Basic dot notation interface for lower semicontinuity -/
 
 
+#print LowerSemicontinuousWithinAt.mono /-
 theorem LowerSemicontinuousWithinAt.mono (h : LowerSemicontinuousWithinAt f s x) (hst : t ⊆ s) :
     LowerSemicontinuousWithinAt f t x := fun y hy =>
   Filter.Eventually.filter_mono (nhdsWithin_mono _ hst) (h y hy)
 #align lower_semicontinuous_within_at.mono LowerSemicontinuousWithinAt.mono
+-/
 
+#print lowerSemicontinuousWithinAt_univ_iff /-
 theorem lowerSemicontinuousWithinAt_univ_iff :
     LowerSemicontinuousWithinAt f univ x ↔ LowerSemicontinuousAt f x := by
   simp [LowerSemicontinuousWithinAt, LowerSemicontinuousAt, nhdsWithin_univ]
 #align lower_semicontinuous_within_at_univ_iff lowerSemicontinuousWithinAt_univ_iff
+-/
 
+#print LowerSemicontinuousAt.lowerSemicontinuousWithinAt /-
 theorem LowerSemicontinuousAt.lowerSemicontinuousWithinAt (s : Set α)
     (h : LowerSemicontinuousAt f x) : LowerSemicontinuousWithinAt f s x := fun y hy =>
   Filter.Eventually.filter_mono nhdsWithin_le_nhds (h y hy)
 #align lower_semicontinuous_at.lower_semicontinuous_within_at LowerSemicontinuousAt.lowerSemicontinuousWithinAt
+-/
 
+#print LowerSemicontinuousOn.lowerSemicontinuousWithinAt /-
 theorem LowerSemicontinuousOn.lowerSemicontinuousWithinAt (h : LowerSemicontinuousOn f s)
     (hx : x ∈ s) : LowerSemicontinuousWithinAt f s x :=
   h x hx
 #align lower_semicontinuous_on.lower_semicontinuous_within_at LowerSemicontinuousOn.lowerSemicontinuousWithinAt
+-/
 
+#print LowerSemicontinuousOn.mono /-
 theorem LowerSemicontinuousOn.mono (h : LowerSemicontinuousOn f s) (hst : t ⊆ s) :
     LowerSemicontinuousOn f t := fun x hx => (h x (hst hx)).mono hst
 #align lower_semicontinuous_on.mono LowerSemicontinuousOn.mono
+-/
 
+#print lowerSemicontinuousOn_univ_iff /-
 theorem lowerSemicontinuousOn_univ_iff : LowerSemicontinuousOn f univ ↔ LowerSemicontinuous f := by
   simp [LowerSemicontinuousOn, LowerSemicontinuous, lowerSemicontinuousWithinAt_univ_iff]
 #align lower_semicontinuous_on_univ_iff lowerSemicontinuousOn_univ_iff
+-/
 
+#print LowerSemicontinuous.lowerSemicontinuousAt /-
 theorem LowerSemicontinuous.lowerSemicontinuousAt (h : LowerSemicontinuous f) (x : α) :
     LowerSemicontinuousAt f x :=
   h x
 #align lower_semicontinuous.lower_semicontinuous_at LowerSemicontinuous.lowerSemicontinuousAt
+-/
 
+#print LowerSemicontinuous.lowerSemicontinuousWithinAt /-
 theorem LowerSemicontinuous.lowerSemicontinuousWithinAt (h : LowerSemicontinuous f) (s : Set α)
     (x : α) : LowerSemicontinuousWithinAt f s x :=
   (h x).LowerSemicontinuousWithinAt s
 #align lower_semicontinuous.lower_semicontinuous_within_at LowerSemicontinuous.lowerSemicontinuousWithinAt
+-/
 
+#print LowerSemicontinuous.lowerSemicontinuousOn /-
 theorem LowerSemicontinuous.lowerSemicontinuousOn (h : LowerSemicontinuous f) (s : Set α) :
     LowerSemicontinuousOn f s := fun x hx => h.LowerSemicontinuousWithinAt s x
 #align lower_semicontinuous.lower_semicontinuous_on LowerSemicontinuous.lowerSemicontinuousOn
+-/
 
 /-! #### Constants -/
 
 
+#print lowerSemicontinuousWithinAt_const /-
 theorem lowerSemicontinuousWithinAt_const : LowerSemicontinuousWithinAt (fun x => z) s x :=
   fun y hy => Filter.eventually_of_forall fun x => hy
 #align lower_semicontinuous_within_at_const lowerSemicontinuousWithinAt_const
+-/
 
+#print lowerSemicontinuousAt_const /-
 theorem lowerSemicontinuousAt_const : LowerSemicontinuousAt (fun x => z) x := fun y hy =>
   Filter.eventually_of_forall fun x => hy
 #align lower_semicontinuous_at_const lowerSemicontinuousAt_const
+-/
 
+#print lowerSemicontinuousOn_const /-
 theorem lowerSemicontinuousOn_const : LowerSemicontinuousOn (fun x => z) s := fun x hx =>
   lowerSemicontinuousWithinAt_const
 #align lower_semicontinuous_on_const lowerSemicontinuousOn_const
+-/
 
+#print lowerSemicontinuous_const /-
 theorem lowerSemicontinuous_const : LowerSemicontinuous fun x : α => z := fun x =>
   lowerSemicontinuousAt_const
 #align lower_semicontinuous_const lowerSemicontinuous_const
+-/
 
 /-! #### Indicators -/
 
@@ -218,6 +244,7 @@ section
 
 variable [Zero β]
 
+#print IsOpen.lowerSemicontinuous_indicator /-
 theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
@@ -228,22 +255,30 @@ theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
   · apply Filter.eventually_of_forall fun x' => _
     by_cases h' : x' ∈ s <;> simp [h', hz.trans_le hy, hz]
 #align is_open.lower_semicontinuous_indicator IsOpen.lowerSemicontinuous_indicator
+-/
 
+#print IsOpen.lowerSemicontinuousOn_indicator /-
 theorem IsOpen.lowerSemicontinuousOn_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousOn (indicator s fun x => y) t :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousOn t
 #align is_open.lower_semicontinuous_on_indicator IsOpen.lowerSemicontinuousOn_indicator
+-/
 
+#print IsOpen.lowerSemicontinuousAt_indicator /-
 theorem IsOpen.lowerSemicontinuousAt_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousAt (indicator s fun x => y) x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousAt x
 #align is_open.lower_semicontinuous_at_indicator IsOpen.lowerSemicontinuousAt_indicator
+-/
 
+#print IsOpen.lowerSemicontinuousWithinAt_indicator /-
 theorem IsOpen.lowerSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousWithinAt t x
 #align is_open.lower_semicontinuous_within_at_indicator IsOpen.lowerSemicontinuousWithinAt_indicator
+-/
 
+#print IsClosed.lowerSemicontinuous_indicator /-
 theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
@@ -254,43 +289,55 @@ theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0)
   · filter_upwards [hs.is_open_compl.mem_nhds h]
     simp (config := { contextual := true }) [hz]
 #align is_closed.lower_semicontinuous_indicator IsClosed.lowerSemicontinuous_indicator
+-/
 
+#print IsClosed.lowerSemicontinuousOn_indicator /-
 theorem IsClosed.lowerSemicontinuousOn_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousOn (indicator s fun x => y) t :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousOn t
 #align is_closed.lower_semicontinuous_on_indicator IsClosed.lowerSemicontinuousOn_indicator
+-/
 
+#print IsClosed.lowerSemicontinuousAt_indicator /-
 theorem IsClosed.lowerSemicontinuousAt_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousAt (indicator s fun x => y) x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousAt x
 #align is_closed.lower_semicontinuous_at_indicator IsClosed.lowerSemicontinuousAt_indicator
+-/
 
+#print IsClosed.lowerSemicontinuousWithinAt_indicator /-
 theorem IsClosed.lowerSemicontinuousWithinAt_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousWithinAt t x
 #align is_closed.lower_semicontinuous_within_at_indicator IsClosed.lowerSemicontinuousWithinAt_indicator
+-/
 
 end
 
 /-! #### Relationship with continuity -/
 
 
+#print lowerSemicontinuous_iff_isOpen_preimage /-
 theorem lowerSemicontinuous_iff_isOpen_preimage :
     LowerSemicontinuous f ↔ ∀ y, IsOpen (f ⁻¹' Ioi y) :=
   ⟨fun H y => isOpen_iff_mem_nhds.2 fun x hx => H x y hx, fun H x y y_lt =>
     IsOpen.mem_nhds (H y) y_lt⟩
 #align lower_semicontinuous_iff_is_open_preimage lowerSemicontinuous_iff_isOpen_preimage
+-/
 
+#print LowerSemicontinuous.isOpen_preimage /-
 theorem LowerSemicontinuous.isOpen_preimage (hf : LowerSemicontinuous f) (y : β) :
     IsOpen (f ⁻¹' Ioi y) :=
   lowerSemicontinuous_iff_isOpen_preimage.1 hf y
 #align lower_semicontinuous.is_open_preimage LowerSemicontinuous.isOpen_preimage
+-/
 
 section
 
 variable {γ : Type _} [LinearOrder γ]
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
+#print lowerSemicontinuous_iff_isClosed_preimage /-
 theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     LowerSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Iic y) :=
   by
@@ -299,29 +346,40 @@ theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]]"
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Iic]
 #align lower_semicontinuous_iff_is_closed_preimage lowerSemicontinuous_iff_isClosed_preimage
+-/
 
+#print LowerSemicontinuous.isClosed_preimage /-
 theorem LowerSemicontinuous.isClosed_preimage {f : α → γ} (hf : LowerSemicontinuous f) (y : γ) :
     IsClosed (f ⁻¹' Iic y) :=
   lowerSemicontinuous_iff_isClosed_preimage.1 hf y
 #align lower_semicontinuous.is_closed_preimage LowerSemicontinuous.isClosed_preimage
+-/
 
 variable [TopologicalSpace γ] [OrderTopology γ]
 
+#print ContinuousWithinAt.lowerSemicontinuousWithinAt /-
 theorem ContinuousWithinAt.lowerSemicontinuousWithinAt {f : α → γ} (h : ContinuousWithinAt f s x) :
     LowerSemicontinuousWithinAt f s x := fun y hy => h (Ioi_mem_nhds hy)
 #align continuous_within_at.lower_semicontinuous_within_at ContinuousWithinAt.lowerSemicontinuousWithinAt
+-/
 
+#print ContinuousAt.lowerSemicontinuousAt /-
 theorem ContinuousAt.lowerSemicontinuousAt {f : α → γ} (h : ContinuousAt f x) :
     LowerSemicontinuousAt f x := fun y hy => h (Ioi_mem_nhds hy)
 #align continuous_at.lower_semicontinuous_at ContinuousAt.lowerSemicontinuousAt
+-/
 
+#print ContinuousOn.lowerSemicontinuousOn /-
 theorem ContinuousOn.lowerSemicontinuousOn {f : α → γ} (h : ContinuousOn f s) :
     LowerSemicontinuousOn f s := fun x hx => (h x hx).LowerSemicontinuousWithinAt
 #align continuous_on.lower_semicontinuous_on ContinuousOn.lowerSemicontinuousOn
+-/
 
+#print Continuous.lowerSemicontinuous /-
 theorem Continuous.lowerSemicontinuous {f : α → γ} (h : Continuous f) : LowerSemicontinuous f :=
   fun x => h.ContinuousAt.LowerSemicontinuousAt
 #align continuous.lower_semicontinuous Continuous.lowerSemicontinuous
+-/
 
 end
 
@@ -334,6 +392,7 @@ variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
+#print ContinuousAt.comp_lowerSemicontinuousWithinAt /-
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     LowerSemicontinuousWithinAt (g ∘ f) s x :=
@@ -349,45 +408,60 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
   · simp only [not_exists, not_lt] at h 
     exact Filter.eventually_of_forall fun a => hy.trans_le (gmon (h (f a)))
 #align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAt
+-/
 
+#print ContinuousAt.comp_lowerSemicontinuousAt /-
 theorem ContinuousAt.comp_lowerSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : LowerSemicontinuousAt f x) (gmon : Monotone g) : LowerSemicontinuousAt (g ∘ f) x :=
   by
   simp only [← lowerSemicontinuousWithinAt_univ_iff] at hf ⊢
   exact hg.comp_lower_semicontinuous_within_at hf gmon
 #align continuous_at.comp_lower_semicontinuous_at ContinuousAt.comp_lowerSemicontinuousAt
+-/
 
+#print Continuous.comp_lowerSemicontinuousOn /-
 theorem Continuous.comp_lowerSemicontinuousOn {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuousOn f s) (gmon : Monotone g) : LowerSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_lowerSemicontinuousWithinAt (hf x hx) gmon
 #align continuous.comp_lower_semicontinuous_on Continuous.comp_lowerSemicontinuousOn
+-/
 
+#print Continuous.comp_lowerSemicontinuous /-
 theorem Continuous.comp_lowerSemicontinuous {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuous f) (gmon : Monotone g) : LowerSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_lowerSemicontinuousAt (hf x) gmon
 #align continuous.comp_lower_semicontinuous Continuous.comp_lowerSemicontinuous
+-/
 
+#print ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone /-
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Antitone g) :
     UpperSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_lowerSemicontinuousWithinAt α _ x s γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_lower_semicontinuous_within_at_antitone ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone
+-/
 
+#print ContinuousAt.comp_lowerSemicontinuousAt_antitone /-
 theorem ContinuousAt.comp_lowerSemicontinuousAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousAt f x) (gmon : Antitone g) :
     UpperSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_lowerSemicontinuousAt α _ x γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_lower_semicontinuous_at_antitone ContinuousAt.comp_lowerSemicontinuousAt_antitone
+-/
 
+#print Continuous.comp_lowerSemicontinuousOn_antitone /-
 theorem Continuous.comp_lowerSemicontinuousOn_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuousOn f s) (gmon : Antitone g) : UpperSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone (hf x hx) gmon
 #align continuous.comp_lower_semicontinuous_on_antitone Continuous.comp_lowerSemicontinuousOn_antitone
+-/
 
+#print Continuous.comp_lowerSemicontinuous_antitone /-
 theorem Continuous.comp_lowerSemicontinuous_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuous f) (gmon : Antitone g) : UpperSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_lowerSemicontinuousAt_antitone (hf x) gmon
 #align continuous.comp_lower_semicontinuous_antitone Continuous.comp_lowerSemicontinuous_antitone
+-/
 
 end
 
@@ -404,6 +478,7 @@ variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [Topologica
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print LowerSemicontinuousWithinAt.add' /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -467,7 +542,9 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         y < f x + g x := h this
         _ ≤ f z + g z := add_le_add (hx₁ (f z)) (hx₂ (g z))
 #align lower_semicontinuous_within_at.add' LowerSemicontinuousWithinAt.add'
+-/
 
+#print LowerSemicontinuousAt.add' /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -477,7 +554,9 @@ theorem LowerSemicontinuousAt.add' {f g : α → γ} (hf : LowerSemicontinuousAt
     LowerSemicontinuousAt (fun z => f z + g z) x := by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *; exact hf.add' hg hcont
 #align lower_semicontinuous_at.add' LowerSemicontinuousAt.add'
+-/
 
+#print LowerSemicontinuousOn.add' /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -487,7 +566,9 @@ theorem LowerSemicontinuousOn.add' {f g : α → γ} (hf : LowerSemicontinuousOn
     LowerSemicontinuousOn (fun z => f z + g z) s := fun x hx =>
   (hf x hx).add' (hg x hx) (hcont x hx)
 #align lower_semicontinuous_on.add' LowerSemicontinuousOn.add'
+-/
 
+#print LowerSemicontinuous.add' /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -496,9 +577,11 @@ theorem LowerSemicontinuous.add' {f g : α → γ} (hf : LowerSemicontinuous f)
     (hcont : ∀ x, ContinuousAt (fun p : γ × γ => p.1 + p.2) (f x, g x)) :
     LowerSemicontinuous fun z => f z + g z := fun x => (hf x).add' (hg x) (hcont x)
 #align lower_semicontinuous.add' LowerSemicontinuous.add'
+-/
 
 variable [ContinuousAdd γ]
 
+#print LowerSemicontinuousWithinAt.add /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -507,7 +590,9 @@ theorem LowerSemicontinuousWithinAt.add {f g : α → γ} (hf : LowerSemicontinu
     LowerSemicontinuousWithinAt (fun z => f z + g z) s x :=
   hf.add' hg continuous_add.ContinuousAt
 #align lower_semicontinuous_within_at.add LowerSemicontinuousWithinAt.add
+-/
 
+#print LowerSemicontinuousAt.add /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -515,7 +600,9 @@ theorem LowerSemicontinuousAt.add {f g : α → γ} (hf : LowerSemicontinuousAt
     (hg : LowerSemicontinuousAt g x) : LowerSemicontinuousAt (fun z => f z + g z) x :=
   hf.add' hg continuous_add.ContinuousAt
 #align lower_semicontinuous_at.add LowerSemicontinuousAt.add
+-/
 
+#print LowerSemicontinuousOn.add /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -523,7 +610,9 @@ theorem LowerSemicontinuousOn.add {f g : α → γ} (hf : LowerSemicontinuousOn
     (hg : LowerSemicontinuousOn g s) : LowerSemicontinuousOn (fun z => f z + g z) s :=
   hf.add' hg fun x hx => continuous_add.ContinuousAt
 #align lower_semicontinuous_on.add LowerSemicontinuousOn.add
+-/
 
+#print LowerSemicontinuous.add /-
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -531,7 +620,9 @@ theorem LowerSemicontinuous.add {f g : α → γ} (hf : LowerSemicontinuous f)
     (hg : LowerSemicontinuous g) : LowerSemicontinuous fun z => f z + g z :=
   hf.add' hg fun x => continuous_add.ContinuousAt
 #align lower_semicontinuous.add LowerSemicontinuous.add
+-/
 
+#print lowerSemicontinuousWithinAt_sum /-
 theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by
@@ -543,7 +634,9 @@ theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
       LowerSemicontinuousWithinAt.add (ha _ (Finset.mem_insert_self i a))
         (IH fun j ja => ha j (Finset.mem_insert_of_mem ja))
 #align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sum
+-/
 
+#print lowerSemicontinuousAt_sum /-
 theorem lowerSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun z => ∑ i in a, f i z) x :=
@@ -551,17 +644,22 @@ theorem lowerSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
   exact lowerSemicontinuousWithinAt_sum ha
 #align lower_semicontinuous_at_sum lowerSemicontinuousAt_sum
+-/
 
+#print lowerSemicontinuousOn_sum /-
 theorem lowerSemicontinuousOn_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun z => ∑ i in a, f i z) s := fun x hx =>
   lowerSemicontinuousWithinAt_sum fun i hi => ha i hi x hx
 #align lower_semicontinuous_on_sum lowerSemicontinuousOn_sum
+-/
 
+#print lowerSemicontinuous_sum /-
 theorem lowerSemicontinuous_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuous (f i)) : LowerSemicontinuous fun z => ∑ i in a, f i z :=
   fun x => lowerSemicontinuousAt_sum fun i hi => ha i hi x
 #align lower_semicontinuous_sum lowerSemicontinuous_sum
+-/
 
 end
 
@@ -572,6 +670,7 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
+#print lowerSemicontinuousWithinAt_ciSup /-
 theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
@@ -583,20 +682,26 @@ theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
     rcases exists_lt_of_lt_ciSup hy with ⟨i, hi⟩
     filter_upwards [h i y hi, bdd] with y hy hy' using hy.trans_le (le_ciSup hy' i)
 #align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSup
+-/
 
+#print lowerSemicontinuousWithinAt_iSup /-
 theorem lowerSemicontinuousWithinAt_iSup {f : ι → α → δ}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
   lowerSemicontinuousWithinAt_ciSup (by simp) h
 #align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_iSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print lowerSemicontinuousWithinAt_biSup /-
 theorem lowerSemicontinuousWithinAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ (i) (hi), f i hi x') s x :=
   lowerSemicontinuousWithinAt_iSup fun i => lowerSemicontinuousWithinAt_iSup fun hi => h i hi
 #align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_biSup
+-/
 
+#print lowerSemicontinuousAt_ciSup /-
 theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddAbove (range fun i => f i y)) (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
@@ -605,53 +710,70 @@ theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
   rw [← nhdsWithin_univ] at bdd 
   exact lowerSemicontinuousWithinAt_ciSup bdd h
 #align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSup
+-/
 
+#print lowerSemicontinuousAt_iSup /-
 theorem lowerSemicontinuousAt_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
   lowerSemicontinuousAt_ciSup (by simp) h
 #align lower_semicontinuous_at_supr lowerSemicontinuousAt_iSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print lowerSemicontinuousAt_biSup /-
 theorem lowerSemicontinuousAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
     LowerSemicontinuousAt (fun x' => ⨆ (i) (hi), f i hi x') x :=
   lowerSemicontinuousAt_iSup fun i => lowerSemicontinuousAt_iSup fun hi => h i hi
 #align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_biSup
+-/
 
+#print lowerSemicontinuousOn_ciSup /-
 theorem lowerSemicontinuousOn_ciSup {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddAbove (range fun i => f i x)) (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s := fun x hx =>
   lowerSemicontinuousWithinAt_ciSup (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
 #align lower_semicontinuous_on_csupr lowerSemicontinuousOn_ciSup
+-/
 
+#print lowerSemicontinuousOn_iSup /-
 theorem lowerSemicontinuousOn_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s :=
   lowerSemicontinuousOn_ciSup (by simp) h
 #align lower_semicontinuous_on_supr lowerSemicontinuousOn_iSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print lowerSemicontinuousOn_biSup /-
 theorem lowerSemicontinuousOn_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
     LowerSemicontinuousOn (fun x' => ⨆ (i) (hi), f i hi x') s :=
   lowerSemicontinuousOn_iSup fun i => lowerSemicontinuousOn_iSup fun hi => h i hi
 #align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_biSup
+-/
 
+#print lowerSemicontinuous_ciSup /-
 theorem lowerSemicontinuous_ciSup {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
     (h : ∀ i, LowerSemicontinuous (f i)) : LowerSemicontinuous fun x' => ⨆ i, f i x' := fun x =>
   lowerSemicontinuousAt_ciSup (eventually_of_forall bdd) fun i => h i x
 #align lower_semicontinuous_csupr lowerSemicontinuous_ciSup
+-/
 
+#print lowerSemicontinuous_iSup /-
 theorem lowerSemicontinuous_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ⨆ i, f i x' :=
   lowerSemicontinuous_ciSup (by simp) h
 #align lower_semicontinuous_supr lowerSemicontinuous_iSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print lowerSemicontinuous_biSup /-
 theorem lowerSemicontinuous_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
     LowerSemicontinuous fun x' => ⨆ (i) (hi), f i hi x' :=
   lowerSemicontinuous_iSup fun i => lowerSemicontinuous_iSup fun hi => h i hi
 #align lower_semicontinuous_bsupr lowerSemicontinuous_biSup
+-/
 
 end
 
@@ -662,6 +784,7 @@ section
 
 variable {ι : Type _}
 
+#print lowerSemicontinuousWithinAt_tsum /-
 theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ∑' i, f i x') s x :=
@@ -670,22 +793,29 @@ theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
   apply lowerSemicontinuousWithinAt_iSup fun b => _
   exact lowerSemicontinuousWithinAt_sum fun i hi => h i
 #align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsum
+-/
 
+#print lowerSemicontinuousAt_tsum /-
 theorem lowerSemicontinuousAt_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ∑' i, f i x') x :=
   by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
   exact lowerSemicontinuousWithinAt_tsum h
 #align lower_semicontinuous_at_tsum lowerSemicontinuousAt_tsum
+-/
 
+#print lowerSemicontinuousOn_tsum /-
 theorem lowerSemicontinuousOn_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ∑' i, f i x') s := fun x hx =>
   lowerSemicontinuousWithinAt_tsum fun i => h i x hx
 #align lower_semicontinuous_on_tsum lowerSemicontinuousOn_tsum
+-/
 
+#print lowerSemicontinuous_tsum /-
 theorem lowerSemicontinuous_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ∑' i, f i x' := fun x => lowerSemicontinuousAt_tsum fun i => h i x
 #align lower_semicontinuous_tsum lowerSemicontinuous_tsum
+-/
 
 end
 
@@ -697,66 +827,92 @@ end
 /-! #### Basic dot notation interface for upper semicontinuity -/
 
 
+#print UpperSemicontinuousWithinAt.mono /-
 theorem UpperSemicontinuousWithinAt.mono (h : UpperSemicontinuousWithinAt f s x) (hst : t ⊆ s) :
     UpperSemicontinuousWithinAt f t x := fun y hy =>
   Filter.Eventually.filter_mono (nhdsWithin_mono _ hst) (h y hy)
 #align upper_semicontinuous_within_at.mono UpperSemicontinuousWithinAt.mono
+-/
 
+#print upperSemicontinuousWithinAt_univ_iff /-
 theorem upperSemicontinuousWithinAt_univ_iff :
     UpperSemicontinuousWithinAt f univ x ↔ UpperSemicontinuousAt f x := by
   simp [UpperSemicontinuousWithinAt, UpperSemicontinuousAt, nhdsWithin_univ]
 #align upper_semicontinuous_within_at_univ_iff upperSemicontinuousWithinAt_univ_iff
+-/
 
+#print UpperSemicontinuousAt.upperSemicontinuousWithinAt /-
 theorem UpperSemicontinuousAt.upperSemicontinuousWithinAt (s : Set α)
     (h : UpperSemicontinuousAt f x) : UpperSemicontinuousWithinAt f s x := fun y hy =>
   Filter.Eventually.filter_mono nhdsWithin_le_nhds (h y hy)
 #align upper_semicontinuous_at.upper_semicontinuous_within_at UpperSemicontinuousAt.upperSemicontinuousWithinAt
+-/
 
+#print UpperSemicontinuousOn.upperSemicontinuousWithinAt /-
 theorem UpperSemicontinuousOn.upperSemicontinuousWithinAt (h : UpperSemicontinuousOn f s)
     (hx : x ∈ s) : UpperSemicontinuousWithinAt f s x :=
   h x hx
 #align upper_semicontinuous_on.upper_semicontinuous_within_at UpperSemicontinuousOn.upperSemicontinuousWithinAt
+-/
 
+#print UpperSemicontinuousOn.mono /-
 theorem UpperSemicontinuousOn.mono (h : UpperSemicontinuousOn f s) (hst : t ⊆ s) :
     UpperSemicontinuousOn f t := fun x hx => (h x (hst hx)).mono hst
 #align upper_semicontinuous_on.mono UpperSemicontinuousOn.mono
+-/
 
+#print upperSemicontinuousOn_univ_iff /-
 theorem upperSemicontinuousOn_univ_iff : UpperSemicontinuousOn f univ ↔ UpperSemicontinuous f := by
   simp [UpperSemicontinuousOn, UpperSemicontinuous, upperSemicontinuousWithinAt_univ_iff]
 #align upper_semicontinuous_on_univ_iff upperSemicontinuousOn_univ_iff
+-/
 
+#print UpperSemicontinuous.upperSemicontinuousAt /-
 theorem UpperSemicontinuous.upperSemicontinuousAt (h : UpperSemicontinuous f) (x : α) :
     UpperSemicontinuousAt f x :=
   h x
 #align upper_semicontinuous.upper_semicontinuous_at UpperSemicontinuous.upperSemicontinuousAt
+-/
 
+#print UpperSemicontinuous.upperSemicontinuousWithinAt /-
 theorem UpperSemicontinuous.upperSemicontinuousWithinAt (h : UpperSemicontinuous f) (s : Set α)
     (x : α) : UpperSemicontinuousWithinAt f s x :=
   (h x).UpperSemicontinuousWithinAt s
 #align upper_semicontinuous.upper_semicontinuous_within_at UpperSemicontinuous.upperSemicontinuousWithinAt
+-/
 
+#print UpperSemicontinuous.upperSemicontinuousOn /-
 theorem UpperSemicontinuous.upperSemicontinuousOn (h : UpperSemicontinuous f) (s : Set α) :
     UpperSemicontinuousOn f s := fun x hx => h.UpperSemicontinuousWithinAt s x
 #align upper_semicontinuous.upper_semicontinuous_on UpperSemicontinuous.upperSemicontinuousOn
+-/
 
 /-! #### Constants -/
 
 
+#print upperSemicontinuousWithinAt_const /-
 theorem upperSemicontinuousWithinAt_const : UpperSemicontinuousWithinAt (fun x => z) s x :=
   fun y hy => Filter.eventually_of_forall fun x => hy
 #align upper_semicontinuous_within_at_const upperSemicontinuousWithinAt_const
+-/
 
+#print upperSemicontinuousAt_const /-
 theorem upperSemicontinuousAt_const : UpperSemicontinuousAt (fun x => z) x := fun y hy =>
   Filter.eventually_of_forall fun x => hy
 #align upper_semicontinuous_at_const upperSemicontinuousAt_const
+-/
 
+#print upperSemicontinuousOn_const /-
 theorem upperSemicontinuousOn_const : UpperSemicontinuousOn (fun x => z) s := fun x hx =>
   upperSemicontinuousWithinAt_const
 #align upper_semicontinuous_on_const upperSemicontinuousOn_const
+-/
 
+#print upperSemicontinuous_const /-
 theorem upperSemicontinuous_const : UpperSemicontinuous fun x : α => z := fun x =>
   upperSemicontinuousAt_const
 #align upper_semicontinuous_const upperSemicontinuous_const
+-/
 
 /-! #### Indicators -/
 
@@ -765,67 +921,88 @@ section
 
 variable [Zero β]
 
+#print IsOpen.upperSemicontinuous_indicator /-
 theorem IsOpen.upperSemicontinuous_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuous (indicator s fun x => y) :=
   @IsOpen.lowerSemicontinuous_indicator α _ βᵒᵈ _ s y _ hs hy
 #align is_open.upper_semicontinuous_indicator IsOpen.upperSemicontinuous_indicator
+-/
 
+#print IsOpen.upperSemicontinuousOn_indicator /-
 theorem IsOpen.upperSemicontinuousOn_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousOn (indicator s fun x => y) t :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousOn t
 #align is_open.upper_semicontinuous_on_indicator IsOpen.upperSemicontinuousOn_indicator
+-/
 
+#print IsOpen.upperSemicontinuousAt_indicator /-
 theorem IsOpen.upperSemicontinuousAt_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousAt (indicator s fun x => y) x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousAt x
 #align is_open.upper_semicontinuous_at_indicator IsOpen.upperSemicontinuousAt_indicator
+-/
 
+#print IsOpen.upperSemicontinuousWithinAt_indicator /-
 theorem IsOpen.upperSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousWithinAt t x
 #align is_open.upper_semicontinuous_within_at_indicator IsOpen.upperSemicontinuousWithinAt_indicator
+-/
 
+#print IsClosed.upperSemicontinuous_indicator /-
 theorem IsClosed.upperSemicontinuous_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuous (indicator s fun x => y) :=
   @IsClosed.lowerSemicontinuous_indicator α _ βᵒᵈ _ s y _ hs hy
 #align is_closed.upper_semicontinuous_indicator IsClosed.upperSemicontinuous_indicator
+-/
 
+#print IsClosed.upperSemicontinuousOn_indicator /-
 theorem IsClosed.upperSemicontinuousOn_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousOn (indicator s fun x => y) t :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousOn t
 #align is_closed.upper_semicontinuous_on_indicator IsClosed.upperSemicontinuousOn_indicator
+-/
 
+#print IsClosed.upperSemicontinuousAt_indicator /-
 theorem IsClosed.upperSemicontinuousAt_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousAt (indicator s fun x => y) x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousAt x
 #align is_closed.upper_semicontinuous_at_indicator IsClosed.upperSemicontinuousAt_indicator
+-/
 
+#print IsClosed.upperSemicontinuousWithinAt_indicator /-
 theorem IsClosed.upperSemicontinuousWithinAt_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousWithinAt t x
 #align is_closed.upper_semicontinuous_within_at_indicator IsClosed.upperSemicontinuousWithinAt_indicator
+-/
 
 end
 
 /-! #### Relationship with continuity -/
 
 
+#print upperSemicontinuous_iff_isOpen_preimage /-
 theorem upperSemicontinuous_iff_isOpen_preimage :
     UpperSemicontinuous f ↔ ∀ y, IsOpen (f ⁻¹' Iio y) :=
   ⟨fun H y => isOpen_iff_mem_nhds.2 fun x hx => H x y hx, fun H x y y_lt =>
     IsOpen.mem_nhds (H y) y_lt⟩
 #align upper_semicontinuous_iff_is_open_preimage upperSemicontinuous_iff_isOpen_preimage
+-/
 
+#print UpperSemicontinuous.isOpen_preimage /-
 theorem UpperSemicontinuous.isOpen_preimage (hf : UpperSemicontinuous f) (y : β) :
     IsOpen (f ⁻¹' Iio y) :=
   upperSemicontinuous_iff_isOpen_preimage.1 hf y
 #align upper_semicontinuous.is_open_preimage UpperSemicontinuous.isOpen_preimage
+-/
 
 section
 
 variable {γ : Type _} [LinearOrder γ]
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
+#print upperSemicontinuous_iff_isClosed_preimage /-
 theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     UpperSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Ici y) :=
   by
@@ -834,29 +1011,40 @@ theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]]"
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Ici]
 #align upper_semicontinuous_iff_is_closed_preimage upperSemicontinuous_iff_isClosed_preimage
+-/
 
+#print UpperSemicontinuous.isClosed_preimage /-
 theorem UpperSemicontinuous.isClosed_preimage {f : α → γ} (hf : UpperSemicontinuous f) (y : γ) :
     IsClosed (f ⁻¹' Ici y) :=
   upperSemicontinuous_iff_isClosed_preimage.1 hf y
 #align upper_semicontinuous.is_closed_preimage UpperSemicontinuous.isClosed_preimage
+-/
 
 variable [TopologicalSpace γ] [OrderTopology γ]
 
+#print ContinuousWithinAt.upperSemicontinuousWithinAt /-
 theorem ContinuousWithinAt.upperSemicontinuousWithinAt {f : α → γ} (h : ContinuousWithinAt f s x) :
     UpperSemicontinuousWithinAt f s x := fun y hy => h (Iio_mem_nhds hy)
 #align continuous_within_at.upper_semicontinuous_within_at ContinuousWithinAt.upperSemicontinuousWithinAt
+-/
 
+#print ContinuousAt.upperSemicontinuousAt /-
 theorem ContinuousAt.upperSemicontinuousAt {f : α → γ} (h : ContinuousAt f x) :
     UpperSemicontinuousAt f x := fun y hy => h (Iio_mem_nhds hy)
 #align continuous_at.upper_semicontinuous_at ContinuousAt.upperSemicontinuousAt
+-/
 
+#print ContinuousOn.upperSemicontinuousOn /-
 theorem ContinuousOn.upperSemicontinuousOn {f : α → γ} (h : ContinuousOn f s) :
     UpperSemicontinuousOn f s := fun x hx => (h x hx).UpperSemicontinuousWithinAt
 #align continuous_on.upper_semicontinuous_on ContinuousOn.upperSemicontinuousOn
+-/
 
+#print Continuous.upperSemicontinuous /-
 theorem Continuous.upperSemicontinuous {f : α → γ} (h : Continuous f) : UpperSemicontinuous f :=
   fun x => h.ContinuousAt.UpperSemicontinuousAt
 #align continuous.upper_semicontinuous Continuous.upperSemicontinuous
+-/
 
 end
 
@@ -869,48 +1057,64 @@ variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
+#print ContinuousAt.comp_upperSemicontinuousWithinAt /-
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     UpperSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_lowerSemicontinuousWithinAt α _ x s γᵒᵈ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon.dual
 #align continuous_at.comp_upper_semicontinuous_within_at ContinuousAt.comp_upperSemicontinuousWithinAt
+-/
 
+#print ContinuousAt.comp_upperSemicontinuousAt /-
 theorem ContinuousAt.comp_upperSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : UpperSemicontinuousAt f x) (gmon : Monotone g) : UpperSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_lowerSemicontinuousAt α _ x γᵒᵈ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon.dual
 #align continuous_at.comp_upper_semicontinuous_at ContinuousAt.comp_upperSemicontinuousAt
+-/
 
+#print Continuous.comp_upperSemicontinuousOn /-
 theorem Continuous.comp_upperSemicontinuousOn {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuousOn f s) (gmon : Monotone g) : UpperSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_upperSemicontinuousWithinAt (hf x hx) gmon
 #align continuous.comp_upper_semicontinuous_on Continuous.comp_upperSemicontinuousOn
+-/
 
+#print Continuous.comp_upperSemicontinuous /-
 theorem Continuous.comp_upperSemicontinuous {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuous f) (gmon : Monotone g) : UpperSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_upperSemicontinuousAt (hf x) gmon
 #align continuous.comp_upper_semicontinuous Continuous.comp_upperSemicontinuous
+-/
 
+#print ContinuousAt.comp_upperSemicontinuousWithinAt_antitone /-
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Antitone g) :
     LowerSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_upperSemicontinuousWithinAt α _ x s γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_upper_semicontinuous_within_at_antitone ContinuousAt.comp_upperSemicontinuousWithinAt_antitone
+-/
 
+#print ContinuousAt.comp_upperSemicontinuousAt_antitone /-
 theorem ContinuousAt.comp_upperSemicontinuousAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousAt f x) (gmon : Antitone g) :
     LowerSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_upperSemicontinuousAt α _ x γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_upper_semicontinuous_at_antitone ContinuousAt.comp_upperSemicontinuousAt_antitone
+-/
 
+#print Continuous.comp_upperSemicontinuousOn_antitone /-
 theorem Continuous.comp_upperSemicontinuousOn_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuousOn f s) (gmon : Antitone g) : LowerSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_upperSemicontinuousWithinAt_antitone (hf x hx) gmon
 #align continuous.comp_upper_semicontinuous_on_antitone Continuous.comp_upperSemicontinuousOn_antitone
+-/
 
+#print Continuous.comp_upperSemicontinuous_antitone /-
 theorem Continuous.comp_upperSemicontinuous_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuous f) (gmon : Antitone g) : LowerSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_upperSemicontinuousAt_antitone (hf x) gmon
 #align continuous.comp_upper_semicontinuous_antitone Continuous.comp_upperSemicontinuous_antitone
+-/
 
 end
 
@@ -922,6 +1126,7 @@ section
 variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
   [OrderTopology γ]
 
+#print UpperSemicontinuousWithinAt.add' /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -931,7 +1136,9 @@ theorem UpperSemicontinuousWithinAt.add' {f g : α → γ} (hf : UpperSemicontin
     UpperSemicontinuousWithinAt (fun z => f z + g z) s x :=
   @LowerSemicontinuousWithinAt.add' α _ x s γᵒᵈ _ _ _ _ _ hf hg hcont
 #align upper_semicontinuous_within_at.add' UpperSemicontinuousWithinAt.add'
+-/
 
+#print UpperSemicontinuousAt.add' /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -941,7 +1148,9 @@ theorem UpperSemicontinuousAt.add' {f g : α → γ} (hf : UpperSemicontinuousAt
     UpperSemicontinuousAt (fun z => f z + g z) x := by
   simp_rw [← upperSemicontinuousWithinAt_univ_iff] at *; exact hf.add' hg hcont
 #align upper_semicontinuous_at.add' UpperSemicontinuousAt.add'
+-/
 
+#print UpperSemicontinuousOn.add' /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -951,7 +1160,9 @@ theorem UpperSemicontinuousOn.add' {f g : α → γ} (hf : UpperSemicontinuousOn
     UpperSemicontinuousOn (fun z => f z + g z) s := fun x hx =>
   (hf x hx).add' (hg x hx) (hcont x hx)
 #align upper_semicontinuous_on.add' UpperSemicontinuousOn.add'
+-/
 
+#print UpperSemicontinuous.add' /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -960,9 +1171,11 @@ theorem UpperSemicontinuous.add' {f g : α → γ} (hf : UpperSemicontinuous f)
     (hcont : ∀ x, ContinuousAt (fun p : γ × γ => p.1 + p.2) (f x, g x)) :
     UpperSemicontinuous fun z => f z + g z := fun x => (hf x).add' (hg x) (hcont x)
 #align upper_semicontinuous.add' UpperSemicontinuous.add'
+-/
 
 variable [ContinuousAdd γ]
 
+#print UpperSemicontinuousWithinAt.add /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -971,7 +1184,9 @@ theorem UpperSemicontinuousWithinAt.add {f g : α → γ} (hf : UpperSemicontinu
     UpperSemicontinuousWithinAt (fun z => f z + g z) s x :=
   hf.add' hg continuous_add.ContinuousAt
 #align upper_semicontinuous_within_at.add UpperSemicontinuousWithinAt.add
+-/
 
+#print UpperSemicontinuousAt.add /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -979,7 +1194,9 @@ theorem UpperSemicontinuousAt.add {f g : α → γ} (hf : UpperSemicontinuousAt
     (hg : UpperSemicontinuousAt g x) : UpperSemicontinuousAt (fun z => f z + g z) x :=
   hf.add' hg continuous_add.ContinuousAt
 #align upper_semicontinuous_at.add UpperSemicontinuousAt.add
+-/
 
+#print UpperSemicontinuousOn.add /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -987,7 +1204,9 @@ theorem UpperSemicontinuousOn.add {f g : α → γ} (hf : UpperSemicontinuousOn
     (hg : UpperSemicontinuousOn g s) : UpperSemicontinuousOn (fun z => f z + g z) s :=
   hf.add' hg fun x hx => continuous_add.ContinuousAt
 #align upper_semicontinuous_on.add UpperSemicontinuousOn.add
+-/
 
+#print UpperSemicontinuous.add /-
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -995,13 +1214,17 @@ theorem UpperSemicontinuous.add {f g : α → γ} (hf : UpperSemicontinuous f)
     (hg : UpperSemicontinuous g) : UpperSemicontinuous fun z => f z + g z :=
   hf.add' hg fun x => continuous_add.ContinuousAt
 #align upper_semicontinuous.add UpperSemicontinuous.add
+-/
 
+#print upperSemicontinuousWithinAt_sum /-
 theorem upperSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x :=
   @lowerSemicontinuousWithinAt_sum α _ x s ι γᵒᵈ _ _ _ _ f a ha
 #align upper_semicontinuous_within_at_sum upperSemicontinuousWithinAt_sum
+-/
 
+#print upperSemicontinuousAt_sum /-
 theorem upperSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun z => ∑ i in a, f i z) x :=
@@ -1009,17 +1232,22 @@ theorem upperSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
   simp_rw [← upperSemicontinuousWithinAt_univ_iff] at *
   exact upperSemicontinuousWithinAt_sum ha
 #align upper_semicontinuous_at_sum upperSemicontinuousAt_sum
+-/
 
+#print upperSemicontinuousOn_sum /-
 theorem upperSemicontinuousOn_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun z => ∑ i in a, f i z) s := fun x hx =>
   upperSemicontinuousWithinAt_sum fun i hi => ha i hi x hx
 #align upper_semicontinuous_on_sum upperSemicontinuousOn_sum
+-/
 
+#print upperSemicontinuous_sum /-
 theorem upperSemicontinuous_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuous (f i)) : UpperSemicontinuous fun z => ∑ i in a, f i z :=
   fun x => upperSemicontinuousAt_sum fun i hi => ha i hi x
 #align upper_semicontinuous_sum upperSemicontinuous_sum
+-/
 
 end
 
@@ -1030,77 +1258,101 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
+#print upperSemicontinuousWithinAt_ciInf /-
 theorem upperSemicontinuousWithinAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
   @lowerSemicontinuousWithinAt_ciSup α _ x s ι δ'ᵒᵈ _ f bdd h
 #align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_ciInf
+-/
 
+#print upperSemicontinuousWithinAt_iInf /-
 theorem upperSemicontinuousWithinAt_iInf {f : ι → α → δ}
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
   @lowerSemicontinuousWithinAt_iSup α _ x s ι δᵒᵈ _ f h
 #align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print upperSemicontinuousWithinAt_biInf /-
 theorem upperSemicontinuousWithinAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ (i) (hi), f i hi x') s x :=
   upperSemicontinuousWithinAt_iInf fun i => upperSemicontinuousWithinAt_iInf fun hi => h i hi
 #align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_biInf
+-/
 
+#print upperSemicontinuousAt_ciInf /-
 theorem upperSemicontinuousAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddBelow (range fun i => f i y)) (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
   @lowerSemicontinuousAt_ciSup α _ x ι δ'ᵒᵈ _ f bdd h
 #align upper_semicontinuous_at_cinfi upperSemicontinuousAt_ciInf
+-/
 
+#print upperSemicontinuousAt_iInf /-
 theorem upperSemicontinuousAt_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
   @lowerSemicontinuousAt_iSup α _ x ι δᵒᵈ _ f h
 #align upper_semicontinuous_at_infi upperSemicontinuousAt_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print upperSemicontinuousAt_biInf /-
 theorem upperSemicontinuousAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
     UpperSemicontinuousAt (fun x' => ⨅ (i) (hi), f i hi x') x :=
   upperSemicontinuousAt_iInf fun i => upperSemicontinuousAt_iInf fun hi => h i hi
 #align upper_semicontinuous_at_binfi upperSemicontinuousAt_biInf
+-/
 
+#print upperSemicontinuousOn_ciInf /-
 theorem upperSemicontinuousOn_ciInf {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddBelow (range fun i => f i x)) (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
   upperSemicontinuousWithinAt_ciInf (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
 #align upper_semicontinuous_on_cinfi upperSemicontinuousOn_ciInf
+-/
 
+#print upperSemicontinuousOn_iInf /-
 theorem upperSemicontinuousOn_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
   upperSemicontinuousWithinAt_iInf fun i => h i x hx
 #align upper_semicontinuous_on_infi upperSemicontinuousOn_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print upperSemicontinuousOn_biInf /-
 theorem upperSemicontinuousOn_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
     UpperSemicontinuousOn (fun x' => ⨅ (i) (hi), f i hi x') s :=
   upperSemicontinuousOn_iInf fun i => upperSemicontinuousOn_iInf fun hi => h i hi
 #align upper_semicontinuous_on_binfi upperSemicontinuousOn_biInf
+-/
 
+#print upperSemicontinuous_ciInf /-
 theorem upperSemicontinuous_ciInf {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
     (h : ∀ i, UpperSemicontinuous (f i)) : UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x =>
   upperSemicontinuousAt_ciInf (eventually_of_forall bdd) fun i => h i x
 #align upper_semicontinuous_cinfi upperSemicontinuous_ciInf
+-/
 
+#print upperSemicontinuous_iInf /-
 theorem upperSemicontinuous_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
     UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_iInf fun i => h i x
 #align upper_semicontinuous_infi upperSemicontinuous_iInf
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print upperSemicontinuous_biInf /-
 theorem upperSemicontinuous_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
     UpperSemicontinuous fun x' => ⨅ (i) (hi), f i hi x' :=
   upperSemicontinuous_iInf fun i => upperSemicontinuous_iInf fun hi => h i hi
 #align upper_semicontinuous_binfi upperSemicontinuous_biInf
+-/
 
 end
 
@@ -1108,6 +1360,7 @@ section
 
 variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
+#print continuousWithinAt_iff_lower_upperSemicontinuousWithinAt /-
 theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ} :
     ContinuousWithinAt f s x ↔
       LowerSemicontinuousWithinAt f s x ∧ UpperSemicontinuousWithinAt f s x :=
@@ -1139,13 +1392,17 @@ theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ}
       rw [this]
       exact mem_of_mem_nhds hv
 #align continuous_within_at_iff_lower_upper_semicontinuous_within_at continuousWithinAt_iff_lower_upperSemicontinuousWithinAt
+-/
 
+#print continuousAt_iff_lower_upperSemicontinuousAt /-
 theorem continuousAt_iff_lower_upperSemicontinuousAt {f : α → γ} :
     ContinuousAt f x ↔ LowerSemicontinuousAt f x ∧ UpperSemicontinuousAt f x := by
   simp_rw [← continuousWithinAt_univ, ← lowerSemicontinuousWithinAt_univ_iff, ←
     upperSemicontinuousWithinAt_univ_iff, continuousWithinAt_iff_lower_upperSemicontinuousWithinAt]
 #align continuous_at_iff_lower_upper_semicontinuous_at continuousAt_iff_lower_upperSemicontinuousAt
+-/
 
+#print continuousOn_iff_lower_upperSemicontinuousOn /-
 theorem continuousOn_iff_lower_upperSemicontinuousOn {f : α → γ} :
     ContinuousOn f s ↔ LowerSemicontinuousOn f s ∧ UpperSemicontinuousOn f s :=
   by
@@ -1153,12 +1410,15 @@ theorem continuousOn_iff_lower_upperSemicontinuousOn {f : α → γ} :
   exact
     ⟨fun H => ⟨fun x hx => (H x hx).1, fun x hx => (H x hx).2⟩, fun H x hx => ⟨H.1 x hx, H.2 x hx⟩⟩
 #align continuous_on_iff_lower_upper_semicontinuous_on continuousOn_iff_lower_upperSemicontinuousOn
+-/
 
+#print continuous_iff_lower_upperSemicontinuous /-
 theorem continuous_iff_lower_upperSemicontinuous {f : α → γ} :
     Continuous f ↔ LowerSemicontinuous f ∧ UpperSemicontinuous f := by
   simp_rw [continuous_iff_continuousOn_univ, continuousOn_iff_lower_upperSemicontinuousOn,
     lowerSemicontinuousOn_univ_iff, upperSemicontinuousOn_univ_iff]
 #align continuous_iff_lower_upper_semicontinuous continuous_iff_lower_upperSemicontinuous
+-/
 
 end
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -346,7 +346,6 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
     calc
       y < g (min (f x) (f a)) := hz (by simp [zlt, ha, le_refl])
       _ ≤ g (f a) := gmon (min_le_right _ _)
-      
   · simp only [not_exists, not_lt] at h 
     exact Filter.eventually_of_forall fun a => hy.trans_le (gmon (h (f a)))
 #align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAt
@@ -437,7 +436,6 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < min (f z) (f x) + min (g z) (g x) := h this
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (min_le_left _ _)
-        
     · simp only [not_exists, not_lt] at hx₂ 
       filter_upwards [hf z₁ z₁lt] with z h₁z
       have A1 : min (f z) (f x) ∈ u := by
@@ -448,7 +446,6 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < min (f z) (f x) + g x := h this
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (hx₂ (g z))
-        
   · simp only [not_exists, not_lt] at hx₁ 
     by_cases hx₂ : ∃ l, l < g x
     · obtain ⟨z₂, z₂lt, h₂⟩ : ∃ z₂ < g x, Ioc z₂ (g x) ⊆ v :=
@@ -462,7 +459,6 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < f x + min (g z) (g x) := h this
         _ ≤ f z + g z := add_le_add (hx₁ (f z)) (min_le_left _ _)
-        
     · simp only [not_exists, not_lt] at hx₁ hx₂ 
       apply Filter.eventually_of_forall
       intro z
@@ -470,7 +466,6 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < f x + g x := h this
         _ ≤ f z + g z := add_le_add (hx₁ (f z)) (hx₂ (g z))
-        
 #align lower_semicontinuous_within_at.add' LowerSemicontinuousWithinAt.add'
 
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an

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

@@ -342,7 +342,7 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
   by_cases h : ∃ l, l < f x
   · obtain ⟨z, zlt, hz⟩ : ∃ z < f x, Ioc z (f x) ⊆ g ⁻¹' Ioi y :=
       exists_Ioc_subset_of_mem_nhds (hg (Ioi_mem_nhds hy)) h
-    filter_upwards [hf z zlt]with a ha
+    filter_upwards [hf z zlt] with a ha
     calc
       y < g (min (f x) (f a)) := hz (by simp [zlt, ha, le_refl])
       _ ≤ g (f a) := gmon (min_le_right _ _)
@@ -416,7 +416,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
   intro y hy
   obtain ⟨u, v, u_open, xu, v_open, xv, h⟩ :
     ∃ u v : Set γ,
-      IsOpen u ∧ f x ∈ u ∧ IsOpen v ∧ g x ∈ v ∧ u ×ˢ v ⊆ { p : γ × γ | y < p.fst + p.snd } :=
+      IsOpen u ∧ f x ∈ u ∧ IsOpen v ∧ g x ∈ v ∧ u ×ˢ v ⊆ {p : γ × γ | y < p.fst + p.snd} :=
     mem_nhds_prod_iff'.1 (hcont (is_open_Ioi.mem_nhds hy))
   by_cases hx₁ : ∃ l, l < f x
   · obtain ⟨z₁, z₁lt, h₁⟩ : ∃ z₁ < f x, Ioc z₁ (f x) ⊆ u :=
@@ -424,7 +424,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
     by_cases hx₂ : ∃ l, l < g x
     · obtain ⟨z₂, z₂lt, h₂⟩ : ∃ z₂ < g x, Ioc z₂ (g x) ⊆ v :=
         exists_Ioc_subset_of_mem_nhds (v_open.mem_nhds xv) hx₂
-      filter_upwards [hf z₁ z₁lt, hg z₂ z₂lt]with z h₁z h₂z
+      filter_upwards [hf z₁ z₁lt, hg z₂ z₂lt] with z h₁z h₂z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
         · simp [H]; exact h₁ ⟨h₁z, H⟩
@@ -439,7 +439,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (min_le_left _ _)
         
     · simp only [not_exists, not_lt] at hx₂ 
-      filter_upwards [hf z₁ z₁lt]with z h₁z
+      filter_upwards [hf z₁ z₁lt] with z h₁z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
         · simp [H]; exact h₁ ⟨h₁z, H⟩
@@ -453,7 +453,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
     by_cases hx₂ : ∃ l, l < g x
     · obtain ⟨z₂, z₂lt, h₂⟩ : ∃ z₂ < g x, Ioc z₂ (g x) ⊆ v :=
         exists_Ioc_subset_of_mem_nhds (v_open.mem_nhds xv) hx₂
-      filter_upwards [hg z₂ z₂lt]with z h₂z
+      filter_upwards [hg z₂ z₂lt] with z h₂z
       have A2 : min (g z) (g x) ∈ v := by
         by_cases H : g z ≤ g x
         · simp [H]; exact h₂ ⟨h₂z, H⟩
@@ -541,12 +541,12 @@ theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by
   classical
-    induction' a using Finset.induction_on with i a ia IH generalizing ha
-    · exact lowerSemicontinuousWithinAt_const
-    · simp only [ia, Finset.sum_insert, not_false_iff]
-      exact
-        LowerSemicontinuousWithinAt.add (ha _ (Finset.mem_insert_self i a))
-          (IH fun j ja => ha j (Finset.mem_insert_of_mem ja))
+  induction' a using Finset.induction_on with i a ia IH generalizing ha
+  · exact lowerSemicontinuousWithinAt_const
+  · simp only [ia, Finset.sum_insert, not_false_iff]
+    exact
+      LowerSemicontinuousWithinAt.add (ha _ (Finset.mem_insert_self i a))
+        (IH fun j ja => ha j (Finset.mem_insert_of_mem ja))
 #align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sum
 
 theorem lowerSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
@@ -586,7 +586,7 @@ theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
   · simpa only [iSup_of_empty'] using lowerSemicontinuousWithinAt_const
   · intro y hy
     rcases exists_lt_of_lt_ciSup hy with ⟨i, hi⟩
-    filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_ciSup hy' i)
+    filter_upwards [h i y hi, bdd] with y hy hy' using hy.trans_le (le_ciSup hy' i)
 #align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSup
 
 theorem lowerSemicontinuousWithinAt_iSup {f : ι → α → δ}
@@ -1125,16 +1125,16 @@ theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ}
   · rcases exists_Ioc_subset_of_mem_nhds hv Hl with ⟨l, lfx, hl⟩
     by_cases Hu : ∃ u, f x < u
     · rcases exists_Ico_subset_of_mem_nhds hv Hu with ⟨u, fxu, hu⟩
-      filter_upwards [h₁ l lfx, h₂ u fxu]with a lfa fau
+      filter_upwards [h₁ l lfx, h₂ u fxu] with a lfa fau
       cases' le_or_gt (f a) (f x) with h h
       · exact hl ⟨lfa, h⟩
       · exact hu ⟨le_of_lt h, fau⟩
     · simp only [not_exists, not_lt] at Hu 
-      filter_upwards [h₁ l lfx]with a lfa using hl ⟨lfa, Hu (f a)⟩
+      filter_upwards [h₁ l lfx] with a lfa using hl ⟨lfa, Hu (f a)⟩
   · simp only [not_exists, not_lt] at Hl 
     by_cases Hu : ∃ u, f x < u
     · rcases exists_Ico_subset_of_mem_nhds hv Hu with ⟨u, fxu, hu⟩
-      filter_upwards [h₂ u fxu]with a lfa
+      filter_upwards [h₂ u fxu] with a lfa
       apply hu
       exact ⟨Hl (f a), lfa⟩
     · simp only [not_exists, not_lt] at Hu 

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

@@ -222,7 +222,7 @@ theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
   intro x z hz
-  by_cases h : x ∈ s <;> simp [h] at hz
+  by_cases h : x ∈ s <;> simp [h] at hz 
   · filter_upwards [hs.mem_nhds h]
     simp (config := { contextual := true }) [hz]
   · apply Filter.eventually_of_forall fun x' => _
@@ -248,7 +248,7 @@ theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0)
     LowerSemicontinuous (indicator s fun x => y) :=
   by
   intro x z hz
-  by_cases h : x ∈ s <;> simp [h] at hz
+  by_cases h : x ∈ s <;> simp [h] at hz 
   · apply Filter.eventually_of_forall fun x' => _
     by_cases h' : x' ∈ s <;> simp [h', hz, hz.trans_le hy]
   · filter_upwards [hs.is_open_compl.mem_nhds h]
@@ -347,14 +347,14 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
       y < g (min (f x) (f a)) := hz (by simp [zlt, ha, le_refl])
       _ ≤ g (f a) := gmon (min_le_right _ _)
       
-  · simp only [not_exists, not_lt] at h
+  · simp only [not_exists, not_lt] at h 
     exact Filter.eventually_of_forall fun a => hy.trans_le (gmon (h (f a)))
 #align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAt
 
 theorem ContinuousAt.comp_lowerSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : LowerSemicontinuousAt f x) (gmon : Monotone g) : LowerSemicontinuousAt (g ∘ f) x :=
   by
-  simp only [← lowerSemicontinuousWithinAt_univ_iff] at hf⊢
+  simp only [← lowerSemicontinuousWithinAt_univ_iff] at hf ⊢
   exact hg.comp_lower_semicontinuous_within_at hf gmon
 #align continuous_at.comp_lower_semicontinuous_at ContinuousAt.comp_lowerSemicontinuousAt
 
@@ -438,7 +438,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         y < min (f z) (f x) + min (g z) (g x) := h this
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (min_le_left _ _)
         
-    · simp only [not_exists, not_lt] at hx₂
+    · simp only [not_exists, not_lt] at hx₂ 
       filter_upwards [hf z₁ z₁lt]with z h₁z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
@@ -449,7 +449,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         y < min (f z) (f x) + g x := h this
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (hx₂ (g z))
         
-  · simp only [not_exists, not_lt] at hx₁
+  · simp only [not_exists, not_lt] at hx₁ 
     by_cases hx₂ : ∃ l, l < g x
     · obtain ⟨z₂, z₂lt, h₂⟩ : ∃ z₂ < g x, Ioc z₂ (g x) ⊆ v :=
         exists_Ioc_subset_of_mem_nhds (v_open.mem_nhds xv) hx₂
@@ -463,7 +463,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         y < f x + min (g z) (g x) := h this
         _ ≤ f z + g z := add_le_add (hx₁ (f z)) (min_le_left _ _)
         
-    · simp only [not_exists, not_lt] at hx₁ hx₂
+    · simp only [not_exists, not_lt] at hx₁ hx₂ 
       apply Filter.eventually_of_forall
       intro z
       have : (f x, g x) ∈ u ×ˢ v := ⟨xu, xv⟩
@@ -607,7 +607,7 @@ theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
   by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
-  rw [← nhdsWithin_univ] at bdd
+  rw [← nhdsWithin_univ] at bdd 
   exact lowerSemicontinuousWithinAt_ciSup bdd h
 #align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSup
 
@@ -1129,15 +1129,15 @@ theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ}
       cases' le_or_gt (f a) (f x) with h h
       · exact hl ⟨lfa, h⟩
       · exact hu ⟨le_of_lt h, fau⟩
-    · simp only [not_exists, not_lt] at Hu
+    · simp only [not_exists, not_lt] at Hu 
       filter_upwards [h₁ l lfx]with a lfa using hl ⟨lfa, Hu (f a)⟩
-  · simp only [not_exists, not_lt] at Hl
+  · simp only [not_exists, not_lt] at Hl 
     by_cases Hu : ∃ u, f x < u
     · rcases exists_Ico_subset_of_mem_nhds hv Hu with ⟨u, fxu, hu⟩
       filter_upwards [h₂ u fxu]with a lfa
       apply hu
       exact ⟨Hl (f a), lfa⟩
-    · simp only [not_exists, not_lt] at Hu
+    · simp only [not_exists, not_lt] at Hu 
       apply Filter.eventually_of_forall
       intro a
       have : f a = f x := le_antisymm (Hu _) (Hl _)

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

@@ -60,7 +60,7 @@ ones for lower semicontinuous functions using `order_dual`.
 -/
 
 
-open Topology BigOperators ENNReal
+open scoped Topology BigOperators ENNReal
 
 open Set Function Filter
 

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

@@ -150,98 +150,44 @@ def UpperSemicontinuous (f : α → β) :=
 /-! #### Basic dot notation interface for lower semicontinuity -/
 
 
-/- warning: lower_semicontinuous_within_at.mono -> LowerSemicontinuousWithinAt.mono is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f t x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α} {t : Set.{u2} α}, (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) t s) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f t x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at.mono LowerSemicontinuousWithinAt.monoₓ'. -/
 theorem LowerSemicontinuousWithinAt.mono (h : LowerSemicontinuousWithinAt f s x) (hst : t ⊆ s) :
     LowerSemicontinuousWithinAt f t x := fun y hy =>
   Filter.Eventually.filter_mono (nhdsWithin_mono _ hst) (h y hy)
 #align lower_semicontinuous_within_at.mono LowerSemicontinuousWithinAt.mono
 
-/- warning: lower_semicontinuous_within_at_univ_iff -> lowerSemicontinuousWithinAt_univ_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α}, Iff (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α) x) (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α}, Iff (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f (Set.univ.{u2} α) x) (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_univ_iff lowerSemicontinuousWithinAt_univ_iffₓ'. -/
 theorem lowerSemicontinuousWithinAt_univ_iff :
     LowerSemicontinuousWithinAt f univ x ↔ LowerSemicontinuousAt f x := by
   simp [LowerSemicontinuousWithinAt, LowerSemicontinuousAt, nhdsWithin_univ]
 #align lower_semicontinuous_within_at_univ_iff lowerSemicontinuousWithinAt_univ_iff
 
-/- warning: lower_semicontinuous_at.lower_semicontinuous_within_at -> LowerSemicontinuousAt.lowerSemicontinuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} (s : Set.{u1} α), (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} (s : Set.{u2} α), (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at.lower_semicontinuous_within_at LowerSemicontinuousAt.lowerSemicontinuousWithinAtₓ'. -/
 theorem LowerSemicontinuousAt.lowerSemicontinuousWithinAt (s : Set α)
     (h : LowerSemicontinuousAt f x) : LowerSemicontinuousWithinAt f s x := fun y hy =>
   Filter.Eventually.filter_mono nhdsWithin_le_nhds (h y hy)
 #align lower_semicontinuous_at.lower_semicontinuous_within_at LowerSemicontinuousAt.lowerSemicontinuousWithinAt
 
-/- warning: lower_semicontinuous_on.lower_semicontinuous_within_at -> LowerSemicontinuousOn.lowerSemicontinuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α}, (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α}, (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.lower_semicontinuous_within_at LowerSemicontinuousOn.lowerSemicontinuousWithinAtₓ'. -/
 theorem LowerSemicontinuousOn.lowerSemicontinuousWithinAt (h : LowerSemicontinuousOn f s)
     (hx : x ∈ s) : LowerSemicontinuousWithinAt f s x :=
   h x hx
 #align lower_semicontinuous_on.lower_semicontinuous_within_at LowerSemicontinuousOn.lowerSemicontinuousWithinAt
 
-/- warning: lower_semicontinuous_on.mono -> LowerSemicontinuousOn.mono is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {s : Set.{u1} α} {t : Set.{u1} α}, (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f t)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {s : Set.{u2} α} {t : Set.{u2} α}, (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) t s) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f t)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.mono LowerSemicontinuousOn.monoₓ'. -/
 theorem LowerSemicontinuousOn.mono (h : LowerSemicontinuousOn f s) (hst : t ⊆ s) :
     LowerSemicontinuousOn f t := fun x hx => (h x (hst hx)).mono hst
 #align lower_semicontinuous_on.mono LowerSemicontinuousOn.mono
 
-/- warning: lower_semicontinuous_on_univ_iff -> lowerSemicontinuousOn_univ_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, Iff (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α)) (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, Iff (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f (Set.univ.{u2} α)) (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_univ_iff lowerSemicontinuousOn_univ_iffₓ'. -/
 theorem lowerSemicontinuousOn_univ_iff : LowerSemicontinuousOn f univ ↔ LowerSemicontinuous f := by
   simp [LowerSemicontinuousOn, LowerSemicontinuous, lowerSemicontinuousWithinAt_univ_iff]
 #align lower_semicontinuous_on_univ_iff lowerSemicontinuousOn_univ_iff
 
-/- warning: lower_semicontinuous.lower_semicontinuous_at -> LowerSemicontinuous.lowerSemicontinuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (x : α), LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (x : α), LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.lower_semicontinuous_at LowerSemicontinuous.lowerSemicontinuousAtₓ'. -/
 theorem LowerSemicontinuous.lowerSemicontinuousAt (h : LowerSemicontinuous f) (x : α) :
     LowerSemicontinuousAt f x :=
   h x
 #align lower_semicontinuous.lower_semicontinuous_at LowerSemicontinuous.lowerSemicontinuousAt
 
-/- warning: lower_semicontinuous.lower_semicontinuous_within_at -> LowerSemicontinuous.lowerSemicontinuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α) (x : α), LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α) (x : α), LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.lower_semicontinuous_within_at LowerSemicontinuous.lowerSemicontinuousWithinAtₓ'. -/
 theorem LowerSemicontinuous.lowerSemicontinuousWithinAt (h : LowerSemicontinuous f) (s : Set α)
     (x : α) : LowerSemicontinuousWithinAt f s x :=
   (h x).LowerSemicontinuousWithinAt s
 #align lower_semicontinuous.lower_semicontinuous_within_at LowerSemicontinuous.lowerSemicontinuousWithinAt
 
-/- warning: lower_semicontinuous.lower_semicontinuous_on -> LowerSemicontinuous.lowerSemicontinuousOn is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α), LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α), LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.lower_semicontinuous_on LowerSemicontinuous.lowerSemicontinuousOnₓ'. -/
 theorem LowerSemicontinuous.lowerSemicontinuousOn (h : LowerSemicontinuous f) (s : Set α) :
     LowerSemicontinuousOn f s := fun x hx => h.LowerSemicontinuousWithinAt s x
 #align lower_semicontinuous.lower_semicontinuous_on LowerSemicontinuous.lowerSemicontinuousOn
@@ -249,42 +195,18 @@ theorem LowerSemicontinuous.lowerSemicontinuousOn (h : LowerSemicontinuous f) (s
 /-! #### Constants -/
 
 
-/- warning: lower_semicontinuous_within_at_const -> lowerSemicontinuousWithinAt_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {z : β}, LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s x
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {z : β}, LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) s x
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_const lowerSemicontinuousWithinAt_constₓ'. -/
 theorem lowerSemicontinuousWithinAt_const : LowerSemicontinuousWithinAt (fun x => z) s x :=
   fun y hy => Filter.eventually_of_forall fun x => hy
 #align lower_semicontinuous_within_at_const lowerSemicontinuousWithinAt_const
 
-/- warning: lower_semicontinuous_at_const -> lowerSemicontinuousAt_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {z : β}, LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) x
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {z : β}, LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) x
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_const lowerSemicontinuousAt_constₓ'. -/
 theorem lowerSemicontinuousAt_const : LowerSemicontinuousAt (fun x => z) x := fun y hy =>
   Filter.eventually_of_forall fun x => hy
 #align lower_semicontinuous_at_const lowerSemicontinuousAt_const
 
-/- warning: lower_semicontinuous_on_const -> lowerSemicontinuousOn_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {z : β}, LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {z : β}, LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) s
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_const lowerSemicontinuousOn_constₓ'. -/
 theorem lowerSemicontinuousOn_const : LowerSemicontinuousOn (fun x => z) s := fun x hx =>
   lowerSemicontinuousWithinAt_const
 #align lower_semicontinuous_on_const lowerSemicontinuousOn_const
 
-/- warning: lower_semicontinuous_const -> lowerSemicontinuous_const is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {z : β}, LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {z : β}, LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_const lowerSemicontinuous_constₓ'. -/
 theorem lowerSemicontinuous_const : LowerSemicontinuous fun x : α => z := fun x =>
   lowerSemicontinuousAt_const
 #align lower_semicontinuous_const lowerSemicontinuous_const
@@ -296,12 +218,6 @@ section
 
 variable [Zero β]
 
-/- warning: is_open.lower_semicontinuous_indicator -> IsOpen.lowerSemicontinuous_indicator is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
-Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_indicator IsOpen.lowerSemicontinuous_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
@@ -313,45 +229,21 @@ theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     by_cases h' : x' ∈ s <;> simp [h', hz.trans_le hy, hz]
 #align is_open.lower_semicontinuous_indicator IsOpen.lowerSemicontinuous_indicator
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_on_indicator IsOpen.lowerSemicontinuousOn_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuousOn_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousOn (indicator s fun x => y) t :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousOn t
 #align is_open.lower_semicontinuous_on_indicator IsOpen.lowerSemicontinuousOn_indicator
 
-/- warning: is_open.lower_semicontinuous_at_indicator -> IsOpen.lowerSemicontinuousAt_indicator is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_at_indicator IsOpen.lowerSemicontinuousAt_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuousAt_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousAt (indicator s fun x => y) x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousAt x
 #align is_open.lower_semicontinuous_at_indicator IsOpen.lowerSemicontinuousAt_indicator
 
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-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
-Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_within_at_indicator IsOpen.lowerSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousWithinAt t x
 #align is_open.lower_semicontinuous_within_at_indicator IsOpen.lowerSemicontinuousWithinAt_indicator
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
-Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_indicator IsClosed.lowerSemicontinuous_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
@@ -363,34 +255,16 @@ theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0)
     simp (config := { contextual := true }) [hz]
 #align is_closed.lower_semicontinuous_indicator IsClosed.lowerSemicontinuous_indicator
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_on_indicator IsClosed.lowerSemicontinuousOn_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuousOn_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousOn (indicator s fun x => y) t :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousOn t
 #align is_closed.lower_semicontinuous_on_indicator IsClosed.lowerSemicontinuousOn_indicator
 
-/- warning: is_closed.lower_semicontinuous_at_indicator -> IsClosed.lowerSemicontinuousAt_indicator is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_at_indicator IsClosed.lowerSemicontinuousAt_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuousAt_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousAt (indicator s fun x => y) x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousAt x
 #align is_closed.lower_semicontinuous_at_indicator IsClosed.lowerSemicontinuousAt_indicator
 
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-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
-Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_within_at_indicator IsClosed.lowerSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuousWithinAt_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousWithinAt t x
@@ -401,24 +275,12 @@ end
 /-! #### Relationship with continuity -/
 
 
-/- warning: lower_semicontinuous_iff_is_open_preimage -> lowerSemicontinuous_iff_isOpen_preimage is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, Iff (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) (forall (y : β), IsOpen.{u1} α _inst_1 (Set.preimage.{u1, u2} α β f (Set.Ioi.{u2} β _inst_2 y)))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, Iff (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) (forall (y : β), IsOpen.{u2} α _inst_1 (Set.preimage.{u2, u1} α β f (Set.Ioi.{u1} β _inst_2 y)))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_iff_is_open_preimage lowerSemicontinuous_iff_isOpen_preimageₓ'. -/
 theorem lowerSemicontinuous_iff_isOpen_preimage :
     LowerSemicontinuous f ↔ ∀ y, IsOpen (f ⁻¹' Ioi y) :=
   ⟨fun H y => isOpen_iff_mem_nhds.2 fun x hx => H x y hx, fun H x y y_lt =>
     IsOpen.mem_nhds (H y) y_lt⟩
 #align lower_semicontinuous_iff_is_open_preimage lowerSemicontinuous_iff_isOpen_preimage
 
-/- warning: lower_semicontinuous.is_open_preimage -> LowerSemicontinuous.isOpen_preimage is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (y : β), IsOpen.{u1} α _inst_1 (Set.preimage.{u1, u2} α β f (Set.Ioi.{u2} β _inst_2 y)))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (y : β), IsOpen.{u2} α _inst_1 (Set.preimage.{u2, u1} α β f (Set.Ioi.{u1} β _inst_2 y)))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.is_open_preimage LowerSemicontinuous.isOpen_preimageₓ'. -/
 theorem LowerSemicontinuous.isOpen_preimage (hf : LowerSemicontinuous f) (y : β) :
     IsOpen (f ⁻¹' Ioi y) :=
   lowerSemicontinuous_iff_isOpen_preimage.1 hf y
@@ -428,12 +290,6 @@ section
 
 variable {γ : Type _} [LinearOrder γ]
 
-/- warning: lower_semicontinuous_iff_is_closed_preimage -> lowerSemicontinuous_iff_isClosed_preimage is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] {f : α -> γ}, Iff (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) (forall (y : γ), IsClosed.{u1} α _inst_1 (Set.preimage.{u1, u2} α γ f (Set.Iic.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) y)))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] {f : α -> γ}, Iff (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) (forall (y : γ), IsClosed.{u2} α _inst_1 (Set.preimage.{u2, u1} α γ f (Set.Iic.{u1} γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) y)))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_iff_is_closed_preimage lowerSemicontinuous_iff_isClosed_preimageₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
 theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     LowerSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Iic y) :=
@@ -444,12 +300,6 @@ theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Iic]
 #align lower_semicontinuous_iff_is_closed_preimage lowerSemicontinuous_iff_isClosed_preimage
 
-/- warning: lower_semicontinuous.is_closed_preimage -> LowerSemicontinuous.isClosed_preimage is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] {f : α -> γ}, (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (forall (y : γ), IsClosed.{u1} α _inst_1 (Set.preimage.{u1, u2} α γ f (Set.Iic.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) y)))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] {f : α -> γ}, (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) -> (forall (y : γ), IsClosed.{u2} α _inst_1 (Set.preimage.{u2, u1} α γ f (Set.Iic.{u1} γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) y)))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.is_closed_preimage LowerSemicontinuous.isClosed_preimageₓ'. -/
 theorem LowerSemicontinuous.isClosed_preimage {f : α → γ} (hf : LowerSemicontinuous f) (y : γ) :
     IsClosed (f ⁻¹' Iic y) :=
   lowerSemicontinuous_iff_isClosed_preimage.1 hf y
@@ -457,42 +307,18 @@ theorem LowerSemicontinuous.isClosed_preimage {f : α → γ} (hf : LowerSemicon
 
 variable [TopologicalSpace γ] [OrderTopology γ]
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f s x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousWithinAt.{u2, u1} α γ _inst_1 _inst_4 f s x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s x)
-Case conversion may be inaccurate. Consider using '#align continuous_within_at.lower_semicontinuous_within_at ContinuousWithinAt.lowerSemicontinuousWithinAtₓ'. -/
 theorem ContinuousWithinAt.lowerSemicontinuousWithinAt {f : α → γ} (h : ContinuousWithinAt f s x) :
     LowerSemicontinuousWithinAt f s x := fun y hy => h (Ioi_mem_nhds hy)
 #align continuous_within_at.lower_semicontinuous_within_at ContinuousWithinAt.lowerSemicontinuousWithinAt
 
-/- warning: continuous_at.lower_semicontinuous_at -> ContinuousAt.lowerSemicontinuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousAt.{u1, u2} α γ _inst_1 _inst_4 f x) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousAt.{u2, u1} α γ _inst_1 _inst_4 f x) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f x)
-Case conversion may be inaccurate. Consider using '#align continuous_at.lower_semicontinuous_at ContinuousAt.lowerSemicontinuousAtₓ'. -/
 theorem ContinuousAt.lowerSemicontinuousAt {f : α → γ} (h : ContinuousAt f x) :
     LowerSemicontinuousAt f x := fun y hy => h (Ioi_mem_nhds hy)
 #align continuous_at.lower_semicontinuous_at ContinuousAt.lowerSemicontinuousAt
 
-/- warning: continuous_on.lower_semicontinuous_on -> ContinuousOn.lowerSemicontinuousOn is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousOn.{u1, u2} α γ _inst_1 _inst_4 f s) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousOn.{u2, u1} α γ _inst_1 _inst_4 f s) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s)
-Case conversion may be inaccurate. Consider using '#align continuous_on.lower_semicontinuous_on ContinuousOn.lowerSemicontinuousOnₓ'. -/
 theorem ContinuousOn.lowerSemicontinuousOn {f : α → γ} (h : ContinuousOn f s) :
     LowerSemicontinuousOn f s := fun x hx => (h x hx).LowerSemicontinuousWithinAt
 #align continuous_on.lower_semicontinuous_on ContinuousOn.lowerSemicontinuousOn
 
-/- warning: continuous.lower_semicontinuous -> Continuous.lowerSemicontinuous is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (Continuous.{u1, u2} α γ _inst_1 _inst_4 f) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (Continuous.{u2, u1} α γ _inst_1 _inst_4 f) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f)
-Case conversion may be inaccurate. Consider using '#align continuous.lower_semicontinuous Continuous.lowerSemicontinuousₓ'. -/
 theorem Continuous.lowerSemicontinuous {f : α → γ} (h : Continuous f) : LowerSemicontinuous f :=
   fun x => h.ContinuousAt.LowerSemicontinuousAt
 #align continuous.lower_semicontinuous Continuous.lowerSemicontinuous
@@ -508,12 +334,6 @@ variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s x)
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s x) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s x)
-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAtₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     LowerSemicontinuousWithinAt (g ∘ f) s x :=
@@ -531,12 +351,6 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
     exact Filter.eventually_of_forall fun a => hy.trans_le (gmon (h (f a)))
 #align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAt
 
-/- warning: continuous_at.comp_lower_semicontinuous_at -> ContinuousAt.comp_lowerSemicontinuousAt is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f x) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) x)
-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_at ContinuousAt.comp_lowerSemicontinuousAtₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : LowerSemicontinuousAt f x) (gmon : Monotone g) : LowerSemicontinuousAt (g ∘ f) x :=
   by
@@ -544,69 +358,33 @@ theorem ContinuousAt.comp_lowerSemicontinuousAt {g : γ → δ} {f : α → γ}
   exact hg.comp_lower_semicontinuous_within_at hf gmon
 #align continuous_at.comp_lower_semicontinuous_at ContinuousAt.comp_lowerSemicontinuousAt
 
-/- warning: continuous.comp_lower_semicontinuous_on -> Continuous.comp_lowerSemicontinuousOn is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous_on Continuous.comp_lowerSemicontinuousOnₓ'. -/
 theorem Continuous.comp_lowerSemicontinuousOn {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuousOn f s) (gmon : Monotone g) : LowerSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_lowerSemicontinuousWithinAt (hf x hx) gmon
 #align continuous.comp_lower_semicontinuous_on Continuous.comp_lowerSemicontinuousOn
 
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-Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous Continuous.comp_lowerSemicontinuousₓ'. -/
 theorem Continuous.comp_lowerSemicontinuous {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuous f) (gmon : Monotone g) : LowerSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_lowerSemicontinuousAt (hf x) gmon
 #align continuous.comp_lower_semicontinuous Continuous.comp_lowerSemicontinuous
 
-/- warning: continuous_at.comp_lower_semicontinuous_within_at_antitone -> ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s x)
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-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_within_at_antitone ContinuousAt.comp_lowerSemicontinuousWithinAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Antitone g) :
     UpperSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_lowerSemicontinuousWithinAt α _ x s γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_lower_semicontinuous_within_at_antitone ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone
 
-/- warning: continuous_at.comp_lower_semicontinuous_at_antitone -> ContinuousAt.comp_lowerSemicontinuousAt_antitone is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f x) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) x)
-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_at_antitone ContinuousAt.comp_lowerSemicontinuousAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousAt f x) (gmon : Antitone g) :
     UpperSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_lowerSemicontinuousAt α _ x γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_lower_semicontinuous_at_antitone ContinuousAt.comp_lowerSemicontinuousAt_antitone
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s)
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s)
-Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous_on_antitone Continuous.comp_lowerSemicontinuousOn_antitoneₓ'. -/
 theorem Continuous.comp_lowerSemicontinuousOn_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuousOn f s) (gmon : Antitone g) : UpperSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone (hf x hx) gmon
 #align continuous.comp_lower_semicontinuous_on_antitone Continuous.comp_lowerSemicontinuousOn_antitone
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f))
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuous.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f))
-Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous_antitone Continuous.comp_lowerSemicontinuous_antitoneₓ'. -/
 theorem Continuous.comp_lowerSemicontinuous_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuous f) (gmon : Antitone g) : UpperSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_lowerSemicontinuousAt_antitone (hf x) gmon
@@ -622,12 +400,6 @@ section
 variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
   [OrderTopology γ]
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s x) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s x) -> (ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x))) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at.add' LowerSemicontinuousWithinAt.add'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -701,12 +473,6 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         
 #align lower_semicontinuous_within_at.add' LowerSemicontinuousWithinAt.add'
 
-/- warning: lower_semicontinuous_at.add' -> LowerSemicontinuousAt.add' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f x) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g x) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) x)
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at.add' LowerSemicontinuousAt.add'ₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -717,12 +483,6 @@ theorem LowerSemicontinuousAt.add' {f g : α → γ} (hf : LowerSemicontinuousAt
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *; exact hf.add' hg hcont
 #align lower_semicontinuous_at.add' LowerSemicontinuousAt.add'
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.add' LowerSemicontinuousOn.add'ₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -733,12 +493,6 @@ theorem LowerSemicontinuousOn.add' {f g : α → γ} (hf : LowerSemicontinuousOn
   (hf x hx).add' (hg x hx) (hcont x hx)
 #align lower_semicontinuous_on.add' LowerSemicontinuousOn.add'
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.add' LowerSemicontinuous.add'ₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -750,12 +504,6 @@ theorem LowerSemicontinuous.add' {f g : α → γ} (hf : LowerSemicontinuous f)
 
 variable [ContinuousAdd γ]
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at.add LowerSemicontinuousWithinAt.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -765,12 +513,6 @@ theorem LowerSemicontinuousWithinAt.add {f g : α → γ} (hf : LowerSemicontinu
   hf.add' hg continuous_add.ContinuousAt
 #align lower_semicontinuous_within_at.add LowerSemicontinuousWithinAt.add
 
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-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f x) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g x) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at.add LowerSemicontinuousAt.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -779,12 +521,6 @@ theorem LowerSemicontinuousAt.add {f g : α → γ} (hf : LowerSemicontinuousAt
   hf.add' hg continuous_add.ContinuousAt
 #align lower_semicontinuous_at.add LowerSemicontinuousAt.add
 
-/- warning: lower_semicontinuous_on.add -> LowerSemicontinuousOn.add is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.add LowerSemicontinuousOn.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -793,12 +529,6 @@ theorem LowerSemicontinuousOn.add {f g : α → γ} (hf : LowerSemicontinuousOn
   hf.add' hg fun x hx => continuous_add.ContinuousAt
 #align lower_semicontinuous_on.add LowerSemicontinuousOn.add
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.add LowerSemicontinuous.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -807,12 +537,6 @@ theorem LowerSemicontinuous.add {f g : α → γ} (hf : LowerSemicontinuous f)
   hf.add' hg fun x => continuous_add.ContinuousAt
 #align lower_semicontinuous.add LowerSemicontinuous.add
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sumₓ'. -/
 theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by
@@ -825,12 +549,6 @@ theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
           (IH fun j ja => ha j (Finset.mem_insert_of_mem ja))
 #align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sum
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_sum lowerSemicontinuousAt_sumₓ'. -/
 theorem lowerSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun z => ∑ i in a, f i z) x :=
@@ -839,24 +557,12 @@ theorem lowerSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
   exact lowerSemicontinuousWithinAt_sum ha
 #align lower_semicontinuous_at_sum lowerSemicontinuousAt_sum
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) s)) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) s)
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-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) s)) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_sum lowerSemicontinuousOn_sumₓ'. -/
 theorem lowerSemicontinuousOn_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun z => ∑ i in a, f i z) s := fun x hx =>
   lowerSemicontinuousWithinAt_sum fun i hi => ha i hi x hx
 #align lower_semicontinuous_on_sum lowerSemicontinuousOn_sum
 
-/- warning: lower_semicontinuous_sum -> lowerSemicontinuous_sum is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (LowerSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i))) -> (LowerSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)))
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-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i))) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_sum lowerSemicontinuous_sumₓ'. -/
 theorem lowerSemicontinuous_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuous (f i)) : LowerSemicontinuous fun z => ∑ i in a, f i z :=
   fun x => lowerSemicontinuousAt_sum fun i hi => ha i hi x
@@ -871,12 +577,6 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSupₓ'. -/
 theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
@@ -889,24 +589,12 @@ theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
     filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_ciSup hy' i)
 #align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSup
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_iSupₓ'. -/
 theorem lowerSemicontinuousWithinAt_iSup {f : ι → α → δ}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
   lowerSemicontinuousWithinAt_ciSup (by simp) h
 #align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_iSup
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuousWithinAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
@@ -914,12 +602,6 @@ theorem lowerSemicontinuousWithinAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p
   lowerSemicontinuousWithinAt_iSup fun i => lowerSemicontinuousWithinAt_iSup fun hi => h i hi
 #align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_biSup
 
-/- warning: lower_semicontinuous_at_csupr -> lowerSemicontinuousAt_ciSup is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iSup.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSupₓ'. -/
 theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddAbove (range fun i => f i y)) (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
@@ -929,23 +611,11 @@ theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
   exact lowerSemicontinuousWithinAt_ciSup bdd h
 #align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSup
 
-/- warning: lower_semicontinuous_at_supr -> lowerSemicontinuousAt_iSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_supr lowerSemicontinuousAt_iSupₓ'. -/
 theorem lowerSemicontinuousAt_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
   lowerSemicontinuousAt_ciSup (by simp) h
 #align lower_semicontinuous_at_supr lowerSemicontinuousAt_iSup
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuousAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
@@ -953,35 +623,17 @@ theorem lowerSemicontinuousAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α
   lowerSemicontinuousAt_iSup fun i => lowerSemicontinuousAt_iSup fun hi => h i hi
 #align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_biSup
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_ciSupₓ'. -/
 theorem lowerSemicontinuousOn_ciSup {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddAbove (range fun i => f i x)) (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s := fun x hx =>
   lowerSemicontinuousWithinAt_ciSup (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
 #align lower_semicontinuous_on_csupr lowerSemicontinuousOn_ciSup
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_supr lowerSemicontinuousOn_iSupₓ'. -/
 theorem lowerSemicontinuousOn_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s :=
   lowerSemicontinuousOn_ciSup (by simp) h
 #align lower_semicontinuous_on_supr lowerSemicontinuousOn_iSup
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuousOn_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
@@ -989,34 +641,16 @@ theorem lowerSemicontinuousOn_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α
   lowerSemicontinuousOn_iSup fun i => lowerSemicontinuousOn_iSup fun hi => h i hi
 #align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_biSup
 
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_csupr lowerSemicontinuous_ciSupₓ'. -/
 theorem lowerSemicontinuous_ciSup {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
     (h : ∀ i, LowerSemicontinuous (f i)) : LowerSemicontinuous fun x' => ⨆ i, f i x' := fun x =>
   lowerSemicontinuousAt_ciSup (eventually_of_forall bdd) fun i => h i x
 #align lower_semicontinuous_csupr lowerSemicontinuous_ciSup
 
-/- warning: lower_semicontinuous_supr -> lowerSemicontinuous_iSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_supr lowerSemicontinuous_iSupₓ'. -/
 theorem lowerSemicontinuous_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ⨆ i, f i x' :=
   lowerSemicontinuous_ciSup (by simp) h
 #align lower_semicontinuous_supr lowerSemicontinuous_iSup
 
-/- warning: lower_semicontinuous_bsupr -> lowerSemicontinuous_biSup is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
-but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iSup.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_bsupr lowerSemicontinuous_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuous_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
@@ -1033,12 +667,6 @@ section
 
 variable {ι : Type _}
 
-/- warning: lower_semicontinuous_within_at_tsum -> lowerSemicontinuousWithinAt_tsum is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousWithinAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')) s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousWithinAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')) s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsumₓ'. -/
 theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ∑' i, f i x') s x :=
@@ -1048,12 +676,6 @@ theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
   exact lowerSemicontinuousWithinAt_sum fun i hi => h i
 #align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsum
 
-/- warning: lower_semicontinuous_at_tsum -> lowerSemicontinuousAt_tsum is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i) x) -> (LowerSemicontinuousAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')) x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i) x) -> (LowerSemicontinuousAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')) x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_tsum lowerSemicontinuousAt_tsumₓ'. -/
 theorem lowerSemicontinuousAt_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ∑' i, f i x') x :=
   by
@@ -1061,23 +683,11 @@ theorem lowerSemicontinuousAt_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, Lo
   exact lowerSemicontinuousWithinAt_tsum h
 #align lower_semicontinuous_at_tsum lowerSemicontinuousAt_tsum
 
-/- warning: lower_semicontinuous_on_tsum -> lowerSemicontinuousOn_tsum is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousOn.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i) s) -> (LowerSemicontinuousOn.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')) s)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousOn.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i) s) -> (LowerSemicontinuousOn.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')) s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_tsum lowerSemicontinuousOn_tsumₓ'. -/
 theorem lowerSemicontinuousOn_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ∑' i, f i x') s := fun x hx =>
   lowerSemicontinuousWithinAt_tsum fun i => h i x hx
 #align lower_semicontinuous_on_tsum lowerSemicontinuousOn_tsum
 
-/- warning: lower_semicontinuous_tsum -> lowerSemicontinuous_tsum is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuous.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i)) -> (LowerSemicontinuous.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuous.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i)) -> (LowerSemicontinuous.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_tsum lowerSemicontinuous_tsumₓ'. -/
 theorem lowerSemicontinuous_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ∑' i, f i x' := fun x => lowerSemicontinuousAt_tsum fun i => h i x
 #align lower_semicontinuous_tsum lowerSemicontinuous_tsum
@@ -1092,98 +702,44 @@ end
 /-! #### Basic dot notation interface for upper semicontinuity -/
 
 
-/- warning: upper_semicontinuous_within_at.mono -> UpperSemicontinuousWithinAt.mono is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f t x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α} {t : Set.{u2} α}, (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) t s) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f t x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at.mono UpperSemicontinuousWithinAt.monoₓ'. -/
 theorem UpperSemicontinuousWithinAt.mono (h : UpperSemicontinuousWithinAt f s x) (hst : t ⊆ s) :
     UpperSemicontinuousWithinAt f t x := fun y hy =>
   Filter.Eventually.filter_mono (nhdsWithin_mono _ hst) (h y hy)
 #align upper_semicontinuous_within_at.mono UpperSemicontinuousWithinAt.mono
 
-/- warning: upper_semicontinuous_within_at_univ_iff -> upperSemicontinuousWithinAt_univ_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α}, Iff (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α) x) (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α}, Iff (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f (Set.univ.{u2} α) x) (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_univ_iff upperSemicontinuousWithinAt_univ_iffₓ'. -/
 theorem upperSemicontinuousWithinAt_univ_iff :
     UpperSemicontinuousWithinAt f univ x ↔ UpperSemicontinuousAt f x := by
   simp [UpperSemicontinuousWithinAt, UpperSemicontinuousAt, nhdsWithin_univ]
 #align upper_semicontinuous_within_at_univ_iff upperSemicontinuousWithinAt_univ_iff
 
-/- warning: upper_semicontinuous_at.upper_semicontinuous_within_at -> UpperSemicontinuousAt.upperSemicontinuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} (s : Set.{u1} α), (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} (s : Set.{u2} α), (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at.upper_semicontinuous_within_at UpperSemicontinuousAt.upperSemicontinuousWithinAtₓ'. -/
 theorem UpperSemicontinuousAt.upperSemicontinuousWithinAt (s : Set α)
     (h : UpperSemicontinuousAt f x) : UpperSemicontinuousWithinAt f s x := fun y hy =>
   Filter.Eventually.filter_mono nhdsWithin_le_nhds (h y hy)
 #align upper_semicontinuous_at.upper_semicontinuous_within_at UpperSemicontinuousAt.upperSemicontinuousWithinAt
 
-/- warning: upper_semicontinuous_on.upper_semicontinuous_within_at -> UpperSemicontinuousOn.upperSemicontinuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α}, (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α}, (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.upper_semicontinuous_within_at UpperSemicontinuousOn.upperSemicontinuousWithinAtₓ'. -/
 theorem UpperSemicontinuousOn.upperSemicontinuousWithinAt (h : UpperSemicontinuousOn f s)
     (hx : x ∈ s) : UpperSemicontinuousWithinAt f s x :=
   h x hx
 #align upper_semicontinuous_on.upper_semicontinuous_within_at UpperSemicontinuousOn.upperSemicontinuousWithinAt
 
-/- warning: upper_semicontinuous_on.mono -> UpperSemicontinuousOn.mono is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {s : Set.{u1} α} {t : Set.{u1} α}, (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f t)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.mono UpperSemicontinuousOn.monoₓ'. -/
 theorem UpperSemicontinuousOn.mono (h : UpperSemicontinuousOn f s) (hst : t ⊆ s) :
     UpperSemicontinuousOn f t := fun x hx => (h x (hst hx)).mono hst
 #align upper_semicontinuous_on.mono UpperSemicontinuousOn.mono
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, Iff (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α)) (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_univ_iff upperSemicontinuousOn_univ_iffₓ'. -/
 theorem upperSemicontinuousOn_univ_iff : UpperSemicontinuousOn f univ ↔ UpperSemicontinuous f := by
   simp [UpperSemicontinuousOn, UpperSemicontinuous, upperSemicontinuousWithinAt_univ_iff]
 #align upper_semicontinuous_on_univ_iff upperSemicontinuousOn_univ_iff
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (x : α), UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.upper_semicontinuous_at UpperSemicontinuous.upperSemicontinuousAtₓ'. -/
 theorem UpperSemicontinuous.upperSemicontinuousAt (h : UpperSemicontinuous f) (x : α) :
     UpperSemicontinuousAt f x :=
   h x
 #align upper_semicontinuous.upper_semicontinuous_at UpperSemicontinuous.upperSemicontinuousAt
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α) (x : α), UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α) (x : α), UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.upper_semicontinuous_within_at UpperSemicontinuous.upperSemicontinuousWithinAtₓ'. -/
 theorem UpperSemicontinuous.upperSemicontinuousWithinAt (h : UpperSemicontinuous f) (s : Set α)
     (x : α) : UpperSemicontinuousWithinAt f s x :=
   (h x).UpperSemicontinuousWithinAt s
 #align upper_semicontinuous.upper_semicontinuous_within_at UpperSemicontinuous.upperSemicontinuousWithinAt
 
-/- warning: upper_semicontinuous.upper_semicontinuous_on -> UpperSemicontinuous.upperSemicontinuousOn is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α), UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α), UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.upper_semicontinuous_on UpperSemicontinuous.upperSemicontinuousOnₓ'. -/
 theorem UpperSemicontinuous.upperSemicontinuousOn (h : UpperSemicontinuous f) (s : Set α) :
     UpperSemicontinuousOn f s := fun x hx => h.UpperSemicontinuousWithinAt s x
 #align upper_semicontinuous.upper_semicontinuous_on UpperSemicontinuous.upperSemicontinuousOn
@@ -1191,42 +747,18 @@ theorem UpperSemicontinuous.upperSemicontinuousOn (h : UpperSemicontinuous f) (s
 /-! #### Constants -/
 
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {z : β}, UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s x
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_const upperSemicontinuousWithinAt_constₓ'. -/
 theorem upperSemicontinuousWithinAt_const : UpperSemicontinuousWithinAt (fun x => z) s x :=
   fun y hy => Filter.eventually_of_forall fun x => hy
 #align upper_semicontinuous_within_at_const upperSemicontinuousWithinAt_const
 
-/- warning: upper_semicontinuous_at_const -> upperSemicontinuousAt_const is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {z : β}, UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) x
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_const upperSemicontinuousAt_constₓ'. -/
 theorem upperSemicontinuousAt_const : UpperSemicontinuousAt (fun x => z) x := fun y hy =>
   Filter.eventually_of_forall fun x => hy
 #align upper_semicontinuous_at_const upperSemicontinuousAt_const
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {z : β}, UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_const upperSemicontinuousOn_constₓ'. -/
 theorem upperSemicontinuousOn_const : UpperSemicontinuousOn (fun x => z) s := fun x hx =>
   upperSemicontinuousWithinAt_const
 #align upper_semicontinuous_on_const upperSemicontinuousOn_const
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {z : β}, UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z)
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {z : β}, UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_const upperSemicontinuous_constₓ'. -/
 theorem upperSemicontinuous_const : UpperSemicontinuous fun x : α => z := fun x =>
   upperSemicontinuousAt_const
 #align upper_semicontinuous_const upperSemicontinuous_const
@@ -1238,89 +770,41 @@ section
 
 variable [Zero β]
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_indicator IsOpen.upperSemicontinuous_indicatorₓ'. -/
 theorem IsOpen.upperSemicontinuous_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuous (indicator s fun x => y) :=
   @IsOpen.lowerSemicontinuous_indicator α _ βᵒᵈ _ s y _ hs hy
 #align is_open.upper_semicontinuous_indicator IsOpen.upperSemicontinuous_indicator
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_on_indicator IsOpen.upperSemicontinuousOn_indicatorₓ'. -/
 theorem IsOpen.upperSemicontinuousOn_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousOn (indicator s fun x => y) t :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousOn t
 #align is_open.upper_semicontinuous_on_indicator IsOpen.upperSemicontinuousOn_indicator
 
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 theorem IsOpen.upperSemicontinuousAt_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousAt (indicator s fun x => y) x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousAt x
 #align is_open.upper_semicontinuous_at_indicator IsOpen.upperSemicontinuousAt_indicator
 
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-Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_within_at_indicator IsOpen.upperSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsOpen.upperSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousWithinAt t x
 #align is_open.upper_semicontinuous_within_at_indicator IsOpen.upperSemicontinuousWithinAt_indicator
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_indicator IsClosed.upperSemicontinuous_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuous_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuous (indicator s fun x => y) :=
   @IsClosed.lowerSemicontinuous_indicator α _ βᵒᵈ _ s y _ hs hy
 #align is_closed.upper_semicontinuous_indicator IsClosed.upperSemicontinuous_indicator
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_on_indicator IsClosed.upperSemicontinuousOn_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuousOn_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousOn (indicator s fun x => y) t :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousOn t
 #align is_closed.upper_semicontinuous_on_indicator IsClosed.upperSemicontinuousOn_indicator
 
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-Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_at_indicator IsClosed.upperSemicontinuousAt_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuousAt_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousAt (indicator s fun x => y) x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousAt x
 #align is_closed.upper_semicontinuous_at_indicator IsClosed.upperSemicontinuousAt_indicator
 
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-Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_within_at_indicator IsClosed.upperSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuousWithinAt_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousWithinAt t x
@@ -1331,24 +815,12 @@ end
 /-! #### Relationship with continuity -/
 
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_iff_is_open_preimage upperSemicontinuous_iff_isOpen_preimageₓ'. -/
 theorem upperSemicontinuous_iff_isOpen_preimage :
     UpperSemicontinuous f ↔ ∀ y, IsOpen (f ⁻¹' Iio y) :=
   ⟨fun H y => isOpen_iff_mem_nhds.2 fun x hx => H x y hx, fun H x y y_lt =>
     IsOpen.mem_nhds (H y) y_lt⟩
 #align upper_semicontinuous_iff_is_open_preimage upperSemicontinuous_iff_isOpen_preimage
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.is_open_preimage UpperSemicontinuous.isOpen_preimageₓ'. -/
 theorem UpperSemicontinuous.isOpen_preimage (hf : UpperSemicontinuous f) (y : β) :
     IsOpen (f ⁻¹' Iio y) :=
   upperSemicontinuous_iff_isOpen_preimage.1 hf y
@@ -1358,12 +830,6 @@ section
 
 variable {γ : Type _} [LinearOrder γ]
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_iff_is_closed_preimage upperSemicontinuous_iff_isClosed_preimageₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
 theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     UpperSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Ici y) :=
@@ -1374,12 +840,6 @@ theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Ici]
 #align upper_semicontinuous_iff_is_closed_preimage upperSemicontinuous_iff_isClosed_preimage
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.is_closed_preimage UpperSemicontinuous.isClosed_preimageₓ'. -/
 theorem UpperSemicontinuous.isClosed_preimage {f : α → γ} (hf : UpperSemicontinuous f) (y : γ) :
     IsClosed (f ⁻¹' Ici y) :=
   upperSemicontinuous_iff_isClosed_preimage.1 hf y
@@ -1387,42 +847,18 @@ theorem UpperSemicontinuous.isClosed_preimage {f : α → γ} (hf : UpperSemicon
 
 variable [TopologicalSpace γ] [OrderTopology γ]
 
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-Case conversion may be inaccurate. Consider using '#align continuous_within_at.upper_semicontinuous_within_at ContinuousWithinAt.upperSemicontinuousWithinAtₓ'. -/
 theorem ContinuousWithinAt.upperSemicontinuousWithinAt {f : α → γ} (h : ContinuousWithinAt f s x) :
     UpperSemicontinuousWithinAt f s x := fun y hy => h (Iio_mem_nhds hy)
 #align continuous_within_at.upper_semicontinuous_within_at ContinuousWithinAt.upperSemicontinuousWithinAt
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align continuous_at.upper_semicontinuous_at ContinuousAt.upperSemicontinuousAtₓ'. -/
 theorem ContinuousAt.upperSemicontinuousAt {f : α → γ} (h : ContinuousAt f x) :
     UpperSemicontinuousAt f x := fun y hy => h (Iio_mem_nhds hy)
 #align continuous_at.upper_semicontinuous_at ContinuousAt.upperSemicontinuousAt
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align continuous_on.upper_semicontinuous_on ContinuousOn.upperSemicontinuousOnₓ'. -/
 theorem ContinuousOn.upperSemicontinuousOn {f : α → γ} (h : ContinuousOn f s) :
     UpperSemicontinuousOn f s := fun x hx => (h x hx).UpperSemicontinuousWithinAt
 #align continuous_on.upper_semicontinuous_on ContinuousOn.upperSemicontinuousOn
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (Continuous.{u1, u2} α γ _inst_1 _inst_4 f) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align continuous.upper_semicontinuous Continuous.upperSemicontinuousₓ'. -/
 theorem Continuous.upperSemicontinuous {f : α → γ} (h : Continuous f) : UpperSemicontinuous f :=
   fun x => h.ContinuousAt.UpperSemicontinuousAt
 #align continuous.upper_semicontinuous Continuous.upperSemicontinuous
@@ -1438,92 +874,44 @@ variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
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-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_within_at ContinuousAt.comp_upperSemicontinuousWithinAtₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     UpperSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_lowerSemicontinuousWithinAt α _ x s γᵒᵈ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon.dual
 #align continuous_at.comp_upper_semicontinuous_within_at ContinuousAt.comp_upperSemicontinuousWithinAt
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
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-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_at ContinuousAt.comp_upperSemicontinuousAtₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : UpperSemicontinuousAt f x) (gmon : Monotone g) : UpperSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_lowerSemicontinuousAt α _ x γᵒᵈ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon.dual
 #align continuous_at.comp_upper_semicontinuous_at ContinuousAt.comp_upperSemicontinuousAt
 
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-Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous_on Continuous.comp_upperSemicontinuousOnₓ'. -/
 theorem Continuous.comp_upperSemicontinuousOn {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuousOn f s) (gmon : Monotone g) : UpperSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_upperSemicontinuousWithinAt (hf x hx) gmon
 #align continuous.comp_upper_semicontinuous_on Continuous.comp_upperSemicontinuousOn
 
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-Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous Continuous.comp_upperSemicontinuousₓ'. -/
 theorem Continuous.comp_upperSemicontinuous {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuous f) (gmon : Monotone g) : UpperSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_upperSemicontinuousAt (hf x) gmon
 #align continuous.comp_upper_semicontinuous Continuous.comp_upperSemicontinuous
 
-/- warning: continuous_at.comp_upper_semicontinuous_within_at_antitone -> ContinuousAt.comp_upperSemicontinuousWithinAt_antitone is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s x)
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-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_within_at_antitone ContinuousAt.comp_upperSemicontinuousWithinAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Antitone g) :
     LowerSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_upperSemicontinuousWithinAt α _ x s γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_upper_semicontinuous_within_at_antitone ContinuousAt.comp_upperSemicontinuousWithinAt_antitone
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f x) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) x)
-Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_at_antitone ContinuousAt.comp_upperSemicontinuousAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousAt f x) (gmon : Antitone g) :
     LowerSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_upperSemicontinuousAt α _ x γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_upper_semicontinuous_at_antitone ContinuousAt.comp_upperSemicontinuousAt_antitone
 
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-Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous_on_antitone Continuous.comp_upperSemicontinuousOn_antitoneₓ'. -/
 theorem Continuous.comp_upperSemicontinuousOn_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuousOn f s) (gmon : Antitone g) : LowerSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_upperSemicontinuousWithinAt_antitone (hf x hx) gmon
 #align continuous.comp_upper_semicontinuous_on_antitone Continuous.comp_upperSemicontinuousOn_antitone
 
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-Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous_antitone Continuous.comp_upperSemicontinuous_antitoneₓ'. -/
 theorem Continuous.comp_upperSemicontinuous_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuous f) (gmon : Antitone g) : LowerSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_upperSemicontinuousAt_antitone (hf x) gmon
@@ -1539,12 +927,6 @@ section
 variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
   [OrderTopology γ]
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at.add' UpperSemicontinuousWithinAt.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -1555,12 +937,6 @@ theorem UpperSemicontinuousWithinAt.add' {f g : α → γ} (hf : UpperSemicontin
   @LowerSemicontinuousWithinAt.add' α _ x s γᵒᵈ _ _ _ _ _ hf hg hcont
 #align upper_semicontinuous_within_at.add' UpperSemicontinuousWithinAt.add'
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at.add' UpperSemicontinuousAt.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -1571,12 +947,6 @@ theorem UpperSemicontinuousAt.add' {f g : α → γ} (hf : UpperSemicontinuousAt
   simp_rw [← upperSemicontinuousWithinAt_univ_iff] at *; exact hf.add' hg hcont
 #align upper_semicontinuous_at.add' UpperSemicontinuousAt.add'
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.add' UpperSemicontinuousOn.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -1587,12 +957,6 @@ theorem UpperSemicontinuousOn.add' {f g : α → γ} (hf : UpperSemicontinuousOn
   (hf x hx).add' (hg x hx) (hcont x hx)
 #align upper_semicontinuous_on.add' UpperSemicontinuousOn.add'
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.add' UpperSemicontinuous.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -1604,12 +968,6 @@ theorem UpperSemicontinuous.add' {f g : α → γ} (hf : UpperSemicontinuous f)
 
 variable [ContinuousAdd γ]
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at.add UpperSemicontinuousWithinAt.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -1619,12 +977,6 @@ theorem UpperSemicontinuousWithinAt.add {f g : α → γ} (hf : UpperSemicontinu
   hf.add' hg continuous_add.ContinuousAt
 #align upper_semicontinuous_within_at.add UpperSemicontinuousWithinAt.add
 
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-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f x) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g x) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at.add UpperSemicontinuousAt.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -1633,12 +985,6 @@ theorem UpperSemicontinuousAt.add {f g : α → γ} (hf : UpperSemicontinuousAt
   hf.add' hg continuous_add.ContinuousAt
 #align upper_semicontinuous_at.add UpperSemicontinuousAt.add
 
-/- warning: upper_semicontinuous_on.add -> UpperSemicontinuousOn.add is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.add UpperSemicontinuousOn.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -1647,12 +993,6 @@ theorem UpperSemicontinuousOn.add {f g : α → γ} (hf : UpperSemicontinuousOn
   hf.add' hg fun x hx => continuous_add.ContinuousAt
 #align upper_semicontinuous_on.add UpperSemicontinuousOn.add
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.add UpperSemicontinuous.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -1661,24 +1001,12 @@ theorem UpperSemicontinuous.add {f g : α → γ} (hf : UpperSemicontinuous f)
   hf.add' hg fun x => continuous_add.ContinuousAt
 #align upper_semicontinuous.add UpperSemicontinuous.add
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_sum upperSemicontinuousWithinAt_sumₓ'. -/
 theorem upperSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x :=
   @lowerSemicontinuousWithinAt_sum α _ x s ι γᵒᵈ _ _ _ _ f a ha
 #align upper_semicontinuous_within_at_sum upperSemicontinuousWithinAt_sum
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_sum upperSemicontinuousAt_sumₓ'. -/
 theorem upperSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun z => ∑ i in a, f i z) x :=
@@ -1687,24 +1015,12 @@ theorem upperSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
   exact upperSemicontinuousWithinAt_sum ha
 #align upper_semicontinuous_at_sum upperSemicontinuousAt_sum
 
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) s)) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) s)
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-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) s)) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) s)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_sum upperSemicontinuousOn_sumₓ'. -/
 theorem upperSemicontinuousOn_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun z => ∑ i in a, f i z) s := fun x hx =>
   upperSemicontinuousWithinAt_sum fun i hi => ha i hi x hx
 #align upper_semicontinuous_on_sum upperSemicontinuousOn_sum
 
-/- warning: upper_semicontinuous_sum -> upperSemicontinuous_sum is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (UpperSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i))) -> (UpperSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)))
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-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i))) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)))
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_sum upperSemicontinuous_sumₓ'. -/
 theorem upperSemicontinuous_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuous (f i)) : UpperSemicontinuous fun z => ∑ i in a, f i z :=
   fun x => upperSemicontinuousAt_sum fun i hi => ha i hi x
@@ -1719,12 +1035,6 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-/- warning: upper_semicontinuous_within_at_cinfi -> upperSemicontinuousWithinAt_ciInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_ciInfₓ'. -/
 theorem upperSemicontinuousWithinAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
@@ -1732,24 +1042,12 @@ theorem upperSemicontinuousWithinAt_ciInf {f : ι → α → δ'}
   @lowerSemicontinuousWithinAt_ciSup α _ x s ι δ'ᵒᵈ _ f bdd h
 #align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_ciInf
 
-/- warning: upper_semicontinuous_within_at_infi -> upperSemicontinuousWithinAt_iInf is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s x)
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_iInfₓ'. -/
 theorem upperSemicontinuousWithinAt_iInf {f : ι → α → δ}
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
   @lowerSemicontinuousWithinAt_iSup α _ x s ι δᵒᵈ _ f h
 #align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_iInf
 
-/- warning: upper_semicontinuous_within_at_binfi -> upperSemicontinuousWithinAt_biInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuousWithinAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
@@ -1757,35 +1055,17 @@ theorem upperSemicontinuousWithinAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p
   upperSemicontinuousWithinAt_iInf fun i => upperSemicontinuousWithinAt_iInf fun hi => h i hi
 #align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_biInf
 
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-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iInf.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_ciInfₓ'. -/
 theorem upperSemicontinuousAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddBelow (range fun i => f i y)) (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
   @lowerSemicontinuousAt_ciSup α _ x ι δ'ᵒᵈ _ f bdd h
 #align upper_semicontinuous_at_cinfi upperSemicontinuousAt_ciInf
 
-/- warning: upper_semicontinuous_at_infi -> upperSemicontinuousAt_iInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_infi upperSemicontinuousAt_iInfₓ'. -/
 theorem upperSemicontinuousAt_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
   @lowerSemicontinuousAt_iSup α _ x ι δᵒᵈ _ f h
 #align upper_semicontinuous_at_infi upperSemicontinuousAt_iInf
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_binfi upperSemicontinuousAt_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuousAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
@@ -1793,35 +1073,17 @@ theorem upperSemicontinuousAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α
   upperSemicontinuousAt_iInf fun i => upperSemicontinuousAt_iInf fun hi => h i hi
 #align upper_semicontinuous_at_binfi upperSemicontinuousAt_biInf
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_ciInfₓ'. -/
 theorem upperSemicontinuousOn_ciInf {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddBelow (range fun i => f i x)) (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
   upperSemicontinuousWithinAt_ciInf (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
 #align upper_semicontinuous_on_cinfi upperSemicontinuousOn_ciInf
 
-/- warning: upper_semicontinuous_on_infi -> upperSemicontinuousOn_iInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_infi upperSemicontinuousOn_iInfₓ'. -/
 theorem upperSemicontinuousOn_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
   upperSemicontinuousWithinAt_iInf fun i => h i x hx
 #align upper_semicontinuous_on_infi upperSemicontinuousOn_iInf
 
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_binfi upperSemicontinuousOn_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuousOn_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
@@ -1829,33 +1091,15 @@ theorem upperSemicontinuousOn_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α
   upperSemicontinuousOn_iInf fun i => upperSemicontinuousOn_iInf fun hi => h i hi
 #align upper_semicontinuous_on_binfi upperSemicontinuousOn_biInf
 
-/- warning: upper_semicontinuous_cinfi -> upperSemicontinuous_ciInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_cinfi upperSemicontinuous_ciInfₓ'. -/
 theorem upperSemicontinuous_ciInf {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
     (h : ∀ i, UpperSemicontinuous (f i)) : UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x =>
   upperSemicontinuousAt_ciInf (eventually_of_forall bdd) fun i => h i x
 #align upper_semicontinuous_cinfi upperSemicontinuous_ciInf
 
-/- warning: upper_semicontinuous_infi -> upperSemicontinuous_iInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_infi upperSemicontinuous_iInfₓ'. -/
 theorem upperSemicontinuous_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
     UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_iInf fun i => h i x
 #align upper_semicontinuous_infi upperSemicontinuous_iInf
 
-/- warning: upper_semicontinuous_binfi -> upperSemicontinuous_biInf is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iInf.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
-but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iInf.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_binfi upperSemicontinuous_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuous_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
@@ -1869,12 +1113,6 @@ section
 
 variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
-/- warning: continuous_within_at_iff_lower_upper_semicontinuous_within_at -> continuousWithinAt_iff_lower_upperSemicontinuousWithinAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f s x) (And (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (ContinuousWithinAt.{u2, u1} α γ _inst_1 _inst_4 f s x) (And (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s x) (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s x))
-Case conversion may be inaccurate. Consider using '#align continuous_within_at_iff_lower_upper_semicontinuous_within_at continuousWithinAt_iff_lower_upperSemicontinuousWithinAtₓ'. -/
 theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ} :
     ContinuousWithinAt f s x ↔
       LowerSemicontinuousWithinAt f s x ∧ UpperSemicontinuousWithinAt f s x :=
@@ -1907,24 +1145,12 @@ theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ}
       exact mem_of_mem_nhds hv
 #align continuous_within_at_iff_lower_upper_semicontinuous_within_at continuousWithinAt_iff_lower_upperSemicontinuousWithinAt
 
-/- warning: continuous_at_iff_lower_upper_semicontinuous_at -> continuousAt_iff_lower_upperSemicontinuousAt is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (ContinuousAt.{u1, u2} α γ _inst_1 _inst_4 f x) (And (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (ContinuousAt.{u2, u1} α γ _inst_1 _inst_4 f x) (And (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f x) (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f x))
-Case conversion may be inaccurate. Consider using '#align continuous_at_iff_lower_upper_semicontinuous_at continuousAt_iff_lower_upperSemicontinuousAtₓ'. -/
 theorem continuousAt_iff_lower_upperSemicontinuousAt {f : α → γ} :
     ContinuousAt f x ↔ LowerSemicontinuousAt f x ∧ UpperSemicontinuousAt f x := by
   simp_rw [← continuousWithinAt_univ, ← lowerSemicontinuousWithinAt_univ_iff, ←
     upperSemicontinuousWithinAt_univ_iff, continuousWithinAt_iff_lower_upperSemicontinuousWithinAt]
 #align continuous_at_iff_lower_upper_semicontinuous_at continuousAt_iff_lower_upperSemicontinuousAt
 
-/- warning: continuous_on_iff_lower_upper_semicontinuous_on -> continuousOn_iff_lower_upperSemicontinuousOn is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (ContinuousOn.{u1, u2} α γ _inst_1 _inst_4 f s) (And (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s) (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (ContinuousOn.{u2, u1} α γ _inst_1 _inst_4 f s) (And (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s) (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s))
-Case conversion may be inaccurate. Consider using '#align continuous_on_iff_lower_upper_semicontinuous_on continuousOn_iff_lower_upperSemicontinuousOnₓ'. -/
 theorem continuousOn_iff_lower_upperSemicontinuousOn {f : α → γ} :
     ContinuousOn f s ↔ LowerSemicontinuousOn f s ∧ UpperSemicontinuousOn f s :=
   by
@@ -1933,12 +1159,6 @@ theorem continuousOn_iff_lower_upperSemicontinuousOn {f : α → γ} :
     ⟨fun H => ⟨fun x hx => (H x hx).1, fun x hx => (H x hx).2⟩, fun H x hx => ⟨H.1 x hx, H.2 x hx⟩⟩
 #align continuous_on_iff_lower_upper_semicontinuous_on continuousOn_iff_lower_upperSemicontinuousOn
 
-/- warning: continuous_iff_lower_upper_semicontinuous -> continuous_iff_lower_upperSemicontinuous is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (Continuous.{u1, u2} α γ _inst_1 _inst_4 f) (And (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f))
-but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (Continuous.{u2, u1} α γ _inst_1 _inst_4 f) (And (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f))
-Case conversion may be inaccurate. Consider using '#align continuous_iff_lower_upper_semicontinuous continuous_iff_lower_upperSemicontinuousₓ'. -/
 theorem continuous_iff_lower_upperSemicontinuous {f : α → γ} :
     Continuous f ↔ LowerSemicontinuous f ∧ UpperSemicontinuous f := by
   simp_rw [continuous_iff_continuousOn_univ, continuousOn_iff_lower_upperSemicontinuousOn,

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

@@ -655,16 +655,12 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       filter_upwards [hf z₁ z₁lt, hg z₂ z₂lt]with z h₁z h₂z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
-        · simp [H]
-          exact h₁ ⟨h₁z, H⟩
-        · simp [le_of_not_le H]
-          exact h₁ ⟨z₁lt, le_rfl⟩
+        · simp [H]; exact h₁ ⟨h₁z, H⟩
+        · simp [le_of_not_le H]; exact h₁ ⟨z₁lt, le_rfl⟩
       have A2 : min (g z) (g x) ∈ v := by
         by_cases H : g z ≤ g x
-        · simp [H]
-          exact h₂ ⟨h₂z, H⟩
-        · simp [le_of_not_le H]
-          exact h₂ ⟨z₂lt, le_rfl⟩
+        · simp [H]; exact h₂ ⟨h₂z, H⟩
+        · simp [le_of_not_le H]; exact h₂ ⟨z₂lt, le_rfl⟩
       have : (min (f z) (f x), min (g z) (g x)) ∈ u ×ˢ v := ⟨A1, A2⟩
       calc
         y < min (f z) (f x) + min (g z) (g x) := h this
@@ -674,10 +670,8 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       filter_upwards [hf z₁ z₁lt]with z h₁z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
-        · simp [H]
-          exact h₁ ⟨h₁z, H⟩
-        · simp [le_of_not_le H]
-          exact h₁ ⟨z₁lt, le_rfl⟩
+        · simp [H]; exact h₁ ⟨h₁z, H⟩
+        · simp [le_of_not_le H]; exact h₁ ⟨z₁lt, le_rfl⟩
       have : (min (f z) (f x), g x) ∈ u ×ˢ v := ⟨A1, xv⟩
       calc
         y < min (f z) (f x) + g x := h this
@@ -690,10 +684,8 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       filter_upwards [hg z₂ z₂lt]with z h₂z
       have A2 : min (g z) (g x) ∈ v := by
         by_cases H : g z ≤ g x
-        · simp [H]
-          exact h₂ ⟨h₂z, H⟩
-        · simp [le_of_not_le H]
-          exact h₂ ⟨z₂lt, le_rfl⟩
+        · simp [H]; exact h₂ ⟨h₂z, H⟩
+        · simp [le_of_not_le H]; exact h₂ ⟨z₂lt, le_rfl⟩
       have : (f x, min (g z) (g x)) ∈ u ×ˢ v := ⟨xu, A2⟩
       calc
         y < f x + min (g z) (g x) := h this
@@ -721,10 +713,8 @@ the lemma uses `[has_continuous_add]`. -/
 theorem LowerSemicontinuousAt.add' {f g : α → γ} (hf : LowerSemicontinuousAt f x)
     (hg : LowerSemicontinuousAt g x)
     (hcont : ContinuousAt (fun p : γ × γ => p.1 + p.2) (f x, g x)) :
-    LowerSemicontinuousAt (fun z => f z + g z) x :=
-  by
-  simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
-  exact hf.add' hg hcont
+    LowerSemicontinuousAt (fun z => f z + g z) x := by
+  simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *; exact hf.add' hg hcont
 #align lower_semicontinuous_at.add' LowerSemicontinuousAt.add'
 
 /- warning: lower_semicontinuous_on.add' -> LowerSemicontinuousOn.add' is a dubious translation:
@@ -1577,10 +1567,8 @@ the lemma uses `[has_continuous_add]`. -/
 theorem UpperSemicontinuousAt.add' {f g : α → γ} (hf : UpperSemicontinuousAt f x)
     (hg : UpperSemicontinuousAt g x)
     (hcont : ContinuousAt (fun p : γ × γ => p.1 + p.2) (f x, g x)) :
-    UpperSemicontinuousAt (fun z => f z + g z) x :=
-  by
-  simp_rw [← upperSemicontinuousWithinAt_univ_iff] at *
-  exact hf.add' hg hcont
+    UpperSemicontinuousAt (fun z => f z + g z) x := by
+  simp_rw [← upperSemicontinuousWithinAt_univ_iff] at *; exact hf.add' hg hcont
 #align upper_semicontinuous_at.add' UpperSemicontinuousAt.add'
 
 /- warning: upper_semicontinuous_on.add' -> UpperSemicontinuousOn.add' is a dubious translation:

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

@@ -298,7 +298,7 @@ variable [Zero β]
 
 /- warning: is_open.lower_semicontinuous_indicator -> IsOpen.lowerSemicontinuous_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
 Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_indicator IsOpen.lowerSemicontinuous_indicatorₓ'. -/
@@ -315,7 +315,7 @@ theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
 
 /- warning: is_open.lower_semicontinuous_on_indicator -> IsOpen.lowerSemicontinuousOn_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
 Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_on_indicator IsOpen.lowerSemicontinuousOn_indicatorₓ'. -/
@@ -326,7 +326,7 @@ theorem IsOpen.lowerSemicontinuousOn_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
 
 /- warning: is_open.lower_semicontinuous_at_indicator -> IsOpen.lowerSemicontinuousAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
 Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_at_indicator IsOpen.lowerSemicontinuousAt_indicatorₓ'. -/
@@ -337,7 +337,7 @@ theorem IsOpen.lowerSemicontinuousAt_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
 
 /- warning: is_open.lower_semicontinuous_within_at_indicator -> IsOpen.lowerSemicontinuousWithinAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
 Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_within_at_indicator IsOpen.lowerSemicontinuousWithinAt_indicatorₓ'. -/
@@ -348,7 +348,7 @@ theorem IsOpen.lowerSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : 0 ≤
 
 /- warning: is_closed.lower_semicontinuous_indicator -> IsClosed.lowerSemicontinuous_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
 Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_indicator IsClosed.lowerSemicontinuous_indicatorₓ'. -/
@@ -365,7 +365,7 @@ theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0)
 
 /- warning: is_closed.lower_semicontinuous_on_indicator -> IsClosed.lowerSemicontinuousOn_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
 Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_on_indicator IsClosed.lowerSemicontinuousOn_indicatorₓ'. -/
@@ -376,7 +376,7 @@ theorem IsClosed.lowerSemicontinuousOn_indicator (hs : IsClosed s) (hy : y ≤ 0
 
 /- warning: is_closed.lower_semicontinuous_at_indicator -> IsClosed.lowerSemicontinuousAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
 Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_at_indicator IsClosed.lowerSemicontinuousAt_indicatorₓ'. -/
@@ -387,7 +387,7 @@ theorem IsClosed.lowerSemicontinuousAt_indicator (hs : IsClosed s) (hy : y ≤ 0
 
 /- warning: is_closed.lower_semicontinuous_within_at_indicator -> IsClosed.lowerSemicontinuousWithinAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
 Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_within_at_indicator IsClosed.lowerSemicontinuousWithinAt_indicatorₓ'. -/
@@ -1250,7 +1250,7 @@ variable [Zero β]
 
 /- warning: is_open.upper_semicontinuous_indicator -> IsOpen.upperSemicontinuous_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
 Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_indicator IsOpen.upperSemicontinuous_indicatorₓ'. -/
@@ -1261,7 +1261,7 @@ theorem IsOpen.upperSemicontinuous_indicator (hs : IsOpen s) (hy : y ≤ 0) :
 
 /- warning: is_open.upper_semicontinuous_on_indicator -> IsOpen.upperSemicontinuousOn_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
 Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_on_indicator IsOpen.upperSemicontinuousOn_indicatorₓ'. -/
@@ -1272,7 +1272,7 @@ theorem IsOpen.upperSemicontinuousOn_indicator (hs : IsOpen s) (hy : y ≤ 0) :
 
 /- warning: is_open.upper_semicontinuous_at_indicator -> IsOpen.upperSemicontinuousAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
 Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_at_indicator IsOpen.upperSemicontinuousAt_indicatorₓ'. -/
@@ -1283,7 +1283,7 @@ theorem IsOpen.upperSemicontinuousAt_indicator (hs : IsOpen s) (hy : y ≤ 0) :
 
 /- warning: is_open.upper_semicontinuous_within_at_indicator -> IsOpen.upperSemicontinuousWithinAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
 Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_within_at_indicator IsOpen.upperSemicontinuousWithinAt_indicatorₓ'. -/
@@ -1294,7 +1294,7 @@ theorem IsOpen.upperSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : y ≤
 
 /- warning: is_closed.upper_semicontinuous_indicator -> IsClosed.upperSemicontinuous_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
 Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_indicator IsClosed.upperSemicontinuous_indicatorₓ'. -/
@@ -1305,7 +1305,7 @@ theorem IsClosed.upperSemicontinuous_indicator (hs : IsClosed s) (hy : 0 ≤ y)
 
 /- warning: is_closed.upper_semicontinuous_on_indicator -> IsClosed.upperSemicontinuousOn_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
 Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_on_indicator IsClosed.upperSemicontinuousOn_indicatorₓ'. -/
@@ -1316,7 +1316,7 @@ theorem IsClosed.upperSemicontinuousOn_indicator (hs : IsClosed s) (hy : 0 ≤ y
 
 /- warning: is_closed.upper_semicontinuous_at_indicator -> IsClosed.upperSemicontinuousAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
 Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_at_indicator IsClosed.upperSemicontinuousAt_indicatorₓ'. -/
@@ -1327,7 +1327,7 @@ theorem IsClosed.upperSemicontinuousAt_indicator (hs : IsClosed s) (hy : 0 ≤ y
 
 /- warning: is_closed.upper_semicontinuous_within_at_indicator -> IsClosed.upperSemicontinuousWithinAt_indicator is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
 Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_within_at_indicator IsClosed.upperSemicontinuousWithinAt_indicatorₓ'. -/

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

@@ -881,158 +881,158 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-/- warning: lower_semicontinuous_within_at_csupr -> lowerSemicontinuousWithinAt_csupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_within_at_csupr -> lowerSemicontinuousWithinAt_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iSup.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupᵢₓ'. -/
-theorem lowerSemicontinuousWithinAt_csupᵢ {f : ι → α → δ'}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => iSup.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSupₓ'. -/
+theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
   by
   cases isEmpty_or_nonempty ι
-  · simpa only [supᵢ_of_empty'] using lowerSemicontinuousWithinAt_const
+  · simpa only [iSup_of_empty'] using lowerSemicontinuousWithinAt_const
   · intro y hy
-    rcases exists_lt_of_lt_csupᵢ hy with ⟨i, hi⟩
-    filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_csupᵢ hy' i)
-#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupᵢ
+    rcases exists_lt_of_lt_ciSup hy with ⟨i, hi⟩
+    filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_ciSup hy' i)
+#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSup
 
-/- warning: lower_semicontinuous_within_at_supr -> lowerSemicontinuousWithinAt_supᵢ is a dubious translation:
+/- warning: lower_semicontinuous_within_at_supr -> lowerSemicontinuousWithinAt_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_supᵢₓ'. -/
-theorem lowerSemicontinuousWithinAt_supᵢ {f : ι → α → δ}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_iSupₓ'. -/
+theorem lowerSemicontinuousWithinAt_iSup {f : ι → α → δ}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
-  lowerSemicontinuousWithinAt_csupᵢ (by simp) h
-#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_supᵢ
+  lowerSemicontinuousWithinAt_ciSup (by simp) h
+#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_iSup
 
-/- warning: lower_semicontinuous_within_at_bsupr -> lowerSemicontinuousWithinAt_bsupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_within_at_bsupr -> lowerSemicontinuousWithinAt_biSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iSup.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuousWithinAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuousWithinAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ (i) (hi), f i hi x') s x :=
-  lowerSemicontinuousWithinAt_supᵢ fun i => lowerSemicontinuousWithinAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupᵢ
+  lowerSemicontinuousWithinAt_iSup fun i => lowerSemicontinuousWithinAt_iSup fun hi => h i hi
+#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_biSup
 
-/- warning: lower_semicontinuous_at_csupr -> lowerSemicontinuousAt_csupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_at_csupr -> lowerSemicontinuousAt_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iSup.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupᵢₓ'. -/
-theorem lowerSemicontinuousAt_csupᵢ {f : ι → α → δ'}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => iSup.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSupₓ'. -/
+theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddAbove (range fun i => f i y)) (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
   by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
   rw [← nhdsWithin_univ] at bdd
-  exact lowerSemicontinuousWithinAt_csupᵢ bdd h
-#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupᵢ
+  exact lowerSemicontinuousWithinAt_ciSup bdd h
+#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSup
 
-/- warning: lower_semicontinuous_at_supr -> lowerSemicontinuousAt_supᵢ is a dubious translation:
+/- warning: lower_semicontinuous_at_supr -> lowerSemicontinuousAt_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢₓ'. -/
-theorem lowerSemicontinuousAt_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_supr lowerSemicontinuousAt_iSupₓ'. -/
+theorem lowerSemicontinuousAt_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
-  lowerSemicontinuousAt_csupᵢ (by simp) h
-#align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢ
+  lowerSemicontinuousAt_ciSup (by simp) h
+#align lower_semicontinuous_at_supr lowerSemicontinuousAt_iSup
 
-/- warning: lower_semicontinuous_at_bsupr -> lowerSemicontinuousAt_bsupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_at_bsupr -> lowerSemicontinuousAt_biSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iSup.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuousAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuousAt_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
     LowerSemicontinuousAt (fun x' => ⨆ (i) (hi), f i hi x') x :=
-  lowerSemicontinuousAt_supᵢ fun i => lowerSemicontinuousAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupᵢ
+  lowerSemicontinuousAt_iSup fun i => lowerSemicontinuousAt_iSup fun hi => h i hi
+#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_biSup
 
-/- warning: lower_semicontinuous_on_csupr -> lowerSemicontinuousOn_csupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_on_csupr -> lowerSemicontinuousOn_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iSup.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupᵢₓ'. -/
-theorem lowerSemicontinuousOn_csupᵢ {f : ι → α → δ'}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => iSup.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_ciSupₓ'. -/
+theorem lowerSemicontinuousOn_ciSup {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddAbove (range fun i => f i x)) (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s := fun x hx =>
-  lowerSemicontinuousWithinAt_csupᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupᵢ
+  lowerSemicontinuousWithinAt_ciSup (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_ciSup
 
-/- warning: lower_semicontinuous_on_supr -> lowerSemicontinuousOn_supᵢ is a dubious translation:
+/- warning: lower_semicontinuous_on_supr -> lowerSemicontinuousOn_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢₓ'. -/
-theorem lowerSemicontinuousOn_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_supr lowerSemicontinuousOn_iSupₓ'. -/
+theorem lowerSemicontinuousOn_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s :=
-  lowerSemicontinuousOn_csupᵢ (by simp) h
-#align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢ
+  lowerSemicontinuousOn_ciSup (by simp) h
+#align lower_semicontinuous_on_supr lowerSemicontinuousOn_iSup
 
-/- warning: lower_semicontinuous_on_bsupr -> lowerSemicontinuousOn_bsupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_on_bsupr -> lowerSemicontinuousOn_biSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iSup.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuousOn_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuousOn_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
     LowerSemicontinuousOn (fun x' => ⨆ (i) (hi), f i hi x') s :=
-  lowerSemicontinuousOn_supᵢ fun i => lowerSemicontinuousOn_supᵢ fun hi => h i hi
-#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupᵢ
+  lowerSemicontinuousOn_iSup fun i => lowerSemicontinuousOn_iSup fun hi => h i hi
+#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_biSup
 
-/- warning: lower_semicontinuous_csupr -> lowerSemicontinuous_csupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_csupr -> lowerSemicontinuous_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iSup.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toSupSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_csupr lowerSemicontinuous_csupᵢₓ'. -/
-theorem lowerSemicontinuous_csupᵢ {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iSup.{u3, u2} δ' (ConditionallyCompleteLattice.toSupSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_csupr lowerSemicontinuous_ciSupₓ'. -/
+theorem lowerSemicontinuous_ciSup {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
     (h : ∀ i, LowerSemicontinuous (f i)) : LowerSemicontinuous fun x' => ⨆ i, f i x' := fun x =>
-  lowerSemicontinuousAt_csupᵢ (eventually_of_forall bdd) fun i => h i x
-#align lower_semicontinuous_csupr lowerSemicontinuous_csupᵢ
+  lowerSemicontinuousAt_ciSup (eventually_of_forall bdd) fun i => h i x
+#align lower_semicontinuous_csupr lowerSemicontinuous_ciSup
 
-/- warning: lower_semicontinuous_supr -> lowerSemicontinuous_supᵢ is a dubious translation:
+/- warning: lower_semicontinuous_supr -> lowerSemicontinuous_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')))
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_supr lowerSemicontinuous_supᵢₓ'. -/
-theorem lowerSemicontinuous_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_supr lowerSemicontinuous_iSupₓ'. -/
+theorem lowerSemicontinuous_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ⨆ i, f i x' :=
-  lowerSemicontinuous_csupᵢ (by simp) h
-#align lower_semicontinuous_supr lowerSemicontinuous_supᵢ
+  lowerSemicontinuous_ciSup (by simp) h
+#align lower_semicontinuous_supr lowerSemicontinuous_iSup
 
-/- warning: lower_semicontinuous_bsupr -> lowerSemicontinuous_bsupᵢ is a dubious translation:
+/- warning: lower_semicontinuous_bsupr -> lowerSemicontinuous_biSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iSup.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iSup.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iSup.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iSup.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_bsupr lowerSemicontinuous_biSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuous_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuous_biSup {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
     LowerSemicontinuous fun x' => ⨆ (i) (hi), f i hi x' :=
-  lowerSemicontinuous_supᵢ fun i => lowerSemicontinuous_supᵢ fun hi => h i hi
-#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupᵢ
+  lowerSemicontinuous_iSup fun i => lowerSemicontinuous_iSup fun hi => h i hi
+#align lower_semicontinuous_bsupr lowerSemicontinuous_biSup
 
 end
 
@@ -1053,8 +1053,8 @@ theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ∑' i, f i x') s x :=
   by
-  simp_rw [ENNReal.tsum_eq_supᵢ_sum]
-  apply lowerSemicontinuousWithinAt_supᵢ fun b => _
+  simp_rw [ENNReal.tsum_eq_iSup_sum]
+  apply lowerSemicontinuousWithinAt_iSup fun b => _
   exact lowerSemicontinuousWithinAt_sum fun i hi => h i
 #align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsum
 
@@ -1731,149 +1731,149 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-/- warning: upper_semicontinuous_within_at_cinfi -> upperSemicontinuousWithinAt_cinfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_within_at_cinfi -> upperSemicontinuousWithinAt_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iInf.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfᵢₓ'. -/
-theorem upperSemicontinuousWithinAt_cinfᵢ {f : ι → α → δ'}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => iInf.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_ciInfₓ'. -/
+theorem upperSemicontinuousWithinAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
-  @lowerSemicontinuousWithinAt_csupᵢ α _ x s ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfᵢ
+  @lowerSemicontinuousWithinAt_ciSup α _ x s ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_ciInf
 
-/- warning: upper_semicontinuous_within_at_infi -> upperSemicontinuousWithinAt_infᵢ is a dubious translation:
+/- warning: upper_semicontinuous_within_at_infi -> upperSemicontinuousWithinAt_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_infᵢₓ'. -/
-theorem upperSemicontinuousWithinAt_infᵢ {f : ι → α → δ}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_iInfₓ'. -/
+theorem upperSemicontinuousWithinAt_iInf {f : ι → α → δ}
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
-  @lowerSemicontinuousWithinAt_supᵢ α _ x s ι δᵒᵈ _ f h
-#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_infᵢ
+  @lowerSemicontinuousWithinAt_iSup α _ x s ι δᵒᵈ _ f h
+#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_iInf
 
-/- warning: upper_semicontinuous_within_at_binfi -> upperSemicontinuousWithinAt_binfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_within_at_binfi -> upperSemicontinuousWithinAt_biInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iInf.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iInf.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuousWithinAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuousWithinAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ (i) (hi), f i hi x') s x :=
-  upperSemicontinuousWithinAt_infᵢ fun i => upperSemicontinuousWithinAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfᵢ
+  upperSemicontinuousWithinAt_iInf fun i => upperSemicontinuousWithinAt_iInf fun hi => h i hi
+#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_biInf
 
-/- warning: upper_semicontinuous_at_cinfi -> upperSemicontinuousAt_cinfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_at_cinfi -> upperSemicontinuousAt_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iInf.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfᵢₓ'. -/
-theorem upperSemicontinuousAt_cinfᵢ {f : ι → α → δ'}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => iInf.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_ciInfₓ'. -/
+theorem upperSemicontinuousAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddBelow (range fun i => f i y)) (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
-  @lowerSemicontinuousAt_csupᵢ α _ x ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfᵢ
+  @lowerSemicontinuousAt_ciSup α _ x ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_ciInf
 
-/- warning: upper_semicontinuous_at_infi -> upperSemicontinuousAt_infᵢ is a dubious translation:
+/- warning: upper_semicontinuous_at_infi -> upperSemicontinuousAt_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_infi upperSemicontinuousAt_infᵢₓ'. -/
-theorem upperSemicontinuousAt_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_infi upperSemicontinuousAt_iInfₓ'. -/
+theorem upperSemicontinuousAt_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
-  @lowerSemicontinuousAt_supᵢ α _ x ι δᵒᵈ _ f h
-#align upper_semicontinuous_at_infi upperSemicontinuousAt_infᵢ
+  @lowerSemicontinuousAt_iSup α _ x ι δᵒᵈ _ f h
+#align upper_semicontinuous_at_infi upperSemicontinuousAt_iInf
 
-/- warning: upper_semicontinuous_at_binfi -> upperSemicontinuousAt_binfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_at_binfi -> upperSemicontinuousAt_biInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iInf.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iInf.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_binfi upperSemicontinuousAt_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuousAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuousAt_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
     UpperSemicontinuousAt (fun x' => ⨅ (i) (hi), f i hi x') x :=
-  upperSemicontinuousAt_infᵢ fun i => upperSemicontinuousAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfᵢ
+  upperSemicontinuousAt_iInf fun i => upperSemicontinuousAt_iInf fun hi => h i hi
+#align upper_semicontinuous_at_binfi upperSemicontinuousAt_biInf
 
-/- warning: upper_semicontinuous_on_cinfi -> upperSemicontinuousOn_cinfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_on_cinfi -> upperSemicontinuousOn_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iInf.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfᵢₓ'. -/
-theorem upperSemicontinuousOn_cinfᵢ {f : ι → α → δ'}
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => iInf.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_ciInfₓ'. -/
+theorem upperSemicontinuousOn_ciInf {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddBelow (range fun i => f i x)) (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
-  upperSemicontinuousWithinAt_cinfᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfᵢ
+  upperSemicontinuousWithinAt_ciInf (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_ciInf
 
-/- warning: upper_semicontinuous_on_infi -> upperSemicontinuousOn_infᵢ is a dubious translation:
+/- warning: upper_semicontinuous_on_infi -> upperSemicontinuousOn_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_infi upperSemicontinuousOn_infᵢₓ'. -/
-theorem upperSemicontinuousOn_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_infi upperSemicontinuousOn_iInfₓ'. -/
+theorem upperSemicontinuousOn_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
-  upperSemicontinuousWithinAt_infᵢ fun i => h i x hx
-#align upper_semicontinuous_on_infi upperSemicontinuousOn_infᵢ
+  upperSemicontinuousWithinAt_iInf fun i => h i x hx
+#align upper_semicontinuous_on_infi upperSemicontinuousOn_iInf
 
-/- warning: upper_semicontinuous_on_binfi -> upperSemicontinuousOn_binfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_on_binfi -> upperSemicontinuousOn_biInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iInf.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iInf.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_binfi upperSemicontinuousOn_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuousOn_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuousOn_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
     UpperSemicontinuousOn (fun x' => ⨅ (i) (hi), f i hi x') s :=
-  upperSemicontinuousOn_infᵢ fun i => upperSemicontinuousOn_infᵢ fun hi => h i hi
-#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfᵢ
+  upperSemicontinuousOn_iInf fun i => upperSemicontinuousOn_iInf fun hi => h i hi
+#align upper_semicontinuous_on_binfi upperSemicontinuousOn_biInf
 
-/- warning: upper_semicontinuous_cinfi -> upperSemicontinuous_cinfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_cinfi -> upperSemicontinuous_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iInf.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toInfSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_cinfi upperSemicontinuous_cinfᵢₓ'. -/
-theorem upperSemicontinuous_cinfᵢ {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => iInf.{u3, u2} δ' (ConditionallyCompleteLattice.toInfSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_cinfi upperSemicontinuous_ciInfₓ'. -/
+theorem upperSemicontinuous_ciInf {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
     (h : ∀ i, UpperSemicontinuous (f i)) : UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x =>
-  upperSemicontinuousAt_cinfᵢ (eventually_of_forall bdd) fun i => h i x
-#align upper_semicontinuous_cinfi upperSemicontinuous_cinfᵢ
+  upperSemicontinuousAt_ciInf (eventually_of_forall bdd) fun i => h i x
+#align upper_semicontinuous_cinfi upperSemicontinuous_ciInf
 
-/- warning: upper_semicontinuous_infi -> upperSemicontinuous_infᵢ is a dubious translation:
+/- warning: upper_semicontinuous_infi -> upperSemicontinuous_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')))
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')))
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_infi upperSemicontinuous_infᵢₓ'. -/
-theorem upperSemicontinuous_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
-    UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_infᵢ fun i => h i x
-#align upper_semicontinuous_infi upperSemicontinuous_infᵢ
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_infi upperSemicontinuous_iInfₓ'. -/
+theorem upperSemicontinuous_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
+    UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_iInf fun i => h i x
+#align upper_semicontinuous_infi upperSemicontinuous_iInf
 
-/- warning: upper_semicontinuous_binfi -> upperSemicontinuous_binfᵢ is a dubious translation:
+/- warning: upper_semicontinuous_binfi -> upperSemicontinuous_biInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => iInf.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => iInf.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
 but is expected to have type
-  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_binfi upperSemicontinuous_binfᵢₓ'. -/
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => iInf.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => iInf.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_binfi upperSemicontinuous_biInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuous_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuous_biInf {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
     UpperSemicontinuous fun x' => ⨅ (i) (hi), f i hi x' :=
-  upperSemicontinuous_infᵢ fun i => upperSemicontinuous_infᵢ fun hi => h i hi
-#align upper_semicontinuous_binfi upperSemicontinuous_binfᵢ
+  upperSemicontinuous_iInf fun i => upperSemicontinuous_iInf fun hi => h i hi
+#align upper_semicontinuous_binfi upperSemicontinuous_biInf
 
 end
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -881,13 +881,13 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-/- warning: lower_semicontinuous_within_at_csupr -> lowerSemicontinuousWithinAt_csupr is a dubious translation:
+/- warning: lower_semicontinuous_within_at_csupr -> lowerSemicontinuousWithinAt_csupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csuprₓ'. -/
-theorem lowerSemicontinuousWithinAt_csupr {f : ι → α → δ'}
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupᵢₓ'. -/
+theorem lowerSemicontinuousWithinAt_csupᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
@@ -897,7 +897,7 @@ theorem lowerSemicontinuousWithinAt_csupr {f : ι → α → δ'}
   · intro y hy
     rcases exists_lt_of_lt_csupᵢ hy with ⟨i, hi⟩
     filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_csupᵢ hy' i)
-#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupr
+#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupᵢ
 
 /- warning: lower_semicontinuous_within_at_supr -> lowerSemicontinuousWithinAt_supᵢ is a dubious translation:
 lean 3 declaration is
@@ -908,36 +908,36 @@ Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_w
 theorem lowerSemicontinuousWithinAt_supᵢ {f : ι → α → δ}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
-  lowerSemicontinuousWithinAt_csupr (by simp) h
+  lowerSemicontinuousWithinAt_csupᵢ (by simp) h
 #align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_supᵢ
 
-/- warning: lower_semicontinuous_within_at_bsupr -> lowerSemicontinuousWithinAt_bsupr is a dubious translation:
+/- warning: lower_semicontinuous_within_at_bsupr -> lowerSemicontinuousWithinAt_bsupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsuprₓ'. -/
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuousWithinAt_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuousWithinAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ (i) (hi), f i hi x') s x :=
   lowerSemicontinuousWithinAt_supᵢ fun i => lowerSemicontinuousWithinAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupr
+#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupᵢ
 
-/- warning: lower_semicontinuous_at_csupr -> lowerSemicontinuousAt_csupr is a dubious translation:
+/- warning: lower_semicontinuous_at_csupr -> lowerSemicontinuousAt_csupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csuprₓ'. -/
-theorem lowerSemicontinuousAt_csupr {f : ι → α → δ'}
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupᵢₓ'. -/
+theorem lowerSemicontinuousAt_csupᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddAbove (range fun i => f i y)) (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
   by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
   rw [← nhdsWithin_univ] at bdd
-  exact lowerSemicontinuousWithinAt_csupr bdd h
-#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupr
+  exact lowerSemicontinuousWithinAt_csupᵢ bdd h
+#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupᵢ
 
 /- warning: lower_semicontinuous_at_supr -> lowerSemicontinuousAt_supᵢ is a dubious translation:
 lean 3 declaration is
@@ -947,33 +947,33 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢₓ'. -/
 theorem lowerSemicontinuousAt_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
-  lowerSemicontinuousAt_csupr (by simp) h
+  lowerSemicontinuousAt_csupᵢ (by simp) h
 #align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢ
 
-/- warning: lower_semicontinuous_at_bsupr -> lowerSemicontinuousAt_bsupr is a dubious translation:
+/- warning: lower_semicontinuous_at_bsupr -> lowerSemicontinuousAt_bsupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsuprₓ'. -/
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuousAt_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuousAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
     LowerSemicontinuousAt (fun x' => ⨆ (i) (hi), f i hi x') x :=
   lowerSemicontinuousAt_supᵢ fun i => lowerSemicontinuousAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupr
+#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupᵢ
 
-/- warning: lower_semicontinuous_on_csupr -> lowerSemicontinuousOn_csupr is a dubious translation:
+/- warning: lower_semicontinuous_on_csupr -> lowerSemicontinuousOn_csupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csuprₓ'. -/
-theorem lowerSemicontinuousOn_csupr {f : ι → α → δ'}
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupᵢₓ'. -/
+theorem lowerSemicontinuousOn_csupᵢ {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddAbove (range fun i => f i x)) (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s := fun x hx =>
-  lowerSemicontinuousWithinAt_csupr (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupr
+  lowerSemicontinuousWithinAt_csupᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupᵢ
 
 /- warning: lower_semicontinuous_on_supr -> lowerSemicontinuousOn_supᵢ is a dubious translation:
 lean 3 declaration is
@@ -983,32 +983,32 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢₓ'. -/
 theorem lowerSemicontinuousOn_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s :=
-  lowerSemicontinuousOn_csupr (by simp) h
+  lowerSemicontinuousOn_csupᵢ (by simp) h
 #align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢ
 
-/- warning: lower_semicontinuous_on_bsupr -> lowerSemicontinuousOn_bsupr is a dubious translation:
+/- warning: lower_semicontinuous_on_bsupr -> lowerSemicontinuousOn_bsupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsuprₓ'. -/
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuousOn_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuousOn_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
     LowerSemicontinuousOn (fun x' => ⨆ (i) (hi), f i hi x') s :=
   lowerSemicontinuousOn_supᵢ fun i => lowerSemicontinuousOn_supᵢ fun hi => h i hi
-#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupr
+#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupᵢ
 
-/- warning: lower_semicontinuous_csupr -> lowerSemicontinuous_csupr is a dubious translation:
+/- warning: lower_semicontinuous_csupr -> lowerSemicontinuous_csupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toSupSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_csupr lowerSemicontinuous_csuprₓ'. -/
-theorem lowerSemicontinuous_csupr {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_csupr lowerSemicontinuous_csupᵢₓ'. -/
+theorem lowerSemicontinuous_csupᵢ {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
     (h : ∀ i, LowerSemicontinuous (f i)) : LowerSemicontinuous fun x' => ⨆ i, f i x' := fun x =>
-  lowerSemicontinuousAt_csupr (eventually_of_forall bdd) fun i => h i x
-#align lower_semicontinuous_csupr lowerSemicontinuous_csupr
+  lowerSemicontinuousAt_csupᵢ (eventually_of_forall bdd) fun i => h i x
+#align lower_semicontinuous_csupr lowerSemicontinuous_csupᵢ
 
 /- warning: lower_semicontinuous_supr -> lowerSemicontinuous_supᵢ is a dubious translation:
 lean 3 declaration is
@@ -1018,21 +1018,21 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_supr lowerSemicontinuous_supᵢₓ'. -/
 theorem lowerSemicontinuous_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ⨆ i, f i x' :=
-  lowerSemicontinuous_csupr (by simp) h
+  lowerSemicontinuous_csupᵢ (by simp) h
 #align lower_semicontinuous_supr lowerSemicontinuous_supᵢ
 
-/- warning: lower_semicontinuous_bsupr -> lowerSemicontinuous_bsupr is a dubious translation:
+/- warning: lower_semicontinuous_bsupr -> lowerSemicontinuous_bsupᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
-Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_bsupr lowerSemicontinuous_bsuprₓ'. -/
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem lowerSemicontinuous_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem lowerSemicontinuous_bsupᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
     LowerSemicontinuous fun x' => ⨆ (i) (hi), f i hi x' :=
   lowerSemicontinuous_supᵢ fun i => lowerSemicontinuous_supᵢ fun hi => h i hi
-#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupr
+#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupᵢ
 
 end
 
@@ -1731,18 +1731,18 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-/- warning: upper_semicontinuous_within_at_cinfi -> upperSemicontinuousWithinAt_cinfi is a dubious translation:
+/- warning: upper_semicontinuous_within_at_cinfi -> upperSemicontinuousWithinAt_cinfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfiₓ'. -/
-theorem upperSemicontinuousWithinAt_cinfi {f : ι → α → δ'}
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfᵢₓ'. -/
+theorem upperSemicontinuousWithinAt_cinfᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
-  @lowerSemicontinuousWithinAt_csupr α _ x s ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfi
+  @lowerSemicontinuousWithinAt_csupᵢ α _ x s ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfᵢ
 
 /- warning: upper_semicontinuous_within_at_infi -> upperSemicontinuousWithinAt_infᵢ is a dubious translation:
 lean 3 declaration is
@@ -1756,30 +1756,30 @@ theorem upperSemicontinuousWithinAt_infᵢ {f : ι → α → δ}
   @lowerSemicontinuousWithinAt_supᵢ α _ x s ι δᵒᵈ _ f h
 #align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_infᵢ
 
-/- warning: upper_semicontinuous_within_at_binfi -> upperSemicontinuousWithinAt_binfi is a dubious translation:
+/- warning: upper_semicontinuous_within_at_binfi -> upperSemicontinuousWithinAt_binfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfiₓ'. -/
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuousWithinAt_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuousWithinAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ (i) (hi), f i hi x') s x :=
   upperSemicontinuousWithinAt_infᵢ fun i => upperSemicontinuousWithinAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfi
+#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfᵢ
 
-/- warning: upper_semicontinuous_at_cinfi -> upperSemicontinuousAt_cinfi is a dubious translation:
+/- warning: upper_semicontinuous_at_cinfi -> upperSemicontinuousAt_cinfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfiₓ'. -/
-theorem upperSemicontinuousAt_cinfi {f : ι → α → δ'}
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfᵢₓ'. -/
+theorem upperSemicontinuousAt_cinfᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddBelow (range fun i => f i y)) (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
-  @lowerSemicontinuousAt_csupr α _ x ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfi
+  @lowerSemicontinuousAt_csupᵢ α _ x ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfᵢ
 
 /- warning: upper_semicontinuous_at_infi -> upperSemicontinuousAt_infᵢ is a dubious translation:
 lean 3 declaration is
@@ -1792,30 +1792,30 @@ theorem upperSemicontinuousAt_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSem
   @lowerSemicontinuousAt_supᵢ α _ x ι δᵒᵈ _ f h
 #align upper_semicontinuous_at_infi upperSemicontinuousAt_infᵢ
 
-/- warning: upper_semicontinuous_at_binfi -> upperSemicontinuousAt_binfi is a dubious translation:
+/- warning: upper_semicontinuous_at_binfi -> upperSemicontinuousAt_binfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfiₓ'. -/
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuousAt_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuousAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
     UpperSemicontinuousAt (fun x' => ⨅ (i) (hi), f i hi x') x :=
   upperSemicontinuousAt_infᵢ fun i => upperSemicontinuousAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfi
+#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfᵢ
 
-/- warning: upper_semicontinuous_on_cinfi -> upperSemicontinuousOn_cinfi is a dubious translation:
+/- warning: upper_semicontinuous_on_cinfi -> upperSemicontinuousOn_cinfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfiₓ'. -/
-theorem upperSemicontinuousOn_cinfi {f : ι → α → δ'}
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfᵢₓ'. -/
+theorem upperSemicontinuousOn_cinfᵢ {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddBelow (range fun i => f i x)) (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
-  upperSemicontinuousWithinAt_cinfi (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfi
+  upperSemicontinuousWithinAt_cinfᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfᵢ
 
 /- warning: upper_semicontinuous_on_infi -> upperSemicontinuousOn_infᵢ is a dubious translation:
 lean 3 declaration is
@@ -1828,29 +1828,29 @@ theorem upperSemicontinuousOn_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSem
   upperSemicontinuousWithinAt_infᵢ fun i => h i x hx
 #align upper_semicontinuous_on_infi upperSemicontinuousOn_infᵢ
 
-/- warning: upper_semicontinuous_on_binfi -> upperSemicontinuousOn_binfi is a dubious translation:
+/- warning: upper_semicontinuous_on_binfi -> upperSemicontinuousOn_binfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfiₓ'. -/
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuousOn_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuousOn_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
     UpperSemicontinuousOn (fun x' => ⨅ (i) (hi), f i hi x') s :=
   upperSemicontinuousOn_infᵢ fun i => upperSemicontinuousOn_infᵢ fun hi => h i hi
-#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfi
+#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfᵢ
 
-/- warning: upper_semicontinuous_cinfi -> upperSemicontinuous_cinfi is a dubious translation:
+/- warning: upper_semicontinuous_cinfi -> upperSemicontinuous_cinfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toInfSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_cinfi upperSemicontinuous_cinfiₓ'. -/
-theorem upperSemicontinuous_cinfi {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_cinfi upperSemicontinuous_cinfᵢₓ'. -/
+theorem upperSemicontinuous_cinfᵢ {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
     (h : ∀ i, UpperSemicontinuous (f i)) : UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x =>
-  upperSemicontinuousAt_cinfi (eventually_of_forall bdd) fun i => h i x
-#align upper_semicontinuous_cinfi upperSemicontinuous_cinfi
+  upperSemicontinuousAt_cinfᵢ (eventually_of_forall bdd) fun i => h i x
+#align upper_semicontinuous_cinfi upperSemicontinuous_cinfᵢ
 
 /- warning: upper_semicontinuous_infi -> upperSemicontinuous_infᵢ is a dubious translation:
 lean 3 declaration is
@@ -1862,18 +1862,18 @@ theorem upperSemicontinuous_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemic
     UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_infᵢ fun i => h i x
 #align upper_semicontinuous_infi upperSemicontinuous_infᵢ
 
-/- warning: upper_semicontinuous_binfi -> upperSemicontinuous_binfi is a dubious translation:
+/- warning: upper_semicontinuous_binfi -> upperSemicontinuous_binfᵢ is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
 but is expected to have type
   forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
-Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_binfi upperSemicontinuous_binfiₓ'. -/
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_binfi upperSemicontinuous_binfᵢₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-theorem upperSemicontinuous_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
+theorem upperSemicontinuous_binfᵢ {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
     UpperSemicontinuous fun x' => ⨅ (i) (hi), f i hi x' :=
   upperSemicontinuous_infᵢ fun i => upperSemicontinuous_infᵢ fun hi => h i hi
-#align upper_semicontinuous_binfi upperSemicontinuous_binfi
+#align upper_semicontinuous_binfi upperSemicontinuous_binfᵢ
 
 end
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.semicontinuous
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Instances.Ennreal
 /-!
 # Semicontinuous maps
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A function `f` from a topological space `α` to an ordered space `β` is lower semicontinuous at a
 point `x` if, for any `y < f x`, for any `x'` close enough to `x`, one has `f x' > y`. In other
 words, `f` can jump up, but it can not jump down.

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -67,61 +67,77 @@ variable {α : Type _} [TopologicalSpace α] {β : Type _} [Preorder β] {f g :
 /-! ### Main definitions -/
 
 
+#print LowerSemicontinuousWithinAt /-
 /-- A real function `f` is lower semicontinuous at `x` within a set `s` if, for any `ε > 0`, for all
 `x'` close enough to `x` in  `s`, then `f x'` is at least `f x - ε`. We formulate this in a general
 preordered space, using an arbitrary `y < f x` instead of `f x - ε`. -/
 def LowerSemicontinuousWithinAt (f : α → β) (s : Set α) (x : α) :=
   ∀ y < f x, ∀ᶠ x' in 𝓝[s] x, y < f x'
 #align lower_semicontinuous_within_at LowerSemicontinuousWithinAt
+-/
 
+#print LowerSemicontinuousOn /-
 /-- A real function `f` is lower semicontinuous on a set `s` if, for any `ε > 0`, for any `x ∈ s`,
 for all `x'` close enough to `x` in `s`, then `f x'` is at least `f x - ε`. We formulate this in
 a general preordered space, using an arbitrary `y < f x` instead of `f x - ε`.-/
 def LowerSemicontinuousOn (f : α → β) (s : Set α) :=
   ∀ x ∈ s, LowerSemicontinuousWithinAt f s x
 #align lower_semicontinuous_on LowerSemicontinuousOn
+-/
 
+#print LowerSemicontinuousAt /-
 /-- A real function `f` is lower semicontinuous at `x` if, for any `ε > 0`, for all `x'` close
 enough to `x`, then `f x'` is at least `f x - ε`. We formulate this in a general preordered space,
 using an arbitrary `y < f x` instead of `f x - ε`. -/
 def LowerSemicontinuousAt (f : α → β) (x : α) :=
   ∀ y < f x, ∀ᶠ x' in 𝓝 x, y < f x'
 #align lower_semicontinuous_at LowerSemicontinuousAt
+-/
 
+#print LowerSemicontinuous /-
 /-- A real function `f` is lower semicontinuous if, for any `ε > 0`, for any `x`, for all `x'` close
 enough to `x`, then `f x'` is at least `f x - ε`. We formulate this in a general preordered space,
 using an arbitrary `y < f x` instead of `f x - ε`. -/
 def LowerSemicontinuous (f : α → β) :=
   ∀ x, LowerSemicontinuousAt f x
 #align lower_semicontinuous LowerSemicontinuous
+-/
 
+#print UpperSemicontinuousWithinAt /-
 /-- A real function `f` is upper semicontinuous at `x` within a set `s` if, for any `ε > 0`, for all
 `x'` close enough to `x` in  `s`, then `f x'` is at most `f x + ε`. We formulate this in a general
 preordered space, using an arbitrary `y > f x` instead of `f x + ε`. -/
 def UpperSemicontinuousWithinAt (f : α → β) (s : Set α) (x : α) :=
   ∀ y, f x < y → ∀ᶠ x' in 𝓝[s] x, f x' < y
 #align upper_semicontinuous_within_at UpperSemicontinuousWithinAt
+-/
 
+#print UpperSemicontinuousOn /-
 /-- A real function `f` is upper semicontinuous on a set `s` if, for any `ε > 0`, for any `x ∈ s`,
 for all `x'` close enough to `x` in `s`, then `f x'` is at most `f x + ε`. We formulate this in a
 general preordered space, using an arbitrary `y > f x` instead of `f x + ε`.-/
 def UpperSemicontinuousOn (f : α → β) (s : Set α) :=
   ∀ x ∈ s, UpperSemicontinuousWithinAt f s x
 #align upper_semicontinuous_on UpperSemicontinuousOn
+-/
 
+#print UpperSemicontinuousAt /-
 /-- A real function `f` is upper semicontinuous at `x` if, for any `ε > 0`, for all `x'` close
 enough to `x`, then `f x'` is at most `f x + ε`. We formulate this in a general preordered space,
 using an arbitrary `y > f x` instead of `f x + ε`. -/
 def UpperSemicontinuousAt (f : α → β) (x : α) :=
   ∀ y, f x < y → ∀ᶠ x' in 𝓝 x, f x' < y
 #align upper_semicontinuous_at UpperSemicontinuousAt
+-/
 
+#print UpperSemicontinuous /-
 /-- A real function `f` is upper semicontinuous if, for any `ε > 0`, for any `x`, for all `x'`
 close enough to `x`, then `f x'` is at most `f x + ε`. We formulate this in a general preordered
 space, using an arbitrary `y > f x` instead of `f x + ε`.-/
 def UpperSemicontinuous (f : α → β) :=
   ∀ x, UpperSemicontinuousAt f x
 #align upper_semicontinuous UpperSemicontinuous
+-/
 
 /-!
 ### Lower semicontinuous functions
@@ -131,44 +147,98 @@ def UpperSemicontinuous (f : α → β) :=
 /-! #### Basic dot notation interface for lower semicontinuity -/
 
 
+/- warning: lower_semicontinuous_within_at.mono -> LowerSemicontinuousWithinAt.mono is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f t x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α} {t : Set.{u2} α}, (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) t s) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f t x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at.mono LowerSemicontinuousWithinAt.monoₓ'. -/
 theorem LowerSemicontinuousWithinAt.mono (h : LowerSemicontinuousWithinAt f s x) (hst : t ⊆ s) :
     LowerSemicontinuousWithinAt f t x := fun y hy =>
   Filter.Eventually.filter_mono (nhdsWithin_mono _ hst) (h y hy)
 #align lower_semicontinuous_within_at.mono LowerSemicontinuousWithinAt.mono
 
+/- warning: lower_semicontinuous_within_at_univ_iff -> lowerSemicontinuousWithinAt_univ_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α}, Iff (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α) x) (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α}, Iff (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f (Set.univ.{u2} α) x) (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_univ_iff lowerSemicontinuousWithinAt_univ_iffₓ'. -/
 theorem lowerSemicontinuousWithinAt_univ_iff :
     LowerSemicontinuousWithinAt f univ x ↔ LowerSemicontinuousAt f x := by
   simp [LowerSemicontinuousWithinAt, LowerSemicontinuousAt, nhdsWithin_univ]
 #align lower_semicontinuous_within_at_univ_iff lowerSemicontinuousWithinAt_univ_iff
 
+/- warning: lower_semicontinuous_at.lower_semicontinuous_within_at -> LowerSemicontinuousAt.lowerSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} (s : Set.{u1} α), (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} (s : Set.{u2} α), (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at.lower_semicontinuous_within_at LowerSemicontinuousAt.lowerSemicontinuousWithinAtₓ'. -/
 theorem LowerSemicontinuousAt.lowerSemicontinuousWithinAt (s : Set α)
     (h : LowerSemicontinuousAt f x) : LowerSemicontinuousWithinAt f s x := fun y hy =>
   Filter.Eventually.filter_mono nhdsWithin_le_nhds (h y hy)
 #align lower_semicontinuous_at.lower_semicontinuous_within_at LowerSemicontinuousAt.lowerSemicontinuousWithinAt
 
+/- warning: lower_semicontinuous_on.lower_semicontinuous_within_at -> LowerSemicontinuousOn.lowerSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α}, (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α}, (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.lower_semicontinuous_within_at LowerSemicontinuousOn.lowerSemicontinuousWithinAtₓ'. -/
 theorem LowerSemicontinuousOn.lowerSemicontinuousWithinAt (h : LowerSemicontinuousOn f s)
     (hx : x ∈ s) : LowerSemicontinuousWithinAt f s x :=
   h x hx
 #align lower_semicontinuous_on.lower_semicontinuous_within_at LowerSemicontinuousOn.lowerSemicontinuousWithinAt
 
+/- warning: lower_semicontinuous_on.mono -> LowerSemicontinuousOn.mono is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {s : Set.{u1} α} {t : Set.{u1} α}, (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f t)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {s : Set.{u2} α} {t : Set.{u2} α}, (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) t s) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f t)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.mono LowerSemicontinuousOn.monoₓ'. -/
 theorem LowerSemicontinuousOn.mono (h : LowerSemicontinuousOn f s) (hst : t ⊆ s) :
     LowerSemicontinuousOn f t := fun x hx => (h x (hst hx)).mono hst
 #align lower_semicontinuous_on.mono LowerSemicontinuousOn.mono
 
+/- warning: lower_semicontinuous_on_univ_iff -> lowerSemicontinuousOn_univ_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, Iff (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α)) (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, Iff (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f (Set.univ.{u2} α)) (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_univ_iff lowerSemicontinuousOn_univ_iffₓ'. -/
 theorem lowerSemicontinuousOn_univ_iff : LowerSemicontinuousOn f univ ↔ LowerSemicontinuous f := by
   simp [LowerSemicontinuousOn, LowerSemicontinuous, lowerSemicontinuousWithinAt_univ_iff]
 #align lower_semicontinuous_on_univ_iff lowerSemicontinuousOn_univ_iff
 
+/- warning: lower_semicontinuous.lower_semicontinuous_at -> LowerSemicontinuous.lowerSemicontinuousAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (x : α), LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (x : α), LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.lower_semicontinuous_at LowerSemicontinuous.lowerSemicontinuousAtₓ'. -/
 theorem LowerSemicontinuous.lowerSemicontinuousAt (h : LowerSemicontinuous f) (x : α) :
     LowerSemicontinuousAt f x :=
   h x
 #align lower_semicontinuous.lower_semicontinuous_at LowerSemicontinuous.lowerSemicontinuousAt
 
+/- warning: lower_semicontinuous.lower_semicontinuous_within_at -> LowerSemicontinuous.lowerSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α) (x : α), LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α) (x : α), LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.lower_semicontinuous_within_at LowerSemicontinuous.lowerSemicontinuousWithinAtₓ'. -/
 theorem LowerSemicontinuous.lowerSemicontinuousWithinAt (h : LowerSemicontinuous f) (s : Set α)
     (x : α) : LowerSemicontinuousWithinAt f s x :=
   (h x).LowerSemicontinuousWithinAt s
 #align lower_semicontinuous.lower_semicontinuous_within_at LowerSemicontinuous.lowerSemicontinuousWithinAt
 
+/- warning: lower_semicontinuous.lower_semicontinuous_on -> LowerSemicontinuous.lowerSemicontinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α), LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α), LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.lower_semicontinuous_on LowerSemicontinuous.lowerSemicontinuousOnₓ'. -/
 theorem LowerSemicontinuous.lowerSemicontinuousOn (h : LowerSemicontinuous f) (s : Set α) :
     LowerSemicontinuousOn f s := fun x hx => h.LowerSemicontinuousWithinAt s x
 #align lower_semicontinuous.lower_semicontinuous_on LowerSemicontinuous.lowerSemicontinuousOn
@@ -176,18 +246,42 @@ theorem LowerSemicontinuous.lowerSemicontinuousOn (h : LowerSemicontinuous f) (s
 /-! #### Constants -/
 
 
+/- warning: lower_semicontinuous_within_at_const -> lowerSemicontinuousWithinAt_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {z : β}, LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s x
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {z : β}, LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) s x
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_const lowerSemicontinuousWithinAt_constₓ'. -/
 theorem lowerSemicontinuousWithinAt_const : LowerSemicontinuousWithinAt (fun x => z) s x :=
   fun y hy => Filter.eventually_of_forall fun x => hy
 #align lower_semicontinuous_within_at_const lowerSemicontinuousWithinAt_const
 
+/- warning: lower_semicontinuous_at_const -> lowerSemicontinuousAt_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {z : β}, LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) x
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {z : β}, LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) x
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_const lowerSemicontinuousAt_constₓ'. -/
 theorem lowerSemicontinuousAt_const : LowerSemicontinuousAt (fun x => z) x := fun y hy =>
   Filter.eventually_of_forall fun x => hy
 #align lower_semicontinuous_at_const lowerSemicontinuousAt_const
 
+/- warning: lower_semicontinuous_on_const -> lowerSemicontinuousOn_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {z : β}, LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {z : β}, LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) s
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_const lowerSemicontinuousOn_constₓ'. -/
 theorem lowerSemicontinuousOn_const : LowerSemicontinuousOn (fun x => z) s := fun x hx =>
   lowerSemicontinuousWithinAt_const
 #align lower_semicontinuous_on_const lowerSemicontinuousOn_const
 
+/- warning: lower_semicontinuous_const -> lowerSemicontinuous_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {z : β}, LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {z : β}, LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_const lowerSemicontinuous_constₓ'. -/
 theorem lowerSemicontinuous_const : LowerSemicontinuous fun x : α => z := fun x =>
   lowerSemicontinuousAt_const
 #align lower_semicontinuous_const lowerSemicontinuous_const
@@ -199,6 +293,12 @@ section
 
 variable [Zero β]
 
+/- warning: is_open.lower_semicontinuous_indicator -> IsOpen.lowerSemicontinuous_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
+Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_indicator IsOpen.lowerSemicontinuous_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
@@ -210,21 +310,45 @@ theorem IsOpen.lowerSemicontinuous_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     by_cases h' : x' ∈ s <;> simp [h', hz.trans_le hy, hz]
 #align is_open.lower_semicontinuous_indicator IsOpen.lowerSemicontinuous_indicator
 
+/- warning: is_open.lower_semicontinuous_on_indicator -> IsOpen.lowerSemicontinuousOn_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
+Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_on_indicator IsOpen.lowerSemicontinuousOn_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuousOn_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousOn (indicator s fun x => y) t :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousOn t
 #align is_open.lower_semicontinuous_on_indicator IsOpen.lowerSemicontinuousOn_indicator
 
+/- warning: is_open.lower_semicontinuous_at_indicator -> IsOpen.lowerSemicontinuousAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
+Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_at_indicator IsOpen.lowerSemicontinuousAt_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuousAt_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousAt (indicator s fun x => y) x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousAt x
 #align is_open.lower_semicontinuous_at_indicator IsOpen.lowerSemicontinuousAt_indicator
 
+/- warning: is_open.lower_semicontinuous_within_at_indicator -> IsOpen.lowerSemicontinuousWithinAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
+Case conversion may be inaccurate. Consider using '#align is_open.lower_semicontinuous_within_at_indicator IsOpen.lowerSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsOpen.lowerSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : 0 ≤ y) :
     LowerSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousWithinAt t x
 #align is_open.lower_semicontinuous_within_at_indicator IsOpen.lowerSemicontinuousWithinAt_indicator
 
+/- warning: is_closed.lower_semicontinuous_indicator -> IsClosed.lowerSemicontinuous_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
+Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_indicator IsClosed.lowerSemicontinuous_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuous (indicator s fun x => y) :=
   by
@@ -236,16 +360,34 @@ theorem IsClosed.lowerSemicontinuous_indicator (hs : IsClosed s) (hy : y ≤ 0)
     simp (config := { contextual := true }) [hz]
 #align is_closed.lower_semicontinuous_indicator IsClosed.lowerSemicontinuous_indicator
 
+/- warning: is_closed.lower_semicontinuous_on_indicator -> IsClosed.lowerSemicontinuousOn_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
+Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_on_indicator IsClosed.lowerSemicontinuousOn_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuousOn_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousOn (indicator s fun x => y) t :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousOn t
 #align is_closed.lower_semicontinuous_on_indicator IsClosed.lowerSemicontinuousOn_indicator
 
+/- warning: is_closed.lower_semicontinuous_at_indicator -> IsClosed.lowerSemicontinuousAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
+Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_at_indicator IsClosed.lowerSemicontinuousAt_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuousAt_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousAt (indicator s fun x => y) x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousAt x
 #align is_closed.lower_semicontinuous_at_indicator IsClosed.lowerSemicontinuousAt_indicator
 
+/- warning: is_closed.lower_semicontinuous_within_at_indicator -> IsClosed.lowerSemicontinuousWithinAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
+Case conversion may be inaccurate. Consider using '#align is_closed.lower_semicontinuous_within_at_indicator IsClosed.lowerSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsClosed.lowerSemicontinuousWithinAt_indicator (hs : IsClosed s) (hy : y ≤ 0) :
     LowerSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.lowerSemicontinuous_indicator hy).LowerSemicontinuousWithinAt t x
@@ -256,12 +398,24 @@ end
 /-! #### Relationship with continuity -/
 
 
+/- warning: lower_semicontinuous_iff_is_open_preimage -> lowerSemicontinuous_iff_isOpen_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, Iff (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) (forall (y : β), IsOpen.{u1} α _inst_1 (Set.preimage.{u1, u2} α β f (Set.Ioi.{u2} β _inst_2 y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, Iff (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) (forall (y : β), IsOpen.{u2} α _inst_1 (Set.preimage.{u2, u1} α β f (Set.Ioi.{u1} β _inst_2 y)))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_iff_is_open_preimage lowerSemicontinuous_iff_isOpen_preimageₓ'. -/
 theorem lowerSemicontinuous_iff_isOpen_preimage :
     LowerSemicontinuous f ↔ ∀ y, IsOpen (f ⁻¹' Ioi y) :=
   ⟨fun H y => isOpen_iff_mem_nhds.2 fun x hx => H x y hx, fun H x y y_lt =>
     IsOpen.mem_nhds (H y) y_lt⟩
 #align lower_semicontinuous_iff_is_open_preimage lowerSemicontinuous_iff_isOpen_preimage
 
+/- warning: lower_semicontinuous.is_open_preimage -> LowerSemicontinuous.isOpen_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (LowerSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (y : β), IsOpen.{u1} α _inst_1 (Set.preimage.{u1, u2} α β f (Set.Ioi.{u2} β _inst_2 y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (LowerSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (y : β), IsOpen.{u2} α _inst_1 (Set.preimage.{u2, u1} α β f (Set.Ioi.{u1} β _inst_2 y)))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.is_open_preimage LowerSemicontinuous.isOpen_preimageₓ'. -/
 theorem LowerSemicontinuous.isOpen_preimage (hf : LowerSemicontinuous f) (y : β) :
     IsOpen (f ⁻¹' Ioi y) :=
   lowerSemicontinuous_iff_isOpen_preimage.1 hf y
@@ -271,6 +425,12 @@ section
 
 variable {γ : Type _} [LinearOrder γ]
 
+/- warning: lower_semicontinuous_iff_is_closed_preimage -> lowerSemicontinuous_iff_isClosed_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] {f : α -> γ}, Iff (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) (forall (y : γ), IsClosed.{u1} α _inst_1 (Set.preimage.{u1, u2} α γ f (Set.Iic.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] {f : α -> γ}, Iff (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) (forall (y : γ), IsClosed.{u2} α _inst_1 (Set.preimage.{u2, u1} α γ f (Set.Iic.{u1} γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) y)))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_iff_is_closed_preimage lowerSemicontinuous_iff_isClosed_preimageₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
 theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     LowerSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Iic y) :=
@@ -281,6 +441,12 @@ theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Iic]
 #align lower_semicontinuous_iff_is_closed_preimage lowerSemicontinuous_iff_isClosed_preimage
 
+/- warning: lower_semicontinuous.is_closed_preimage -> LowerSemicontinuous.isClosed_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] {f : α -> γ}, (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (forall (y : γ), IsClosed.{u1} α _inst_1 (Set.preimage.{u1, u2} α γ f (Set.Iic.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] {f : α -> γ}, (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) -> (forall (y : γ), IsClosed.{u2} α _inst_1 (Set.preimage.{u2, u1} α γ f (Set.Iic.{u1} γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) y)))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.is_closed_preimage LowerSemicontinuous.isClosed_preimageₓ'. -/
 theorem LowerSemicontinuous.isClosed_preimage {f : α → γ} (hf : LowerSemicontinuous f) (y : γ) :
     IsClosed (f ⁻¹' Iic y) :=
   lowerSemicontinuous_iff_isClosed_preimage.1 hf y
@@ -288,18 +454,42 @@ theorem LowerSemicontinuous.isClosed_preimage {f : α → γ} (hf : LowerSemicon
 
 variable [TopologicalSpace γ] [OrderTopology γ]
 
+/- warning: continuous_within_at.lower_semicontinuous_within_at -> ContinuousWithinAt.lowerSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f s x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousWithinAt.{u2, u1} α γ _inst_1 _inst_4 f s x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s x)
+Case conversion may be inaccurate. Consider using '#align continuous_within_at.lower_semicontinuous_within_at ContinuousWithinAt.lowerSemicontinuousWithinAtₓ'. -/
 theorem ContinuousWithinAt.lowerSemicontinuousWithinAt {f : α → γ} (h : ContinuousWithinAt f s x) :
     LowerSemicontinuousWithinAt f s x := fun y hy => h (Ioi_mem_nhds hy)
 #align continuous_within_at.lower_semicontinuous_within_at ContinuousWithinAt.lowerSemicontinuousWithinAt
 
+/- warning: continuous_at.lower_semicontinuous_at -> ContinuousAt.lowerSemicontinuousAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousAt.{u1, u2} α γ _inst_1 _inst_4 f x) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousAt.{u2, u1} α γ _inst_1 _inst_4 f x) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.lower_semicontinuous_at ContinuousAt.lowerSemicontinuousAtₓ'. -/
 theorem ContinuousAt.lowerSemicontinuousAt {f : α → γ} (h : ContinuousAt f x) :
     LowerSemicontinuousAt f x := fun y hy => h (Ioi_mem_nhds hy)
 #align continuous_at.lower_semicontinuous_at ContinuousAt.lowerSemicontinuousAt
 
+/- warning: continuous_on.lower_semicontinuous_on -> ContinuousOn.lowerSemicontinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousOn.{u1, u2} α γ _inst_1 _inst_4 f s) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousOn.{u2, u1} α γ _inst_1 _inst_4 f s) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s)
+Case conversion may be inaccurate. Consider using '#align continuous_on.lower_semicontinuous_on ContinuousOn.lowerSemicontinuousOnₓ'. -/
 theorem ContinuousOn.lowerSemicontinuousOn {f : α → γ} (h : ContinuousOn f s) :
     LowerSemicontinuousOn f s := fun x hx => (h x hx).LowerSemicontinuousWithinAt
 #align continuous_on.lower_semicontinuous_on ContinuousOn.lowerSemicontinuousOn
 
+/- warning: continuous.lower_semicontinuous -> Continuous.lowerSemicontinuous is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (Continuous.{u1, u2} α γ _inst_1 _inst_4 f) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (Continuous.{u2, u1} α γ _inst_1 _inst_4 f) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f)
+Case conversion may be inaccurate. Consider using '#align continuous.lower_semicontinuous Continuous.lowerSemicontinuousₓ'. -/
 theorem Continuous.lowerSemicontinuous {f : α → γ} (h : Continuous f) : LowerSemicontinuous f :=
   fun x => h.ContinuousAt.LowerSemicontinuousAt
 #align continuous.lower_semicontinuous Continuous.lowerSemicontinuous
@@ -315,6 +505,12 @@ variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
+/- warning: continuous_at.comp_lower_semicontinuous_within_at -> ContinuousAt.comp_lowerSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s x) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAtₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     LowerSemicontinuousWithinAt (g ∘ f) s x :=
@@ -332,6 +528,12 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
     exact Filter.eventually_of_forall fun a => hy.trans_le (gmon (h (f a)))
 #align continuous_at.comp_lower_semicontinuous_within_at ContinuousAt.comp_lowerSemicontinuousWithinAt
 
+/- warning: continuous_at.comp_lower_semicontinuous_at -> ContinuousAt.comp_lowerSemicontinuousAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f x) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_at ContinuousAt.comp_lowerSemicontinuousAtₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : LowerSemicontinuousAt f x) (gmon : Monotone g) : LowerSemicontinuousAt (g ∘ f) x :=
   by
@@ -339,33 +541,69 @@ theorem ContinuousAt.comp_lowerSemicontinuousAt {g : γ → δ} {f : α → γ}
   exact hg.comp_lower_semicontinuous_within_at hf gmon
 #align continuous_at.comp_lower_semicontinuous_at ContinuousAt.comp_lowerSemicontinuousAt
 
+/- warning: continuous.comp_lower_semicontinuous_on -> Continuous.comp_lowerSemicontinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s)
+Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous_on Continuous.comp_lowerSemicontinuousOnₓ'. -/
 theorem Continuous.comp_lowerSemicontinuousOn {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuousOn f s) (gmon : Monotone g) : LowerSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_lowerSemicontinuousWithinAt (hf x hx) gmon
 #align continuous.comp_lower_semicontinuous_on Continuous.comp_lowerSemicontinuousOn
 
+/- warning: continuous.comp_lower_semicontinuous -> Continuous.comp_lowerSemicontinuous is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuous.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f))
+Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous Continuous.comp_lowerSemicontinuousₓ'. -/
 theorem Continuous.comp_lowerSemicontinuous {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuous f) (gmon : Monotone g) : LowerSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_lowerSemicontinuousAt (hf x) gmon
 #align continuous.comp_lower_semicontinuous Continuous.comp_lowerSemicontinuous
 
+/- warning: continuous_at.comp_lower_semicontinuous_within_at_antitone -> ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s x) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_within_at_antitone ContinuousAt.comp_lowerSemicontinuousWithinAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Antitone g) :
     UpperSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_lowerSemicontinuousWithinAt α _ x s γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_lower_semicontinuous_within_at_antitone ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone
 
+/- warning: continuous_at.comp_lower_semicontinuous_at_antitone -> ContinuousAt.comp_lowerSemicontinuousAt_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f x) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_lower_semicontinuous_at_antitone ContinuousAt.comp_lowerSemicontinuousAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_lowerSemicontinuousAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousAt f x) (gmon : Antitone g) :
     UpperSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_lowerSemicontinuousAt α _ x γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_lower_semicontinuous_at_antitone ContinuousAt.comp_lowerSemicontinuousAt_antitone
 
+/- warning: continuous.comp_lower_semicontinuous_on_antitone -> Continuous.comp_lowerSemicontinuousOn_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s)
+Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous_on_antitone Continuous.comp_lowerSemicontinuousOn_antitoneₓ'. -/
 theorem Continuous.comp_lowerSemicontinuousOn_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuousOn f s) (gmon : Antitone g) : UpperSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_lowerSemicontinuousWithinAt_antitone (hf x hx) gmon
 #align continuous.comp_lower_semicontinuous_on_antitone Continuous.comp_lowerSemicontinuousOn_antitone
 
+/- warning: continuous.comp_lower_semicontinuous_antitone -> Continuous.comp_lowerSemicontinuous_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (LowerSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuous.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f))
+Case conversion may be inaccurate. Consider using '#align continuous.comp_lower_semicontinuous_antitone Continuous.comp_lowerSemicontinuous_antitoneₓ'. -/
 theorem Continuous.comp_lowerSemicontinuous_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : LowerSemicontinuous f) (gmon : Antitone g) : UpperSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_lowerSemicontinuousAt_antitone (hf x) gmon
@@ -381,6 +619,12 @@ section
 variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
   [OrderTopology γ]
 
+/- warning: lower_semicontinuous_within_at.add' -> LowerSemicontinuousWithinAt.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s x) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s x) -> (ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x))) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at.add' LowerSemicontinuousWithinAt.add'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -462,6 +706,12 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         
 #align lower_semicontinuous_within_at.add' LowerSemicontinuousWithinAt.add'
 
+/- warning: lower_semicontinuous_at.add' -> LowerSemicontinuousAt.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f x) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g x) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f x) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g x) -> (ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x))) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at.add' LowerSemicontinuousAt.add'ₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -474,6 +724,12 @@ theorem LowerSemicontinuousAt.add' {f g : α → γ} (hf : LowerSemicontinuousAt
   exact hf.add' hg hcont
 #align lower_semicontinuous_at.add' LowerSemicontinuousAt.add'
 
+/- warning: lower_semicontinuous_on.add' -> LowerSemicontinuousOn.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x)))) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s) -> (forall (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x)))) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.add' LowerSemicontinuousOn.add'ₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -484,6 +740,12 @@ theorem LowerSemicontinuousOn.add' {f g : α → γ} (hf : LowerSemicontinuousOn
   (hf x hx).add' (hg x hx) (hcont x hx)
 #align lower_semicontinuous_on.add' LowerSemicontinuousOn.add'
 
+/- warning: lower_semicontinuous.add' -> LowerSemicontinuous.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g) -> (forall (x : α), ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g) -> (forall (x : α), ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x))) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.add' LowerSemicontinuous.add'ₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -495,6 +757,12 @@ theorem LowerSemicontinuous.add' {f g : α → γ} (hf : LowerSemicontinuous f)
 
 variable [ContinuousAdd γ]
 
+/- warning: lower_semicontinuous_within_at.add -> LowerSemicontinuousWithinAt.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s x) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s x) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at.add LowerSemicontinuousWithinAt.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -504,6 +772,12 @@ theorem LowerSemicontinuousWithinAt.add {f g : α → γ} (hf : LowerSemicontinu
   hf.add' hg continuous_add.ContinuousAt
 #align lower_semicontinuous_within_at.add LowerSemicontinuousWithinAt.add
 
+/- warning: lower_semicontinuous_at.add -> LowerSemicontinuousAt.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f x) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g x) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f x) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g x) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at.add LowerSemicontinuousAt.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -512,6 +786,12 @@ theorem LowerSemicontinuousAt.add {f g : α → γ} (hf : LowerSemicontinuousAt
   hf.add' hg continuous_add.ContinuousAt
 #align lower_semicontinuous_at.add LowerSemicontinuousAt.add
 
+/- warning: lower_semicontinuous_on.add -> LowerSemicontinuousOn.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on.add LowerSemicontinuousOn.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -520,6 +800,12 @@ theorem LowerSemicontinuousOn.add {f g : α → γ} (hf : LowerSemicontinuousOn
   hf.add' hg fun x hx => continuous_add.ContinuousAt
 #align lower_semicontinuous_on.add LowerSemicontinuousOn.add
 
+/- warning: lower_semicontinuous.add -> LowerSemicontinuous.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g) -> (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous.add LowerSemicontinuous.addₓ'. -/
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -528,6 +814,12 @@ theorem LowerSemicontinuous.add {f g : α → γ} (hf : LowerSemicontinuous f)
   hf.add' hg fun x => continuous_add.ContinuousAt
 #align lower_semicontinuous.add LowerSemicontinuous.add
 
+/- warning: lower_semicontinuous_within_at_sum -> lowerSemicontinuousWithinAt_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) s x)) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) s x)) -> (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sumₓ'. -/
 theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x := by
@@ -540,6 +832,12 @@ theorem lowerSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
           (IH fun j ja => ha j (Finset.mem_insert_of_mem ja))
 #align lower_semicontinuous_within_at_sum lowerSemicontinuousWithinAt_sum
 
+/- warning: lower_semicontinuous_at_sum -> lowerSemicontinuousAt_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) x)) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) x)) -> (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_sum lowerSemicontinuousAt_sumₓ'. -/
 theorem lowerSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun z => ∑ i in a, f i z) x :=
@@ -548,12 +846,24 @@ theorem lowerSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
   exact lowerSemicontinuousWithinAt_sum ha
 #align lower_semicontinuous_at_sum lowerSemicontinuousAt_sum
 
+/- warning: lower_semicontinuous_on_sum -> lowerSemicontinuousOn_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) s)) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) s)) -> (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_sum lowerSemicontinuousOn_sumₓ'. -/
 theorem lowerSemicontinuousOn_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun z => ∑ i in a, f i z) s := fun x hx =>
   lowerSemicontinuousWithinAt_sum fun i hi => ha i hi x hx
 #align lower_semicontinuous_on_sum lowerSemicontinuousOn_sum
 
+/- warning: lower_semicontinuous_sum -> lowerSemicontinuous_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (LowerSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i))) -> (LowerSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i))) -> (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_sum lowerSemicontinuous_sumₓ'. -/
 theorem lowerSemicontinuous_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, LowerSemicontinuous (f i)) : LowerSemicontinuous fun z => ∑ i in a, f i z :=
   fun x => lowerSemicontinuousAt_sum fun i hi => ha i hi x
@@ -568,6 +878,12 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
+/- warning: lower_semicontinuous_within_at_csupr -> lowerSemicontinuousWithinAt_csupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csuprₓ'. -/
 theorem lowerSemicontinuousWithinAt_csupr {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
@@ -580,12 +896,24 @@ theorem lowerSemicontinuousWithinAt_csupr {f : ι → α → δ'}
     filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_csupᵢ hy' i)
 #align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupr
 
+/- warning: lower_semicontinuous_within_at_supr -> lowerSemicontinuousWithinAt_supᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_supᵢₓ'. -/
 theorem lowerSemicontinuousWithinAt_supᵢ {f : ι → α → δ}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
   lowerSemicontinuousWithinAt_csupr (by simp) h
 #align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_supᵢ
 
+/- warning: lower_semicontinuous_within_at_bsupr -> lowerSemicontinuousWithinAt_bsupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (LowerSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsuprₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuousWithinAt_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
@@ -593,6 +921,12 @@ theorem lowerSemicontinuousWithinAt_bsupr {p : ι → Prop} {f : ∀ (i) (h : p
   lowerSemicontinuousWithinAt_supᵢ fun i => lowerSemicontinuousWithinAt_supᵢ fun hi => h i hi
 #align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupr
 
+/- warning: lower_semicontinuous_at_csupr -> lowerSemicontinuousAt_csupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csuprₓ'. -/
 theorem lowerSemicontinuousAt_csupr {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddAbove (range fun i => f i y)) (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
@@ -602,11 +936,23 @@ theorem lowerSemicontinuousAt_csupr {f : ι → α → δ'}
   exact lowerSemicontinuousWithinAt_csupr bdd h
 #align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupr
 
+/- warning: lower_semicontinuous_at_supr -> lowerSemicontinuousAt_supᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢₓ'. -/
 theorem lowerSemicontinuousAt_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
   lowerSemicontinuousAt_csupr (by simp) h
 #align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢ
 
+/- warning: lower_semicontinuous_at_bsupr -> lowerSemicontinuousAt_bsupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (LowerSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsuprₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuousAt_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
@@ -614,17 +960,35 @@ theorem lowerSemicontinuousAt_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α
   lowerSemicontinuousAt_supᵢ fun i => lowerSemicontinuousAt_supᵢ fun hi => h i hi
 #align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupr
 
+/- warning: lower_semicontinuous_on_csupr -> lowerSemicontinuousOn_csupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddAbove.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toSupSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csuprₓ'. -/
 theorem lowerSemicontinuousOn_csupr {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddAbove (range fun i => f i x)) (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s := fun x hx =>
   lowerSemicontinuousWithinAt_csupr (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
 #align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupr
 
+/- warning: lower_semicontinuous_on_supr -> lowerSemicontinuousOn_supᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢₓ'. -/
 theorem lowerSemicontinuousOn_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s :=
   lowerSemicontinuousOn_csupr (by simp) h
 #align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢ
 
+/- warning: lower_semicontinuous_on_bsupr -> lowerSemicontinuousOn_bsupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (LowerSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsuprₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuousOn_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
@@ -632,16 +996,34 @@ theorem lowerSemicontinuousOn_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α
   lowerSemicontinuousOn_supᵢ fun i => lowerSemicontinuousOn_supᵢ fun hi => h i hi
 #align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupr
 
+/- warning: lower_semicontinuous_csupr -> lowerSemicontinuous_csupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasSup.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddAbove.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => supᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toSupSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_csupr lowerSemicontinuous_csuprₓ'. -/
 theorem lowerSemicontinuous_csupr {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
     (h : ∀ i, LowerSemicontinuous (f i)) : LowerSemicontinuous fun x' => ⨆ i, f i x' := fun x =>
   lowerSemicontinuousAt_csupr (eventually_of_forall bdd) fun i => h i x
 #align lower_semicontinuous_csupr lowerSemicontinuous_csupr
 
+/- warning: lower_semicontinuous_supr -> lowerSemicontinuous_supᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')))
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_supr lowerSemicontinuous_supᵢₓ'. -/
 theorem lowerSemicontinuous_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ⨆ i, f i x' :=
   lowerSemicontinuous_csupr (by simp) h
 #align lower_semicontinuous_supr lowerSemicontinuous_supᵢ
 
+/- warning: lower_semicontinuous_bsupr -> lowerSemicontinuous_bsupr is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => supᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => supᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasSup.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (LowerSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => supᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => supᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toSupSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_bsupr lowerSemicontinuous_bsuprₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem lowerSemicontinuous_bsupr {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
@@ -658,6 +1040,12 @@ section
 
 variable {ι : Type _}
 
+/- warning: lower_semicontinuous_within_at_tsum -> lowerSemicontinuousWithinAt_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousWithinAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')) s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousWithinAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i) s x) -> (LowerSemicontinuousWithinAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsumₓ'. -/
 theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ∑' i, f i x') s x :=
@@ -667,6 +1055,12 @@ theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
   exact lowerSemicontinuousWithinAt_sum fun i hi => h i
 #align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsum
 
+/- warning: lower_semicontinuous_at_tsum -> lowerSemicontinuousAt_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i) x) -> (LowerSemicontinuousAt.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i) x) -> (LowerSemicontinuousAt.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_at_tsum lowerSemicontinuousAt_tsumₓ'. -/
 theorem lowerSemicontinuousAt_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ∑' i, f i x') x :=
   by
@@ -674,11 +1068,23 @@ theorem lowerSemicontinuousAt_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, Lo
   exact lowerSemicontinuousWithinAt_tsum h
 #align lower_semicontinuous_at_tsum lowerSemicontinuousAt_tsum
 
+/- warning: lower_semicontinuous_on_tsum -> lowerSemicontinuousOn_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousOn.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i) s) -> (LowerSemicontinuousOn.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')) s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuousOn.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i) s) -> (LowerSemicontinuousOn.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_on_tsum lowerSemicontinuousOn_tsumₓ'. -/
 theorem lowerSemicontinuousOn_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ∑' i, f i x') s := fun x hx =>
   lowerSemicontinuousWithinAt_tsum fun i => h i x hx
 #align lower_semicontinuous_on_tsum lowerSemicontinuousOn_tsum
 
+/- warning: lower_semicontinuous_tsum -> lowerSemicontinuous_tsum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Type.{u2}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuous.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (f i)) -> (LowerSemicontinuous.{u1, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedAddCommMonoid.toPartialOrder.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))) (fun (x' : α) => tsum.{0, u2} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace ι (fun (i : ι) => f i x')))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {ι : Type.{u1}} {f : ι -> α -> ENNReal}, (forall (i : ι), LowerSemicontinuous.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (f i)) -> (LowerSemicontinuous.{u2, 0} α _inst_1 ENNReal (PartialOrder.toPreorder.{0} ENNReal (OrderedSemiring.toPartialOrder.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))) (fun (x' : α) => tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align lower_semicontinuous_tsum lowerSemicontinuous_tsumₓ'. -/
 theorem lowerSemicontinuous_tsum {f : ι → α → ℝ≥0∞} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ∑' i, f i x' := fun x => lowerSemicontinuousAt_tsum fun i => h i x
 #align lower_semicontinuous_tsum lowerSemicontinuous_tsum
@@ -693,44 +1099,98 @@ end
 /-! #### Basic dot notation interface for upper semicontinuity -/
 
 
+/- warning: upper_semicontinuous_within_at.mono -> UpperSemicontinuousWithinAt.mono is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f t x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α} {t : Set.{u2} α}, (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) t s) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f t x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at.mono UpperSemicontinuousWithinAt.monoₓ'. -/
 theorem UpperSemicontinuousWithinAt.mono (h : UpperSemicontinuousWithinAt f s x) (hst : t ⊆ s) :
     UpperSemicontinuousWithinAt f t x := fun y hy =>
   Filter.Eventually.filter_mono (nhdsWithin_mono _ hst) (h y hy)
 #align upper_semicontinuous_within_at.mono UpperSemicontinuousWithinAt.mono
 
+/- warning: upper_semicontinuous_within_at_univ_iff -> upperSemicontinuousWithinAt_univ_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α}, Iff (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α) x) (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α}, Iff (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f (Set.univ.{u2} α) x) (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_univ_iff upperSemicontinuousWithinAt_univ_iffₓ'. -/
 theorem upperSemicontinuousWithinAt_univ_iff :
     UpperSemicontinuousWithinAt f univ x ↔ UpperSemicontinuousAt f x := by
   simp [UpperSemicontinuousWithinAt, UpperSemicontinuousAt, nhdsWithin_univ]
 #align upper_semicontinuous_within_at_univ_iff upperSemicontinuousWithinAt_univ_iff
 
+/- warning: upper_semicontinuous_at.upper_semicontinuous_within_at -> UpperSemicontinuousAt.upperSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} (s : Set.{u1} α), (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} (s : Set.{u2} α), (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at.upper_semicontinuous_within_at UpperSemicontinuousAt.upperSemicontinuousWithinAtₓ'. -/
 theorem UpperSemicontinuousAt.upperSemicontinuousWithinAt (s : Set α)
     (h : UpperSemicontinuousAt f x) : UpperSemicontinuousWithinAt f s x := fun y hy =>
   Filter.Eventually.filter_mono nhdsWithin_le_nhds (h y hy)
 #align upper_semicontinuous_at.upper_semicontinuous_within_at UpperSemicontinuousAt.upperSemicontinuousWithinAt
 
+/- warning: upper_semicontinuous_on.upper_semicontinuous_within_at -> UpperSemicontinuousOn.upperSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {x : α} {s : Set.{u1} α}, (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {x : α} {s : Set.{u2} α}, (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s) -> (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.upper_semicontinuous_within_at UpperSemicontinuousOn.upperSemicontinuousWithinAtₓ'. -/
 theorem UpperSemicontinuousOn.upperSemicontinuousWithinAt (h : UpperSemicontinuousOn f s)
     (hx : x ∈ s) : UpperSemicontinuousWithinAt f s x :=
   h x hx
 #align upper_semicontinuous_on.upper_semicontinuous_within_at UpperSemicontinuousOn.upperSemicontinuousWithinAt
 
+/- warning: upper_semicontinuous_on.mono -> UpperSemicontinuousOn.mono is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β} {s : Set.{u1} α} {t : Set.{u1} α}, (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f t)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β} {s : Set.{u2} α} {t : Set.{u2} α}, (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) t s) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f t)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.mono UpperSemicontinuousOn.monoₓ'. -/
 theorem UpperSemicontinuousOn.mono (h : UpperSemicontinuousOn f s) (hst : t ⊆ s) :
     UpperSemicontinuousOn f t := fun x hx => (h x (hst hx)).mono hst
 #align upper_semicontinuous_on.mono UpperSemicontinuousOn.mono
 
+/- warning: upper_semicontinuous_on_univ_iff -> upperSemicontinuousOn_univ_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, Iff (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f (Set.univ.{u1} α)) (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, Iff (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f (Set.univ.{u2} α)) (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_univ_iff upperSemicontinuousOn_univ_iffₓ'. -/
 theorem upperSemicontinuousOn_univ_iff : UpperSemicontinuousOn f univ ↔ UpperSemicontinuous f := by
   simp [UpperSemicontinuousOn, UpperSemicontinuous, upperSemicontinuousWithinAt_univ_iff]
 #align upper_semicontinuous_on_univ_iff upperSemicontinuousOn_univ_iff
 
+/- warning: upper_semicontinuous.upper_semicontinuous_at -> UpperSemicontinuous.upperSemicontinuousAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (x : α), UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 f x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (x : α), UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 f x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.upper_semicontinuous_at UpperSemicontinuous.upperSemicontinuousAtₓ'. -/
 theorem UpperSemicontinuous.upperSemicontinuousAt (h : UpperSemicontinuous f) (x : α) :
     UpperSemicontinuousAt f x :=
   h x
 #align upper_semicontinuous.upper_semicontinuous_at UpperSemicontinuous.upperSemicontinuousAt
 
+/- warning: upper_semicontinuous.upper_semicontinuous_within_at -> UpperSemicontinuous.upperSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α) (x : α), UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α) (x : α), UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 f s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.upper_semicontinuous_within_at UpperSemicontinuous.upperSemicontinuousWithinAtₓ'. -/
 theorem UpperSemicontinuous.upperSemicontinuousWithinAt (h : UpperSemicontinuous f) (s : Set α)
     (x : α) : UpperSemicontinuousWithinAt f s x :=
   (h x).UpperSemicontinuousWithinAt s
 #align upper_semicontinuous.upper_semicontinuous_within_at UpperSemicontinuous.upperSemicontinuousWithinAt
 
+/- warning: upper_semicontinuous.upper_semicontinuous_on -> UpperSemicontinuous.upperSemicontinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u1} α), UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 f s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (s : Set.{u2} α), UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 f s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.upper_semicontinuous_on UpperSemicontinuous.upperSemicontinuousOnₓ'. -/
 theorem UpperSemicontinuous.upperSemicontinuousOn (h : UpperSemicontinuous f) (s : Set α) :
     UpperSemicontinuousOn f s := fun x hx => h.UpperSemicontinuousWithinAt s x
 #align upper_semicontinuous.upper_semicontinuous_on UpperSemicontinuous.upperSemicontinuousOn
@@ -738,18 +1198,42 @@ theorem UpperSemicontinuous.upperSemicontinuousOn (h : UpperSemicontinuous f) (s
 /-! #### Constants -/
 
 
+/- warning: upper_semicontinuous_within_at_const -> upperSemicontinuousWithinAt_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {z : β}, UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s x
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {z : β}, UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) s x
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_const upperSemicontinuousWithinAt_constₓ'. -/
 theorem upperSemicontinuousWithinAt_const : UpperSemicontinuousWithinAt (fun x => z) s x :=
   fun y hy => Filter.eventually_of_forall fun x => hy
 #align upper_semicontinuous_within_at_const upperSemicontinuousWithinAt_const
 
+/- warning: upper_semicontinuous_at_const -> upperSemicontinuousAt_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {z : β}, UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) x
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {z : β}, UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) x
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_const upperSemicontinuousAt_constₓ'. -/
 theorem upperSemicontinuousAt_const : UpperSemicontinuousAt (fun x => z) x := fun y hy =>
   Filter.eventually_of_forall fun x => hy
 #align upper_semicontinuous_at_const upperSemicontinuousAt_const
 
+/- warning: upper_semicontinuous_on_const -> upperSemicontinuousOn_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {z : β}, UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z) s
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {z : β}, UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z) s
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_const upperSemicontinuousOn_constₓ'. -/
 theorem upperSemicontinuousOn_const : UpperSemicontinuousOn (fun x => z) s := fun x hx =>
   upperSemicontinuousWithinAt_const
 #align upper_semicontinuous_on_const upperSemicontinuousOn_const
 
+/- warning: upper_semicontinuous_const -> upperSemicontinuous_const is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {z : β}, UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (fun (x : α) => z)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {z : β}, UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (fun (x : α) => z)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_const upperSemicontinuous_constₓ'. -/
 theorem upperSemicontinuous_const : UpperSemicontinuous fun x : α => z := fun x =>
   upperSemicontinuousAt_const
 #align upper_semicontinuous_const upperSemicontinuous_const
@@ -761,41 +1245,89 @@ section
 
 variable [Zero β]
 
+/- warning: is_open.upper_semicontinuous_indicator -> IsOpen.upperSemicontinuous_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
+Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_indicator IsOpen.upperSemicontinuous_indicatorₓ'. -/
 theorem IsOpen.upperSemicontinuous_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuous (indicator s fun x => y) :=
   @IsOpen.lowerSemicontinuous_indicator α _ βᵒᵈ _ s y _ hs hy
 #align is_open.upper_semicontinuous_indicator IsOpen.upperSemicontinuous_indicator
 
+/- warning: is_open.upper_semicontinuous_on_indicator -> IsOpen.upperSemicontinuousOn_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
+Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_on_indicator IsOpen.upperSemicontinuousOn_indicatorₓ'. -/
 theorem IsOpen.upperSemicontinuousOn_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousOn (indicator s fun x => y) t :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousOn t
 #align is_open.upper_semicontinuous_on_indicator IsOpen.upperSemicontinuousOn_indicator
 
+/- warning: is_open.upper_semicontinuous_at_indicator -> IsOpen.upperSemicontinuousAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
+Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_at_indicator IsOpen.upperSemicontinuousAt_indicatorₓ'. -/
 theorem IsOpen.upperSemicontinuousAt_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousAt (indicator s fun x => y) x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousAt x
 #align is_open.upper_semicontinuous_at_indicator IsOpen.upperSemicontinuousAt_indicator
 
+/- warning: is_open.upper_semicontinuous_within_at_indicator -> IsOpen.upperSemicontinuousWithinAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsOpen.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) y (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3)))) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsOpen.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) y (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3))) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
+Case conversion may be inaccurate. Consider using '#align is_open.upper_semicontinuous_within_at_indicator IsOpen.upperSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsOpen.upperSemicontinuousWithinAt_indicator (hs : IsOpen s) (hy : y ≤ 0) :
     UpperSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousWithinAt t x
 #align is_open.upper_semicontinuous_within_at_indicator IsOpen.upperSemicontinuousWithinAt_indicator
 
+/- warning: is_closed.upper_semicontinuous_indicator -> IsClosed.upperSemicontinuous_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)))
+Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_indicator IsClosed.upperSemicontinuous_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuous_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuous (indicator s fun x => y) :=
   @IsClosed.lowerSemicontinuous_indicator α _ βᵒᵈ _ s y _ hs hy
 #align is_closed.upper_semicontinuous_indicator IsClosed.upperSemicontinuous_indicator
 
+/- warning: is_closed.upper_semicontinuous_on_indicator -> IsClosed.upperSemicontinuousOn_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t)
+Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_on_indicator IsClosed.upperSemicontinuousOn_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuousOn_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousOn (indicator s fun x => y) t :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousOn t
 #align is_closed.upper_semicontinuous_on_indicator IsClosed.upperSemicontinuousOn_indicator
 
+/- warning: is_closed.upper_semicontinuous_at_indicator -> IsClosed.upperSemicontinuousAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) x)
+Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_at_indicator IsClosed.upperSemicontinuousAt_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuousAt_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousAt (indicator s fun x => y) x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousAt x
 #align is_closed.upper_semicontinuous_at_indicator IsClosed.upperSemicontinuousAt_indicator
 
+/- warning: is_closed.upper_semicontinuous_within_at_indicator -> IsClosed.upperSemicontinuousWithinAt_indicator is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {x : α} {s : Set.{u1} α} {t : Set.{u1} α} {y : β} [_inst_3 : Zero.{u2} β], (IsClosed.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β _inst_2) (OfNat.ofNat.{u2} β 0 (OfNat.mk.{u2} β 0 (Zero.zero.{u2} β _inst_3))) y) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 β _inst_2 (Set.indicator.{u1, u2} α β _inst_3 s (fun (x : α) => y)) t x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {x : α} {s : Set.{u2} α} {t : Set.{u2} α} {y : β} [_inst_3 : Zero.{u1} β], (IsClosed.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β _inst_2) (OfNat.ofNat.{u1} β 0 (Zero.toOfNat0.{u1} β _inst_3)) y) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 β _inst_2 (Set.indicator.{u2, u1} α β _inst_3 s (fun (x : α) => y)) t x)
+Case conversion may be inaccurate. Consider using '#align is_closed.upper_semicontinuous_within_at_indicator IsClosed.upperSemicontinuousWithinAt_indicatorₓ'. -/
 theorem IsClosed.upperSemicontinuousWithinAt_indicator (hs : IsClosed s) (hy : 0 ≤ y) :
     UpperSemicontinuousWithinAt (indicator s fun x => y) t x :=
   (hs.upperSemicontinuous_indicator hy).UpperSemicontinuousWithinAt t x
@@ -806,12 +1338,24 @@ end
 /-! #### Relationship with continuity -/
 
 
+/- warning: upper_semicontinuous_iff_is_open_preimage -> upperSemicontinuous_iff_isOpen_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, Iff (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) (forall (y : β), IsOpen.{u1} α _inst_1 (Set.preimage.{u1, u2} α β f (Set.Iio.{u2} β _inst_2 y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, Iff (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) (forall (y : β), IsOpen.{u2} α _inst_1 (Set.preimage.{u2, u1} α β f (Set.Iio.{u1} β _inst_2 y)))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_iff_is_open_preimage upperSemicontinuous_iff_isOpen_preimageₓ'. -/
 theorem upperSemicontinuous_iff_isOpen_preimage :
     UpperSemicontinuous f ↔ ∀ y, IsOpen (f ⁻¹' Iio y) :=
   ⟨fun H y => isOpen_iff_mem_nhds.2 fun x hx => H x y hx, fun H x y y_lt =>
     IsOpen.mem_nhds (H y) y_lt⟩
 #align upper_semicontinuous_iff_is_open_preimage upperSemicontinuous_iff_isOpen_preimage
 
+/- warning: upper_semicontinuous.is_open_preimage -> UpperSemicontinuous.isOpen_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {β : Type.{u2}} [_inst_2 : Preorder.{u2} β] {f : α -> β}, (UpperSemicontinuous.{u1, u2} α _inst_1 β _inst_2 f) -> (forall (y : β), IsOpen.{u1} α _inst_1 (Set.preimage.{u1, u2} α β f (Set.Iio.{u2} β _inst_2 y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {β : Type.{u1}} [_inst_2 : Preorder.{u1} β] {f : α -> β}, (UpperSemicontinuous.{u2, u1} α _inst_1 β _inst_2 f) -> (forall (y : β), IsOpen.{u2} α _inst_1 (Set.preimage.{u2, u1} α β f (Set.Iio.{u1} β _inst_2 y)))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.is_open_preimage UpperSemicontinuous.isOpen_preimageₓ'. -/
 theorem UpperSemicontinuous.isOpen_preimage (hf : UpperSemicontinuous f) (y : β) :
     IsOpen (f ⁻¹' Iio y) :=
   upperSemicontinuous_iff_isOpen_preimage.1 hf y
@@ -821,6 +1365,12 @@ section
 
 variable {γ : Type _} [LinearOrder γ]
 
+/- warning: upper_semicontinuous_iff_is_closed_preimage -> upperSemicontinuous_iff_isClosed_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] {f : α -> γ}, Iff (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) (forall (y : γ), IsClosed.{u1} α _inst_1 (Set.preimage.{u1, u2} α γ f (Set.Ici.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] {f : α -> γ}, Iff (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) (forall (y : γ), IsClosed.{u2} α _inst_1 (Set.preimage.{u2, u1} α γ f (Set.Ici.{u1} γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) y)))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_iff_is_closed_preimage upperSemicontinuous_iff_isClosed_preimageₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
 theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     UpperSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Ici y) :=
@@ -831,6 +1381,12 @@ theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Ici]
 #align upper_semicontinuous_iff_is_closed_preimage upperSemicontinuous_iff_isClosed_preimage
 
+/- warning: upper_semicontinuous.is_closed_preimage -> UpperSemicontinuous.isClosed_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] {f : α -> γ}, (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (forall (y : γ), IsClosed.{u1} α _inst_1 (Set.preimage.{u1, u2} α γ f (Set.Ici.{u2} γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) y)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] {f : α -> γ}, (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) -> (forall (y : γ), IsClosed.{u2} α _inst_1 (Set.preimage.{u2, u1} α γ f (Set.Ici.{u1} γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) y)))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.is_closed_preimage UpperSemicontinuous.isClosed_preimageₓ'. -/
 theorem UpperSemicontinuous.isClosed_preimage {f : α → γ} (hf : UpperSemicontinuous f) (y : γ) :
     IsClosed (f ⁻¹' Ici y) :=
   upperSemicontinuous_iff_isClosed_preimage.1 hf y
@@ -838,18 +1394,42 @@ theorem UpperSemicontinuous.isClosed_preimage {f : α → γ} (hf : UpperSemicon
 
 variable [TopologicalSpace γ] [OrderTopology γ]
 
+/- warning: continuous_within_at.upper_semicontinuous_within_at -> ContinuousWithinAt.upperSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f s x) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousWithinAt.{u2, u1} α γ _inst_1 _inst_4 f s x) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s x)
+Case conversion may be inaccurate. Consider using '#align continuous_within_at.upper_semicontinuous_within_at ContinuousWithinAt.upperSemicontinuousWithinAtₓ'. -/
 theorem ContinuousWithinAt.upperSemicontinuousWithinAt {f : α → γ} (h : ContinuousWithinAt f s x) :
     UpperSemicontinuousWithinAt f s x := fun y hy => h (Iio_mem_nhds hy)
 #align continuous_within_at.upper_semicontinuous_within_at ContinuousWithinAt.upperSemicontinuousWithinAt
 
+/- warning: continuous_at.upper_semicontinuous_at -> ContinuousAt.upperSemicontinuousAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousAt.{u1, u2} α γ _inst_1 _inst_4 f x) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousAt.{u2, u1} α γ _inst_1 _inst_4 f x) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.upper_semicontinuous_at ContinuousAt.upperSemicontinuousAtₓ'. -/
 theorem ContinuousAt.upperSemicontinuousAt {f : α → γ} (h : ContinuousAt f x) :
     UpperSemicontinuousAt f x := fun y hy => h (Iio_mem_nhds hy)
 #align continuous_at.upper_semicontinuous_at ContinuousAt.upperSemicontinuousAt
 
+/- warning: continuous_on.upper_semicontinuous_on -> ContinuousOn.upperSemicontinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (ContinuousOn.{u1, u2} α γ _inst_1 _inst_4 f s) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (ContinuousOn.{u2, u1} α γ _inst_1 _inst_4 f s) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s)
+Case conversion may be inaccurate. Consider using '#align continuous_on.upper_semicontinuous_on ContinuousOn.upperSemicontinuousOnₓ'. -/
 theorem ContinuousOn.upperSemicontinuousOn {f : α → γ} (h : ContinuousOn f s) :
     UpperSemicontinuousOn f s := fun x hx => (h x hx).UpperSemicontinuousWithinAt
 #align continuous_on.upper_semicontinuous_on ContinuousOn.upperSemicontinuousOn
 
+/- warning: continuous.upper_semicontinuous -> Continuous.upperSemicontinuous is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, (Continuous.{u1, u2} α γ _inst_1 _inst_4 f) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, (Continuous.{u2, u1} α γ _inst_1 _inst_4 f) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f)
+Case conversion may be inaccurate. Consider using '#align continuous.upper_semicontinuous Continuous.upperSemicontinuousₓ'. -/
 theorem Continuous.upperSemicontinuous {f : α → γ} (h : Continuous f) : UpperSemicontinuous f :=
   fun x => h.ContinuousAt.UpperSemicontinuousAt
 #align continuous.upper_semicontinuous Continuous.upperSemicontinuous
@@ -865,44 +1445,92 @@ variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
+/- warning: continuous_at.comp_upper_semicontinuous_within_at -> ContinuousAt.comp_upperSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s x) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_within_at ContinuousAt.comp_upperSemicontinuousWithinAtₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     UpperSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_lowerSemicontinuousWithinAt α _ x s γᵒᵈ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon.dual
 #align continuous_at.comp_upper_semicontinuous_within_at ContinuousAt.comp_upperSemicontinuousWithinAt
 
+/- warning: continuous_at.comp_upper_semicontinuous_at -> ContinuousAt.comp_upperSemicontinuousAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f x) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_at ContinuousAt.comp_upperSemicontinuousAtₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : UpperSemicontinuousAt f x) (gmon : Monotone g) : UpperSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_lowerSemicontinuousAt α _ x γᵒᵈ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon.dual
 #align continuous_at.comp_upper_semicontinuous_at ContinuousAt.comp_upperSemicontinuousAt
 
+/- warning: continuous.comp_upper_semicontinuous_on -> Continuous.comp_upperSemicontinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s)
+Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous_on Continuous.comp_upperSemicontinuousOnₓ'. -/
 theorem Continuous.comp_upperSemicontinuousOn {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuousOn f s) (gmon : Monotone g) : UpperSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_upperSemicontinuousWithinAt (hf x hx) gmon
 #align continuous.comp_upper_semicontinuous_on Continuous.comp_upperSemicontinuousOn
 
+/- warning: continuous.comp_upper_semicontinuous -> Continuous.comp_upperSemicontinuous is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (Monotone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f) -> (Monotone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (UpperSemicontinuous.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f))
+Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous Continuous.comp_upperSemicontinuousₓ'. -/
 theorem Continuous.comp_upperSemicontinuous {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuous f) (gmon : Monotone g) : UpperSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_upperSemicontinuousAt (hf x) gmon
 #align continuous.comp_upper_semicontinuous Continuous.comp_upperSemicontinuous
 
+/- warning: continuous_at.comp_upper_semicontinuous_within_at_antitone -> ContinuousAt.comp_upperSemicontinuousWithinAt_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s x) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_within_at_antitone ContinuousAt.comp_upperSemicontinuousWithinAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Antitone g) :
     LowerSemicontinuousWithinAt (g ∘ f) s x :=
   @ContinuousAt.comp_upperSemicontinuousWithinAt α _ x s γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_upper_semicontinuous_within_at_antitone ContinuousAt.comp_upperSemicontinuousWithinAt_antitone
 
+/- warning: continuous_at.comp_upper_semicontinuous_at_antitone -> ContinuousAt.comp_upperSemicontinuousAt_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u2, u3} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (ContinuousAt.{u3, u2} γ δ _inst_4 _inst_7 g (f x)) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f x) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousAt.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) x)
+Case conversion may be inaccurate. Consider using '#align continuous_at.comp_upper_semicontinuous_at_antitone ContinuousAt.comp_upperSemicontinuousAt_antitoneₓ'. -/
 theorem ContinuousAt.comp_upperSemicontinuousAt_antitone {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousAt f x) (gmon : Antitone g) :
     LowerSemicontinuousAt (g ∘ f) x :=
   @ContinuousAt.comp_upperSemicontinuousAt α _ x γ _ _ _ δᵒᵈ _ _ _ g f hg hf gmon
 #align continuous_at.comp_upper_semicontinuous_at_antitone ContinuousAt.comp_upperSemicontinuousAt_antitone
 
+/- warning: continuous.comp_upper_semicontinuous_on_antitone -> Continuous.comp_upperSemicontinuousOn_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f s) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuousOn.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f) s)
+Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous_on_antitone Continuous.comp_upperSemicontinuousOn_antitoneₓ'. -/
 theorem Continuous.comp_upperSemicontinuousOn_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuousOn f s) (gmon : Antitone g) : LowerSemicontinuousOn (g ∘ f) s :=
   fun x hx => hg.ContinuousAt.comp_upperSemicontinuousWithinAt_antitone (hf x hx) gmon
 #align continuous.comp_upper_semicontinuous_on_antitone Continuous.comp_upperSemicontinuousOn_antitone
 
+/- warning: continuous.comp_upper_semicontinuous_antitone -> Continuous.comp_upperSemicontinuous_antitone is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {δ : Type.{u3}} [_inst_6 : LinearOrder.{u3} δ] [_inst_7 : TopologicalSpace.{u3} δ] [_inst_8 : OrderTopology.{u3} δ _inst_7 (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u2, u3} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) -> (Antitone.{u2, u3} γ δ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) g) -> (LowerSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (SemilatticeInf.toPartialOrder.{u3} δ (Lattice.toSemilatticeInf.{u3} δ (LinearOrder.toLattice.{u3} δ _inst_6)))) (Function.comp.{succ u1, succ u2, succ u3} α γ δ g f))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u3}} [_inst_3 : LinearOrder.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3)))))] {δ : Type.{u2}} [_inst_6 : LinearOrder.{u2} δ] [_inst_7 : TopologicalSpace.{u2} δ] [_inst_8 : OrderTopology.{u2} δ _inst_7 (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6)))))] {g : γ -> δ} {f : α -> γ}, (Continuous.{u3, u2} γ δ _inst_4 _inst_7 g) -> (UpperSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) f) -> (Antitone.{u3, u2} γ δ (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (DistribLattice.toLattice.{u3} γ (instDistribLattice.{u3} γ _inst_3))))) (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) g) -> (LowerSemicontinuous.{u1, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (SemilatticeInf.toPartialOrder.{u2} δ (Lattice.toSemilatticeInf.{u2} δ (DistribLattice.toLattice.{u2} δ (instDistribLattice.{u2} δ _inst_6))))) (Function.comp.{succ u1, succ u3, succ u2} α γ δ g f))
+Case conversion may be inaccurate. Consider using '#align continuous.comp_upper_semicontinuous_antitone Continuous.comp_upperSemicontinuous_antitoneₓ'. -/
 theorem Continuous.comp_upperSemicontinuous_antitone {g : γ → δ} {f : α → γ} (hg : Continuous g)
     (hf : UpperSemicontinuous f) (gmon : Antitone g) : LowerSemicontinuous (g ∘ f) := fun x =>
   hg.ContinuousAt.comp_upperSemicontinuousAt_antitone (hf x) gmon
@@ -918,6 +1546,12 @@ section
 variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
   [OrderTopology γ]
 
+/- warning: upper_semicontinuous_within_at.add' -> UpperSemicontinuousWithinAt.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s x) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s x) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s x) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s x) -> (ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x))) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at.add' UpperSemicontinuousWithinAt.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -928,6 +1562,12 @@ theorem UpperSemicontinuousWithinAt.add' {f g : α → γ} (hf : UpperSemicontin
   @LowerSemicontinuousWithinAt.add' α _ x s γᵒᵈ _ _ _ _ _ hf hg hcont
 #align upper_semicontinuous_within_at.add' UpperSemicontinuousWithinAt.add'
 
+/- warning: upper_semicontinuous_at.add' -> UpperSemicontinuousAt.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f x) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g x) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f x) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g x) -> (ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x))) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at.add' UpperSemicontinuousAt.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -940,6 +1580,12 @@ theorem UpperSemicontinuousAt.add' {f g : α → γ} (hf : UpperSemicontinuousAt
   exact hf.add' hg hcont
 #align upper_semicontinuous_at.add' UpperSemicontinuousAt.add'
 
+/- warning: upper_semicontinuous_on.add' -> UpperSemicontinuousOn.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x)))) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s) -> (forall (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x)))) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.add' UpperSemicontinuousOn.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -950,6 +1596,12 @@ theorem UpperSemicontinuousOn.add' {f g : α → γ} (hf : UpperSemicontinuousOn
   (hf x hx).add' (hg x hx) (hcont x hx)
 #align upper_semicontinuous_on.add' UpperSemicontinuousOn.add'
 
+/- warning: upper_semicontinuous.add' -> UpperSemicontinuous.add' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g) -> (forall (x : α), ContinuousAt.{u2, u2} (Prod.{u2, u2} γ γ) γ (Prod.topologicalSpace.{u2, u2} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u2, u2} γ γ) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (Prod.fst.{u2, u2} γ γ p) (Prod.snd.{u2, u2} γ γ p)) (Prod.mk.{u2, u2} γ γ (f x) (g x))) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g) -> (forall (x : α), ContinuousAt.{u1, u1} (Prod.{u1, u1} γ γ) γ (instTopologicalSpaceProd.{u1, u1} γ γ _inst_4 _inst_4) _inst_4 (fun (p : Prod.{u1, u1} γ γ) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) (Prod.mk.{u1, u1} γ γ (f x) (g x))) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.add' UpperSemicontinuous.add'ₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
 explicit continuity assumption on addition, for application to `ereal`. The unprimed version of
 the lemma uses `[has_continuous_add]`. -/
@@ -961,6 +1613,12 @@ theorem UpperSemicontinuous.add' {f g : α → γ} (hf : UpperSemicontinuous f)
 
 variable [ContinuousAdd γ]
 
+/- warning: upper_semicontinuous_within_at.add -> UpperSemicontinuousWithinAt.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s x) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s x) -> (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s x) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s x) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at.add UpperSemicontinuousWithinAt.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -970,6 +1628,12 @@ theorem UpperSemicontinuousWithinAt.add {f g : α → γ} (hf : UpperSemicontinu
   hf.add' hg continuous_add.ContinuousAt
 #align upper_semicontinuous_within_at.add UpperSemicontinuousWithinAt.add
 
+/- warning: upper_semicontinuous_at.add -> UpperSemicontinuousAt.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f x) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g x) -> (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f x) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g x) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at.add UpperSemicontinuousAt.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -978,6 +1642,12 @@ theorem UpperSemicontinuousAt.add {f g : α → γ} (hf : UpperSemicontinuousAt
   hf.add' hg continuous_add.ContinuousAt
 #align upper_semicontinuous_at.add UpperSemicontinuousAt.add
 
+/- warning: upper_semicontinuous_on.add -> UpperSemicontinuousOn.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f s) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g s) -> (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)) s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f s) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g s) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on.add UpperSemicontinuousOn.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -986,6 +1656,12 @@ theorem UpperSemicontinuousOn.add {f g : α → γ} (hf : UpperSemicontinuousOn
   hf.add' hg fun x hx => continuous_add.ContinuousAt
 #align upper_semicontinuous_on.add UpperSemicontinuousOn.add
 
+/- warning: upper_semicontinuous.add -> UpperSemicontinuous.add is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrderedAddCommMonoid.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u2} γ _inst_4 (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) f) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) g) -> (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (OrderedAddCommMonoid.toPartialOrder.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u2, u2, u2} γ γ γ (instHAdd.{u2} γ (AddZeroClass.toHasAdd.{u2} γ (AddMonoid.toAddZeroClass.{u2} γ (AddCommMonoid.toAddMonoid.{u2} γ (OrderedAddCommMonoid.toAddCommMonoid.{u2} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u2} γ _inst_3)))))) (f z) (g z)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : α -> γ} {g : α -> γ}, (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) f) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) g) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => HAdd.hAdd.{u1, u1, u1} γ γ γ (instHAdd.{u1} γ (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))) (f z) (g z)))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous.add UpperSemicontinuous.addₓ'. -/
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with
 `[has_continuous_add]`. The primed version of the lemma uses an explicit continuity assumption on
 addition, for application to `ereal`. -/
@@ -994,12 +1670,24 @@ theorem UpperSemicontinuous.add {f g : α → γ} (hf : UpperSemicontinuous f)
   hf.add' hg fun x => continuous_add.ContinuousAt
 #align upper_semicontinuous.add UpperSemicontinuous.add
 
+/- warning: upper_semicontinuous_within_at_sum -> upperSemicontinuousWithinAt_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) s x)) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) s x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) s x)) -> (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_sum upperSemicontinuousWithinAt_sumₓ'. -/
 theorem upperSemicontinuousWithinAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun z => ∑ i in a, f i z) s x :=
   @lowerSemicontinuousWithinAt_sum α _ x s ι γᵒᵈ _ _ _ _ f a ha
 #align upper_semicontinuous_within_at_sum upperSemicontinuousWithinAt_sum
 
+/- warning: upper_semicontinuous_at_sum -> upperSemicontinuousAt_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) x)) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) x)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) x)) -> (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_sum upperSemicontinuousAt_sumₓ'. -/
 theorem upperSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun z => ∑ i in a, f i z) x :=
@@ -1008,12 +1696,24 @@ theorem upperSemicontinuousAt_sum {f : ι → α → γ} {a : Finset ι}
   exact upperSemicontinuousWithinAt_sum ha
 #align upper_semicontinuous_at_sum upperSemicontinuousAt_sum
 
+/- warning: upper_semicontinuous_on_sum -> upperSemicontinuousOn_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i) s)) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)) s)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i) s)) -> (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_sum upperSemicontinuousOn_sumₓ'. -/
 theorem upperSemicontinuousOn_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun z => ∑ i in a, f i z) s := fun x hx =>
   upperSemicontinuousWithinAt_sum fun i hi => ha i hi x hx
 #align upper_semicontinuous_on_sum upperSemicontinuousOn_sum
 
+/- warning: upper_semicontinuous_sum -> upperSemicontinuous_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Type.{u2}} {γ : Type.{u3}} [_inst_3 : LinearOrderedAddCommMonoid.{u3} γ] [_inst_4 : TopologicalSpace.{u3} γ] [_inst_5 : OrderTopology.{u3} γ _inst_4 (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u3} γ _inst_4 (AddZeroClass.toHasAdd.{u3} γ (AddMonoid.toAddZeroClass.{u3} γ (AddCommMonoid.toAddMonoid.{u3} γ (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)))))] {f : ι -> α -> γ} {a : Finset.{u2} ι}, (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i a) -> (UpperSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (f i))) -> (UpperSemicontinuous.{u1, u3} α _inst_1 γ (PartialOrder.toPreorder.{u3} γ (OrderedAddCommMonoid.toPartialOrder.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3))) (fun (z : α) => Finset.sum.{u3, u2} γ ι (OrderedAddCommMonoid.toAddCommMonoid.{u3} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u3} γ _inst_3)) a (fun (i : ι) => f i z)))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {ι : Type.{u3}} {γ : Type.{u1}} [_inst_3 : LinearOrderedAddCommMonoid.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3)))] [_inst_6 : ContinuousAdd.{u1} γ _inst_4 (AddZeroClass.toAdd.{u1} γ (AddMonoid.toAddZeroClass.{u1} γ (AddCommMonoid.toAddMonoid.{u1} γ (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3))))] {f : ι -> α -> γ} {a : Finset.{u3} ι}, (forall (i : ι), (Membership.mem.{u3, u3} ι (Finset.{u3} ι) (Finset.instMembershipFinset.{u3} ι) i a) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (f i))) -> (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (OrderedAddCommMonoid.toPartialOrder.{u1} γ (LinearOrderedAddCommMonoid.toOrderedAddCommMonoid.{u1} γ _inst_3))) (fun (z : α) => Finset.sum.{u1, u3} γ ι (LinearOrderedAddCommMonoid.toAddCommMonoid.{u1} γ _inst_3) a (fun (i : ι) => f i z)))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_sum upperSemicontinuous_sumₓ'. -/
 theorem upperSemicontinuous_sum {f : ι → α → γ} {a : Finset ι}
     (ha : ∀ i ∈ a, UpperSemicontinuous (f i)) : UpperSemicontinuous fun z => ∑ i in a, f i z :=
   fun x => upperSemicontinuousAt_sum fun i hi => ha i hi x
@@ -1028,6 +1728,12 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
+/- warning: upper_semicontinuous_within_at_cinfi -> upperSemicontinuousWithinAt_cinfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u1} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhdsWithin.{u3} α _inst_1 x s)) -> (forall (i : ι), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfiₓ'. -/
 theorem upperSemicontinuousWithinAt_cinfi {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
@@ -1035,12 +1741,24 @@ theorem upperSemicontinuousWithinAt_cinfi {f : ι → α → δ'}
   @lowerSemicontinuousWithinAt_csupr α _ x s ι δ'ᵒᵈ _ f bdd h
 #align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfi
 
+/- warning: upper_semicontinuous_within_at_infi -> upperSemicontinuousWithinAt_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_infᵢₓ'. -/
 theorem upperSemicontinuousWithinAt_infᵢ {f : ι → α → δ}
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
   @lowerSemicontinuousWithinAt_supᵢ α _ x s ι δᵒᵈ _ f h
 #align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_infᵢ
 
+/- warning: upper_semicontinuous_within_at_binfi -> upperSemicontinuousWithinAt_binfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s x) -> (UpperSemicontinuousWithinAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfiₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuousWithinAt_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
@@ -1048,17 +1766,35 @@ theorem upperSemicontinuousWithinAt_binfi {p : ι → Prop} {f : ∀ (i) (h : p
   upperSemicontinuousWithinAt_infᵢ fun i => upperSemicontinuousWithinAt_infᵢ fun hi => h i hi
 #align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfi
 
+/- warning: upper_semicontinuous_at_cinfi -> upperSemicontinuousAt_cinfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u1} α (fun (y : α) => BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i y))) (nhds.{u1} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (Filter.Eventually.{u3} α (fun (y : α) => BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i y))) (nhds.{u3} α _inst_1 x)) -> (forall (i : ι), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfiₓ'. -/
 theorem upperSemicontinuousAt_cinfi {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddBelow (range fun i => f i y)) (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
   @lowerSemicontinuousAt_csupr α _ x ι δ'ᵒᵈ _ f bdd h
 #align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfi
 
+/- warning: upper_semicontinuous_at_infi -> upperSemicontinuousAt_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_infi upperSemicontinuousAt_infᵢₓ'. -/
 theorem upperSemicontinuousAt_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
   @lowerSemicontinuousAt_supᵢ α _ x ι δᵒᵈ _ f h
 #align upper_semicontinuous_at_infi upperSemicontinuousAt_infᵢ
 
+/- warning: upper_semicontinuous_at_binfi -> upperSemicontinuousAt_binfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) x)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {x : α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) x) -> (UpperSemicontinuousAt.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) x)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfiₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuousAt_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
@@ -1066,17 +1802,35 @@ theorem upperSemicontinuousAt_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α
   upperSemicontinuousAt_infᵢ fun i => upperSemicontinuousAt_infᵢ fun hi => h i hi
 #align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfi
 
+/- warning: upper_semicontinuous_on_cinfi -> upperSemicontinuousOn_cinfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ' : Type.{u2}} [_inst_4 : ConditionallyCompleteLinearOrder.{u2} δ'] {f : ι -> α -> δ'}, (forall (x : α), (Membership.mem.{u3, u3} α (Set.{u3} α) (Set.instMembershipSet.{u3} α) x s) -> (BddBelow.{u2} δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (Set.range.{u2, u1} δ' ι (fun (i : ι) => f i x)))) -> (forall (i : ι), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (f i) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ' (PartialOrder.toPreorder.{u2} δ' (SemilatticeInf.toPartialOrder.{u2} δ' (Lattice.toSemilatticeInf.{u2} δ' (ConditionallyCompleteLattice.toLattice.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u2, u1} δ' (ConditionallyCompleteLattice.toInfSet.{u2} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ' _inst_4)) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfiₓ'. -/
 theorem upperSemicontinuousOn_cinfi {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddBelow (range fun i => f i x)) (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
   upperSemicontinuousWithinAt_cinfi (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
 #align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfi
 
+/- warning: upper_semicontinuous_on_infi -> upperSemicontinuousOn_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')) s)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_infi upperSemicontinuousOn_infᵢₓ'. -/
 theorem upperSemicontinuousOn_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
   upperSemicontinuousWithinAt_infᵢ fun i => h i x hx
 #align upper_semicontinuous_on_infi upperSemicontinuousOn_infᵢ
 
+/- warning: upper_semicontinuous_on_binfi -> upperSemicontinuousOn_binfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))) s)
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {s : Set.{u3} α} {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi) s) -> (UpperSemicontinuousOn.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))) s)
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfiₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuousOn_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
@@ -1084,15 +1838,33 @@ theorem upperSemicontinuousOn_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α
   upperSemicontinuousOn_infᵢ fun i => upperSemicontinuousOn_infᵢ fun hi => h i hi
 #align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfi
 
+/- warning: upper_semicontinuous_cinfi -> upperSemicontinuous_cinfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toHasInf.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ' : Type.{u3}} [_inst_4 : ConditionallyCompleteLinearOrder.{u3} δ'] {f : ι -> α -> δ'}, (forall (x : α), BddBelow.{u3} δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (Set.range.{u3, u2} δ' ι (fun (i : ι) => f i x))) -> (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ' (PartialOrder.toPreorder.{u3} δ' (SemilatticeInf.toPartialOrder.{u3} δ' (Lattice.toSemilatticeInf.{u3} δ' (ConditionallyCompleteLattice.toLattice.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4))))) (fun (x' : α) => infᵢ.{u3, u2} δ' (ConditionallyCompleteLattice.toInfSet.{u3} δ' (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u3} δ' _inst_4)) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_cinfi upperSemicontinuous_cinfiₓ'. -/
 theorem upperSemicontinuous_cinfi {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
     (h : ∀ i, UpperSemicontinuous (f i)) : UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x =>
   upperSemicontinuousAt_cinfi (eventually_of_forall bdd) fun i => h i x
 #align upper_semicontinuous_cinfi upperSemicontinuous_cinfi
 
+/- warning: upper_semicontinuous_infi -> upperSemicontinuous_infᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => f i x')))
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {f : ι -> α -> δ}, (forall (i : ι), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => f i x')))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_infi upperSemicontinuous_infᵢₓ'. -/
 theorem upperSemicontinuous_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
     UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_infᵢ fun i => h i x
 #align upper_semicontinuous_infi upperSemicontinuous_infᵢ
 
+/- warning: upper_semicontinuous_binfi -> upperSemicontinuous_binfi is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {ι : Sort.{u2}} {δ : Type.{u3}} [_inst_3 : CompleteLinearOrder.{u3} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u1, u3} α _inst_1 δ (PartialOrder.toPreorder.{u3} δ (CompleteSemilatticeInf.toPartialOrder.{u3} δ (CompleteLattice.toCompleteSemilatticeInf.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3)))) (fun (x' : α) => infᵢ.{u3, u2} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) ι (fun (i : ι) => infᵢ.{u3, 0} δ (ConditionallyCompleteLattice.toHasInf.{u3} δ (CompleteLattice.toConditionallyCompleteLattice.{u3} δ (CompleteLinearOrder.toCompleteLattice.{u3} δ _inst_3))) (p i) (fun (hi : p i) => f i hi x'))))
+but is expected to have type
+  forall {α : Type.{u3}} [_inst_1 : TopologicalSpace.{u3} α] {ι : Sort.{u1}} {δ : Type.{u2}} [_inst_3 : CompleteLinearOrder.{u2} δ] {p : ι -> Prop} {f : forall (i : ι), (p i) -> α -> δ}, (forall (i : ι) (hi : p i), UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (f i hi)) -> (UpperSemicontinuous.{u3, u2} α _inst_1 δ (PartialOrder.toPreorder.{u2} δ (CompleteSemilatticeInf.toPartialOrder.{u2} δ (CompleteLattice.toCompleteSemilatticeInf.{u2} δ (CompleteLinearOrder.toCompleteLattice.{u2} δ _inst_3)))) (fun (x' : α) => infᵢ.{u2, u1} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) ι (fun (i : ι) => infᵢ.{u2, 0} δ (ConditionallyCompleteLattice.toInfSet.{u2} δ (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} δ (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} δ (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{u2} δ _inst_3)))) (p i) (fun (hi : p i) => f i hi x'))))
+Case conversion may be inaccurate. Consider using '#align upper_semicontinuous_binfi upperSemicontinuous_binfiₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 theorem upperSemicontinuous_binfi {p : ι → Prop} {f : ∀ (i) (h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
@@ -1106,6 +1878,12 @@ section
 
 variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
+/- warning: continuous_within_at_iff_lower_upper_semicontinuous_within_at -> continuousWithinAt_iff_lower_upperSemicontinuousWithinAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (ContinuousWithinAt.{u1, u2} α γ _inst_1 _inst_4 f s x) (And (LowerSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x) (UpperSemicontinuousWithinAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s x))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (ContinuousWithinAt.{u2, u1} α γ _inst_1 _inst_4 f s x) (And (LowerSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s x) (UpperSemicontinuousWithinAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s x))
+Case conversion may be inaccurate. Consider using '#align continuous_within_at_iff_lower_upper_semicontinuous_within_at continuousWithinAt_iff_lower_upperSemicontinuousWithinAtₓ'. -/
 theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ} :
     ContinuousWithinAt f s x ↔
       LowerSemicontinuousWithinAt f s x ∧ UpperSemicontinuousWithinAt f s x :=
@@ -1138,12 +1916,24 @@ theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ}
       exact mem_of_mem_nhds hv
 #align continuous_within_at_iff_lower_upper_semicontinuous_within_at continuousWithinAt_iff_lower_upperSemicontinuousWithinAt
 
+/- warning: continuous_at_iff_lower_upper_semicontinuous_at -> continuousAt_iff_lower_upperSemicontinuousAt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {x : α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (ContinuousAt.{u1, u2} α γ _inst_1 _inst_4 f x) (And (LowerSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x) (UpperSemicontinuousAt.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f x))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {x : α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (ContinuousAt.{u2, u1} α γ _inst_1 _inst_4 f x) (And (LowerSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f x) (UpperSemicontinuousAt.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f x))
+Case conversion may be inaccurate. Consider using '#align continuous_at_iff_lower_upper_semicontinuous_at continuousAt_iff_lower_upperSemicontinuousAtₓ'. -/
 theorem continuousAt_iff_lower_upperSemicontinuousAt {f : α → γ} :
     ContinuousAt f x ↔ LowerSemicontinuousAt f x ∧ UpperSemicontinuousAt f x := by
   simp_rw [← continuousWithinAt_univ, ← lowerSemicontinuousWithinAt_univ_iff, ←
     upperSemicontinuousWithinAt_univ_iff, continuousWithinAt_iff_lower_upperSemicontinuousWithinAt]
 #align continuous_at_iff_lower_upper_semicontinuous_at continuousAt_iff_lower_upperSemicontinuousAt
 
+/- warning: continuous_on_iff_lower_upper_semicontinuous_on -> continuousOn_iff_lower_upperSemicontinuousOn is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {s : Set.{u1} α} {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (ContinuousOn.{u1, u2} α γ _inst_1 _inst_4 f s) (And (LowerSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s) (UpperSemicontinuousOn.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f s))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {s : Set.{u2} α} {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (ContinuousOn.{u2, u1} α γ _inst_1 _inst_4 f s) (And (LowerSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s) (UpperSemicontinuousOn.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f s))
+Case conversion may be inaccurate. Consider using '#align continuous_on_iff_lower_upper_semicontinuous_on continuousOn_iff_lower_upperSemicontinuousOnₓ'. -/
 theorem continuousOn_iff_lower_upperSemicontinuousOn {f : α → γ} :
     ContinuousOn f s ↔ LowerSemicontinuousOn f s ∧ UpperSemicontinuousOn f s :=
   by
@@ -1152,6 +1942,12 @@ theorem continuousOn_iff_lower_upperSemicontinuousOn {f : α → γ} :
     ⟨fun H => ⟨fun x hx => (H x hx).1, fun x hx => (H x hx).2⟩, fun H x hx => ⟨H.1 x hx, H.2 x hx⟩⟩
 #align continuous_on_iff_lower_upper_semicontinuous_on continuousOn_iff_lower_upperSemicontinuousOn
 
+/- warning: continuous_iff_lower_upper_semicontinuous -> continuous_iff_lower_upperSemicontinuous is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} α] {γ : Type.{u2}} [_inst_3 : LinearOrder.{u2} γ] [_inst_4 : TopologicalSpace.{u2} γ] [_inst_5 : OrderTopology.{u2} γ _inst_4 (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3))))] {f : α -> γ}, Iff (Continuous.{u1, u2} α γ _inst_1 _inst_4 f) (And (LowerSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f) (UpperSemicontinuous.{u1, u2} α _inst_1 γ (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (LinearOrder.toLattice.{u2} γ _inst_3)))) f))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} α] {γ : Type.{u1}} [_inst_3 : LinearOrder.{u1} γ] [_inst_4 : TopologicalSpace.{u1} γ] [_inst_5 : OrderTopology.{u1} γ _inst_4 (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3)))))] {f : α -> γ}, Iff (Continuous.{u2, u1} α γ _inst_1 _inst_4 f) (And (LowerSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f) (UpperSemicontinuous.{u2, u1} α _inst_1 γ (PartialOrder.toPreorder.{u1} γ (SemilatticeInf.toPartialOrder.{u1} γ (Lattice.toSemilatticeInf.{u1} γ (DistribLattice.toLattice.{u1} γ (instDistribLattice.{u1} γ _inst_3))))) f))
+Case conversion may be inaccurate. Consider using '#align continuous_iff_lower_upper_semicontinuous continuous_iff_lower_upperSemicontinuousₓ'. -/
 theorem continuous_iff_lower_upperSemicontinuous {f : α → γ} :
     Continuous f ↔ LowerSemicontinuous f ∧ UpperSemicontinuous f := by
   simp_rw [continuous_iff_continuousOn_univ, continuousOn_iff_lower_upperSemicontinuousOn,

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -271,13 +271,13 @@ section
 
 variable {γ : Type _} [LinearOrder γ]
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
 theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     LowerSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Iic y) :=
   by
   rw [lowerSemicontinuous_iff_isOpen_preimage]
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]]"
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Iic]
 #align lower_semicontinuous_iff_is_closed_preimage lowerSemicontinuous_iff_isClosed_preimage
 
@@ -821,13 +821,13 @@ section
 
 variable {γ : Type _} [LinearOrder γ]
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]] -/
 theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     UpperSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Ici y) :=
   by
   rw [upperSemicontinuous_iff_isOpen_preimage]
   trace
-    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:76:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]]"
+    "./././Mathport/Syntax/Translate/Tactic/Builtin.lean:73:14: unsupported tactic `congrm #[[expr ∀ y, (_ : exprProp())]]"
   rw [← isOpen_compl_iff, ← preimage_compl, compl_Ici]
 #align upper_semicontinuous_iff_is_closed_preimage upperSemicontinuous_iff_isClosed_preimage
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -57,7 +57,7 @@ ones for lower semicontinuous functions using `order_dual`.
 -/
 
 
-open Topology BigOperators Ennreal
+open Topology BigOperators ENNReal
 
 open Set Function Filter
 
@@ -662,7 +662,7 @@ theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ∑' i, f i x') s x :=
   by
-  simp_rw [Ennreal.tsum_eq_supᵢ_sum]
+  simp_rw [ENNReal.tsum_eq_supᵢ_sum]
   apply lowerSemicontinuousWithinAt_supᵢ fun b => _
   exact lowerSemicontinuousWithinAt_sum fun i hi => h i
 #align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsum

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

Notably, these cause issues on nightly-2024-04-25

Co-authored-by: adamtopaz <github@adamtopaz.com>

@@ -358,7 +358,9 @@ theorem lowerSemicontinuous_iff_isClosed_epigraph {f : α → γ} :
     rw [nhds_prod_eq, le_prod] at h'
     calc f x ≤ liminf f (𝓝 x) := hf x
     _ ≤ liminf f (map Prod.fst F) := liminf_le_liminf_of_le h'.1
-    _ ≤ liminf Prod.snd F := liminf_le_liminf <| (eventually_principal.2 fun _ ↦ id).filter_mono h
+    _ = liminf (f ∘ Prod.fst) F := (Filter.liminf_comp _ _ _).symm
+    _ ≤ liminf Prod.snd F := liminf_le_liminf <| by
+          simpa using (eventually_principal.2 fun (_ : α × γ) ↦ id).filter_mono h
     _ = y := h'.2.liminf_eq
   · rw [lowerSemicontinuous_iff_isClosed_preimage]
     exact fun hf y ↦ hf.preimage (Continuous.Prod.mk_left y)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -87,7 +87,7 @@ def LowerSemicontinuousWithinAt (f : α → β) (s : Set α) (x : α) :=
 
 /-- A real function `f` is lower semicontinuous on a set `s` if, for any `ε > 0`, for any `x ∈ s`,
 for all `x'` close enough to `x` in `s`, then `f x'` is at least `f x - ε`. We formulate this in
-a general preordered space, using an arbitrary `y < f x` instead of `f x - ε`.-/
+a general preordered space, using an arbitrary `y < f x` instead of `f x - ε`. -/
 def LowerSemicontinuousOn (f : α → β) (s : Set α) :=
   ∀ x ∈ s, LowerSemicontinuousWithinAt f s x
 #align lower_semicontinuous_on LowerSemicontinuousOn
@@ -115,7 +115,7 @@ def UpperSemicontinuousWithinAt (f : α → β) (s : Set α) (x : α) :=
 
 /-- A real function `f` is upper semicontinuous on a set `s` if, for any `ε > 0`, for any `x ∈ s`,
 for all `x'` close enough to `x` in `s`, then `f x'` is at most `f x + ε`. We formulate this in a
-general preordered space, using an arbitrary `y > f x` instead of `f x + ε`.-/
+general preordered space, using an arbitrary `y > f x` instead of `f x + ε`. -/
 def UpperSemicontinuousOn (f : α → β) (s : Set α) :=
   ∀ x ∈ s, UpperSemicontinuousWithinAt f s x
 #align upper_semicontinuous_on UpperSemicontinuousOn
@@ -129,7 +129,7 @@ def UpperSemicontinuousAt (f : α → β) (x : α) :=
 
 /-- A real function `f` is upper semicontinuous if, for any `ε > 0`, for any `x`, for all `x'`
 close enough to `x`, then `f x'` is at most `f x + ε`. We formulate this in a general preordered
-space, using an arbitrary `y > f x` instead of `f x + ε`.-/
+space, using an arbitrary `y > f x` instead of `f x + ε`. -/
 def UpperSemicontinuous (f : α → β) :=
   ∀ x, UpperSemicontinuousAt f x
 #align upper_semicontinuous UpperSemicontinuous

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -379,9 +379,7 @@ end
 section
 
 variable {γ : Type*} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
-
 variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
-
 variable {ι : Type*} [TopologicalSpace ι]
 
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
@@ -961,9 +959,7 @@ end
 section
 
 variable {γ : Type*} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
-
 variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
-
 variable {ι : Type*} [TopologicalSpace ι]
 
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt {g : γ → δ} {f : α → γ}

Only the other direction exists currently, it seems.

@@ -34,9 +34,10 @@ We build a basic API using dot notation around these notions, and we prove that
 * `indicator s (fun _ ↦ y)` is lower semicontinuous when `s` is open and `0 ≤ y`,
   or when `s` is closed and `y ≤ 0`;
 * continuous functions are lower semicontinuous;
-* composition with a continuous monotone functions maps lower semicontinuous functions to lower
+* left composition with a continuous monotone functions maps lower semicontinuous functions to lower
   semicontinuous functions. If the function is anti-monotone, it instead maps lower semicontinuous
   functions to upper semicontinuous functions;
+* right composition with continuous functions preserves lower and upper semicontinuity;
 * a sum of two (or finitely many) lower semicontinuous functions is lower semicontinuous;
 * a supremum of a family of lower semicontinuous functions is lower semicontinuous;
 * An infinite sum of `ℝ≥0∞`-valued lower semicontinuous functions is lower semicontinuous.
@@ -381,6 +382,8 @@ variable {γ : Type*} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
+variable {ι : Type*} [TopologicalSpace ι]
+
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     LowerSemicontinuousWithinAt (g ∘ f) s x := by
@@ -435,6 +438,21 @@ theorem Continuous.comp_lowerSemicontinuous_antitone {g : γ → δ} {f : α →
   hg.continuousAt.comp_lowerSemicontinuousAt_antitone (hf x) gmon
 #align continuous.comp_lower_semicontinuous_antitone Continuous.comp_lowerSemicontinuous_antitone
 
+theorem LowerSemicontinuousAt.comp_continuousAt {f : α → β} {g : ι → α} {x : ι}
+    (hf : LowerSemicontinuousAt f (g x)) (hg : ContinuousAt g x) :
+    LowerSemicontinuousAt (fun x ↦ f (g x)) x :=
+  fun _ lt ↦ hg.eventually (hf _ lt)
+
+theorem LowerSemicontinuousAt.comp_continuousAt_of_eq {f : α → β} {g : ι → α} {y : α} {x : ι}
+    (hf : LowerSemicontinuousAt f y) (hg : ContinuousAt g x) (hy : g x = y) :
+    LowerSemicontinuousAt (fun x ↦ f (g x)) x := by
+  rw [← hy] at hf
+  exact comp_continuousAt hf hg
+
+theorem LowerSemicontinuous.comp_continuous {f : α → β} {g : ι → α}
+    (hf : LowerSemicontinuous f) (hg : Continuous g) : LowerSemicontinuous fun x ↦ f (g x) :=
+  fun x ↦ (hf (g x)).comp_continuousAt hg.continuousAt
+
 end
 
 /-! #### Addition -/
@@ -946,6 +964,8 @@ variable {γ : Type*} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
+variable {ι : Type*} [TopologicalSpace ι]
+
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Monotone g) :
     UpperSemicontinuousWithinAt (g ∘ f) s x :=
@@ -989,6 +1009,21 @@ theorem Continuous.comp_upperSemicontinuous_antitone {g : γ → δ} {f : α →
   hg.continuousAt.comp_upperSemicontinuousAt_antitone (hf x) gmon
 #align continuous.comp_upper_semicontinuous_antitone Continuous.comp_upperSemicontinuous_antitone
 
+theorem UpperSemicontinuousAt.comp_continuousAt {f : α → β} {g : ι → α} {x : ι}
+    (hf : UpperSemicontinuousAt f (g x)) (hg : ContinuousAt g x) :
+    UpperSemicontinuousAt (fun x ↦ f (g x)) x :=
+  fun _ lt ↦ hg.eventually (hf _ lt)
+
+theorem UpperSemicontinuousAt.comp_continuousAt_of_eq {f : α → β} {g : ι → α} {y : α} {x : ι}
+    (hf : UpperSemicontinuousAt f y) (hg : ContinuousAt g x) (hy : g x = y) :
+    UpperSemicontinuousAt (fun x ↦ f (g x)) x := by
+  rw [← hy] at hf
+  exact comp_continuousAt hf hg
+
+theorem UpperSemicontinuous.comp_continuous {f : α → β} {g : ι → α}
+    (hf : UpperSemicontinuous f) (hg : Continuous g) : UpperSemicontinuous fun x ↦ f (g x) :=
+  fun x ↦ (hf (g x)).comp_continuousAt hg.continuousAt
+
 end
 
 /-! #### Addition -/

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

• In lines I was modifying anyway, I also converted => to ↦.
• Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
• Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

@@ -31,8 +31,8 @@ We introduce 4 definitions related to lower semicontinuity:
 
 We build a basic API using dot notation around these notions, and we prove that
 * constant functions are lower semicontinuous;
-* `indicator s (λ _, y)` is lower semicontinuous when `s` is open and `0 ≤ y`, or when `s` is closed
-  and `y ≤ 0`;
+* `indicator s (fun _ ↦ y)` is lower semicontinuous when `s` is open and `0 ≤ y`,
+  or when `s` is closed and `y ≤ 0`;
 * continuous functions are lower semicontinuous;
 * composition with a continuous monotone functions maps lower semicontinuous functions to lower
   semicontinuous functions. If the function is anti-monotone, it instead maps lower semicontinuous

@@ -51,7 +51,7 @@ restrictions on the order on the codomain):
 * `lowerSemicontinuous_iff_isOpen_preimage` in a linear order;
 * `lowerSemicontinuous_iff_isClosed_preimage` in a linear order;
 * `lowerSemicontinuousAt_iff_le_liminf` in a dense complete linear order;
-* `lowerSemicontinuous_iff_IsClosed_epigraph` in a dense complete linear order with the order
+* `lowerSemicontinuous_iff_isClosed_epigraph` in a dense complete linear order with the order
   topology.
 
 ## Implementation details
@@ -349,7 +349,7 @@ alias ⟨LowerSemicontinuousOn.le_liminf, _⟩ := lowerSemicontinuousOn_iff_le_l
 
 variable [TopologicalSpace γ] [OrderTopology γ]
 
-theorem lowerSemicontinuous_iff_IsClosed_epigraph {f : α → γ} :
+theorem lowerSemicontinuous_iff_isClosed_epigraph {f : α → γ} :
     LowerSemicontinuous f ↔ IsClosed {p : α × γ | f p.1 ≤ p.2} := by
   constructor
   · rw [lowerSemicontinuous_iff_le_liminf, isClosed_iff_forall_filter]
@@ -362,7 +362,13 @@ theorem lowerSemicontinuous_iff_IsClosed_epigraph {f : α → γ} :
   · rw [lowerSemicontinuous_iff_isClosed_preimage]
     exact fun hf y ↦ hf.preimage (Continuous.Prod.mk_left y)
 
-alias ⟨LowerSemicontinuous.IsClosed_epigraph, _⟩ := lowerSemicontinuous_iff_IsClosed_epigraph
+@[deprecated] -- 2024-03-02
+alias lowerSemicontinuous_iff_IsClosed_epigraph := lowerSemicontinuous_iff_isClosed_epigraph
+
+alias ⟨LowerSemicontinuous.isClosed_epigraph, _⟩ := lowerSemicontinuous_iff_isClosed_epigraph
+
+@[deprecated] -- 2024-03-02
+alias LowerSemicontinuous.IsClosed_epigraph := LowerSemicontinuous.isClosed_epigraph
 
 end
 
@@ -926,7 +932,7 @@ variable [TopologicalSpace γ] [OrderTopology γ]
 
 theorem upperSemicontinuous_iff_IsClosed_hypograph {f : α → γ} :
     UpperSemicontinuous f ↔ IsClosed {p : α × γ | p.2 ≤ f p.1} :=
-  lowerSemicontinuous_iff_IsClosed_epigraph (γ := γᵒᵈ)
+  lowerSemicontinuous_iff_isClosed_epigraph (γ := γᵒᵈ)
 
 alias ⟨UpperSemicontinuous.IsClosed_hypograph, _⟩ := upperSemicontinuous_iff_IsClosed_hypograph
 

We add lowerSemicontinuousAt_iff_le_liminf, lowerSemicontinuous_iff_IsClosed_epigraph and variants.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -46,11 +46,24 @@ Similar results are stated and proved for upper semicontinuity.
 We also prove that a function is continuous if and only if it is both lower and upper
 semicontinuous.
 
+We have some equivalent definitions of lower- and upper-semicontinuity (under certain
+restrictions on the order on the codomain):
+* `lowerSemicontinuous_iff_isOpen_preimage` in a linear order;
+* `lowerSemicontinuous_iff_isClosed_preimage` in a linear order;
+* `lowerSemicontinuousAt_iff_le_liminf` in a dense complete linear order;
+* `lowerSemicontinuous_iff_IsClosed_epigraph` in a dense complete linear order with the order
+  topology.
+
 ## Implementation details
 
 All the nontrivial results for upper semicontinuous functions are deduced from the corresponding
 ones for lower semicontinuous functions using `OrderDual`.
 
+## References
+
+* <https://en.wikipedia.org/wiki/Closed_convex_function>
+* <https://en.wikipedia.org/wiki/Semi-continuity>
+
 -/
 
 
@@ -297,6 +310,62 @@ theorem Continuous.lowerSemicontinuous {f : α → γ} (h : Continuous f) : Lowe
 
 end
 
+/-! #### Equivalent definitions -/
+
+section
+
+variable {γ : Type*} [CompleteLinearOrder γ] [DenselyOrdered γ]
+
+theorem lowerSemicontinuousWithinAt_iff_le_liminf {f : α → γ} :
+    LowerSemicontinuousWithinAt f s x ↔ f x ≤ liminf f (𝓝[s] x) := by
+  constructor
+  · intro hf; unfold LowerSemicontinuousWithinAt at hf
+    contrapose! hf
+    obtain ⟨y, lty, ylt⟩ := exists_between hf; use y
+    exact ⟨ylt, fun h => lty.not_le
+      (le_liminf_of_le (by isBoundedDefault) (h.mono fun _ hx => le_of_lt hx))⟩
+  exact fun hf y ylt => eventually_lt_of_lt_liminf (ylt.trans_le hf)
+
+alias ⟨LowerSemicontinuousWithinAt.le_liminf, _⟩ := lowerSemicontinuousWithinAt_iff_le_liminf
+
+theorem lowerSemicontinuousAt_iff_le_liminf {f : α → γ} :
+    LowerSemicontinuousAt f x ↔ f x ≤ liminf f (𝓝 x) := by
+  rw [← lowerSemicontinuousWithinAt_univ_iff, lowerSemicontinuousWithinAt_iff_le_liminf,
+    ← nhdsWithin_univ]
+
+alias ⟨LowerSemicontinuousAt.le_liminf, _⟩ := lowerSemicontinuousAt_iff_le_liminf
+
+theorem lowerSemicontinuous_iff_le_liminf {f : α → γ} :
+    LowerSemicontinuous f ↔ ∀ x, f x ≤ liminf f (𝓝 x) := by
+  simp only [← lowerSemicontinuousAt_iff_le_liminf, LowerSemicontinuous]
+
+alias ⟨LowerSemicontinuous.le_liminf, _⟩ := lowerSemicontinuous_iff_le_liminf
+
+theorem lowerSemicontinuousOn_iff_le_liminf {f : α → γ} :
+    LowerSemicontinuousOn f s ↔ ∀ x ∈ s, f x ≤ liminf f (𝓝[s] x) := by
+  simp only [← lowerSemicontinuousWithinAt_iff_le_liminf, LowerSemicontinuousOn]
+
+alias ⟨LowerSemicontinuousOn.le_liminf, _⟩ := lowerSemicontinuousOn_iff_le_liminf
+
+variable [TopologicalSpace γ] [OrderTopology γ]
+
+theorem lowerSemicontinuous_iff_IsClosed_epigraph {f : α → γ} :
+    LowerSemicontinuous f ↔ IsClosed {p : α × γ | f p.1 ≤ p.2} := by
+  constructor
+  · rw [lowerSemicontinuous_iff_le_liminf, isClosed_iff_forall_filter]
+    rintro hf ⟨x, y⟩ F F_ne h h'
+    rw [nhds_prod_eq, le_prod] at h'
+    calc f x ≤ liminf f (𝓝 x) := hf x
+    _ ≤ liminf f (map Prod.fst F) := liminf_le_liminf_of_le h'.1
+    _ ≤ liminf Prod.snd F := liminf_le_liminf <| (eventually_principal.2 fun _ ↦ id).filter_mono h
+    _ = y := h'.2.liminf_eq
+  · rw [lowerSemicontinuous_iff_isClosed_preimage]
+    exact fun hf y ↦ hf.preimage (Continuous.Prod.mk_left y)
+
+alias ⟨LowerSemicontinuous.IsClosed_epigraph, _⟩ := lowerSemicontinuous_iff_IsClosed_epigraph
+
+end
+
 /-! ### Composition -/
 
 
@@ -823,8 +892,47 @@ theorem Continuous.upperSemicontinuous {f : α → γ} (h : Continuous f) : Uppe
 
 end
 
-/-! ### Composition -/
+/-! #### Equivalent definitions -/
+
+section
+
+variable {γ : Type*} [CompleteLinearOrder γ] [DenselyOrdered γ]
+
+theorem upperSemicontinuousWithinAt_iff_limsup_le {f : α → γ} :
+    UpperSemicontinuousWithinAt f s x ↔ limsup f (𝓝[s] x) ≤ f x :=
+  lowerSemicontinuousWithinAt_iff_le_liminf (γ := γᵒᵈ)
+
+alias ⟨UpperSemicontinuousWithinAt.limsup_le, _⟩ := upperSemicontinuousWithinAt_iff_limsup_le
+
+theorem upperSemicontinuousAt_iff_limsup_le {f : α → γ} :
+    UpperSemicontinuousAt f x ↔ limsup f (𝓝 x) ≤ f x :=
+  lowerSemicontinuousAt_iff_le_liminf (γ := γᵒᵈ)
+
+alias ⟨UpperSemicontinuousAt.limsup_le, _⟩ := upperSemicontinuousAt_iff_limsup_le
+
+theorem upperSemicontinuous_iff_limsup_le {f : α → γ} :
+    UpperSemicontinuous f ↔ ∀ x, limsup f (𝓝 x) ≤ f x :=
+  lowerSemicontinuous_iff_le_liminf (γ := γᵒᵈ)
+
+alias ⟨UpperSemicontinuous.limsup_le, _⟩ := upperSemicontinuous_iff_limsup_le
 
+theorem upperSemicontinuousOn_iff_limsup_le {f : α → γ} :
+    UpperSemicontinuousOn f s ↔ ∀ x ∈ s, limsup f (𝓝[s] x) ≤ f x :=
+  lowerSemicontinuousOn_iff_le_liminf (γ := γᵒᵈ)
+
+alias ⟨UpperSemicontinuousOn.limsup_le, _⟩ := upperSemicontinuousOn_iff_limsup_le
+
+variable [TopologicalSpace γ] [OrderTopology γ]
+
+theorem upperSemicontinuous_iff_IsClosed_hypograph {f : α → γ} :
+    UpperSemicontinuous f ↔ IsClosed {p : α × γ | p.2 ≤ f p.1} :=
+  lowerSemicontinuous_iff_IsClosed_epigraph (γ := γᵒᵈ)
+
+alias ⟨UpperSemicontinuous.IsClosed_hypograph, _⟩ := upperSemicontinuous_iff_IsClosed_hypograph
+
+end
+
+/-! ### Composition -/
 
 section
 

Changes in this PR shouldn't change the public API. The only changes about ∃ x ∈ s, _ is inside a proof.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -564,7 +564,7 @@ theorem lowerSemicontinuousWithinAt_iSup {f : ι → α → δ}
   lowerSemicontinuousWithinAt_ciSup (by simp) h
 #align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_iSup
 
-theorem lowerSemicontinuousWithinAt_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousWithinAt_biSup {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ (i) (hi), f i hi x') s x :=
   lowerSemicontinuousWithinAt_iSup fun i => lowerSemicontinuousWithinAt_iSup fun hi => h i hi
@@ -583,7 +583,7 @@ theorem lowerSemicontinuousAt_iSup {f : ι → α → δ} (h : ∀ i, LowerSemic
   lowerSemicontinuousAt_ciSup (by simp) h
 #align lower_semicontinuous_at_supr lowerSemicontinuousAt_iSup
 
-theorem lowerSemicontinuousAt_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousAt_biSup {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
     LowerSemicontinuousAt (fun x' => ⨆ (i) (hi), f i hi x') x :=
   lowerSemicontinuousAt_iSup fun i => lowerSemicontinuousAt_iSup fun hi => h i hi
@@ -600,7 +600,7 @@ theorem lowerSemicontinuousOn_iSup {f : ι → α → δ} (h : ∀ i, LowerSemic
   lowerSemicontinuousOn_ciSup (by simp) h
 #align lower_semicontinuous_on_supr lowerSemicontinuousOn_iSup
 
-theorem lowerSemicontinuousOn_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousOn_biSup {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
     LowerSemicontinuousOn (fun x' => ⨆ (i) (hi), f i hi x') s :=
   lowerSemicontinuousOn_iSup fun i => lowerSemicontinuousOn_iSup fun hi => h i hi
@@ -616,7 +616,7 @@ theorem lowerSemicontinuous_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicon
   lowerSemicontinuous_ciSup (by simp) h
 #align lower_semicontinuous_supr lowerSemicontinuous_iSup
 
-theorem lowerSemicontinuous_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuous_biSup {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
     LowerSemicontinuous fun x' => ⨆ (i) (hi), f i hi x' :=
   lowerSemicontinuous_iSup fun i => lowerSemicontinuous_iSup fun hi => h i hi
@@ -1006,7 +1006,7 @@ theorem upperSemicontinuousWithinAt_iInf {f : ι → α → δ}
   @lowerSemicontinuousWithinAt_iSup α _ x s ι δᵒᵈ _ f h
 #align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_iInf
 
-theorem upperSemicontinuousWithinAt_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousWithinAt_biInf {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ (i) (hi), f i hi x') s x :=
   upperSemicontinuousWithinAt_iInf fun i => upperSemicontinuousWithinAt_iInf fun hi => h i hi
@@ -1023,7 +1023,7 @@ theorem upperSemicontinuousAt_iInf {f : ι → α → δ} (h : ∀ i, UpperSemic
   @lowerSemicontinuousAt_iSup α _ x ι δᵒᵈ _ f h
 #align upper_semicontinuous_at_infi upperSemicontinuousAt_iInf
 
-theorem upperSemicontinuousAt_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousAt_biInf {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
     UpperSemicontinuousAt (fun x' => ⨅ (i) (hi), f i hi x') x :=
   upperSemicontinuousAt_iInf fun i => upperSemicontinuousAt_iInf fun hi => h i hi
@@ -1040,7 +1040,7 @@ theorem upperSemicontinuousOn_iInf {f : ι → α → δ} (h : ∀ i, UpperSemic
   upperSemicontinuousWithinAt_iInf fun i => h i x hx
 #align upper_semicontinuous_on_infi upperSemicontinuousOn_iInf
 
-theorem upperSemicontinuousOn_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousOn_biInf {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
     UpperSemicontinuousOn (fun x' => ⨅ (i) (hi), f i hi x') s :=
   upperSemicontinuousOn_iInf fun i => upperSemicontinuousOn_iInf fun hi => h i hi
@@ -1055,7 +1055,7 @@ theorem upperSemicontinuous_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicon
     UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_iInf fun i => h i x
 #align upper_semicontinuous_infi upperSemicontinuous_iInf
 
-theorem upperSemicontinuous_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuous_biInf {p : ι → Prop} {f : ∀ i, p i → α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
     UpperSemicontinuous fun x' => ⨅ (i) (hi), f i hi x' :=
   upperSemicontinuous_iInf fun i => upperSemicontinuous_iInf fun hi => h i hi

Function.support is a very basic definition. Nevertheless, it is a pretty heavy import because it imports most objects a support lemma can be written about.

This PR reverses the dependencies between those objects and Function.support, so that the latter can become a much more lightweight import.

Only two import could not easily be reversed, namely the ones to Data.Set.Finite and Order.ConditionallyCompleteLattice.Basic, so I created two new files instead.

I credit:

• Yury for https://github.com/leanprover-community/mathlib/pull/6791
• Oliver for https://github.com/leanprover-community/mathlib/pull/7439

@@ -3,7 +3,7 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathlib.Algebra.IndicatorFunction
+import Mathlib.Algebra.Function.Indicator
 import Mathlib.Topology.ContinuousOn
 import Mathlib.Topology.Instances.ENNReal
 

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -313,7 +313,7 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
   by_cases h : ∃ l, l < f x
   · obtain ⟨z, zlt, hz⟩ : ∃ z < f x, Ioc z (f x) ⊆ g ⁻¹' Ioi y :=
       exists_Ioc_subset_of_mem_nhds (hg (Ioi_mem_nhds hy)) h
-    filter_upwards [hf z zlt]with a ha
+    filter_upwards [hf z zlt] with a ha
     calc
       y < g (min (f x) (f a)) := hz (by simp [zlt, ha, le_refl])
       _ ≤ g (f a) := gmon (min_le_right _ _)
@@ -388,7 +388,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
     by_cases hx₂ : ∃ l, l < g x
     · obtain ⟨z₂, z₂lt, h₂⟩ : ∃ z₂ < g x, Ioc z₂ (g x) ⊆ v :=
         exists_Ioc_subset_of_mem_nhds (v_open.mem_nhds xv) hx₂
-      filter_upwards [hf z₁ z₁lt, hg z₂ z₂lt]with z h₁z h₂z
+      filter_upwards [hf z₁ z₁lt, hg z₂ z₂lt] with z h₁z h₂z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
         · simp [H]
@@ -407,7 +407,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
         _ ≤ f z + g z := add_le_add (min_le_left _ _) (min_le_left _ _)
 
     · simp only [not_exists, not_lt] at hx₂
-      filter_upwards [hf z₁ z₁lt]with z h₁z
+      filter_upwards [hf z₁ z₁lt] with z h₁z
       have A1 : min (f z) (f x) ∈ u := by
         by_cases H : f z ≤ f x
         · simp [H]
@@ -423,7 +423,7 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
     by_cases hx₂ : ∃ l, l < g x
     · obtain ⟨z₂, z₂lt, h₂⟩ : ∃ z₂ < g x, Ioc z₂ (g x) ⊆ v :=
         exists_Ioc_subset_of_mem_nhds (v_open.mem_nhds xv) hx₂
-      filter_upwards [hg z₂ z₂lt]with z h₂z
+      filter_upwards [hg z₂ z₂lt] with z h₂z
       have A2 : min (g z) (g x) ∈ v := by
         by_cases H : g z ≤ g x
         · simp [H]
@@ -555,7 +555,7 @@ theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
   · simpa only [iSup_of_empty'] using lowerSemicontinuousWithinAt_const
   · intro y hy
     rcases exists_lt_of_lt_ciSup hy with ⟨i, hi⟩
-    filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_ciSup hy' i)
+    filter_upwards [h i y hi, bdd] with y hy hy' using hy.trans_le (le_ciSup hy' i)
 #align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSup
 
 theorem lowerSemicontinuousWithinAt_iSup {f : ι → α → δ}
@@ -1078,16 +1078,16 @@ theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ}
   · rcases exists_Ioc_subset_of_mem_nhds hv Hl with ⟨l, lfx, hl⟩
     by_cases Hu : ∃ u, f x < u
     · rcases exists_Ico_subset_of_mem_nhds hv Hu with ⟨u, fxu, hu⟩
-      filter_upwards [h₁ l lfx, h₂ u fxu]with a lfa fau
+      filter_upwards [h₁ l lfx, h₂ u fxu] with a lfa fau
       cases' le_or_gt (f a) (f x) with h h
       · exact hl ⟨lfa, h⟩
       · exact hu ⟨le_of_lt h, fau⟩
     · simp only [not_exists, not_lt] at Hu
-      filter_upwards [h₁ l lfx]with a lfa using hl ⟨lfa, Hu (f a)⟩
+      filter_upwards [h₁ l lfx] with a lfa using hl ⟨lfa, Hu (f a)⟩
   · simp only [not_exists, not_lt] at Hl
     by_cases Hu : ∃ u, f x < u
     · rcases exists_Ico_subset_of_mem_nhds hv Hu with ⟨u, fxu, hu⟩
-      filter_upwards [h₂ u fxu]with a lfa
+      filter_upwards [h₂ u fxu] with a lfa
       apply hu
       exact ⟨Hl (f a), lfa⟩
     · simp only [not_exists, not_lt] at Hu

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

This has nice performance benefits.

@@ -58,7 +58,7 @@ open Topology BigOperators ENNReal
 
 open Set Function Filter
 
-variable {α : Type _} [TopologicalSpace α] {β : Type _} [Preorder β] {f g : α → β} {x : α}
+variable {α : Type*} [TopologicalSpace α] {β : Type*} [Preorder β] {f g : α → β} {x : α}
   {s t : Set α} {y z : β}
 
 /-! ### Main definitions -/
@@ -264,7 +264,7 @@ theorem LowerSemicontinuous.isOpen_preimage (hf : LowerSemicontinuous f) (y : β
 
 section
 
-variable {γ : Type _} [LinearOrder γ]
+variable {γ : Type*} [LinearOrder γ]
 
 theorem lowerSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     LowerSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Iic y) := by
@@ -302,9 +302,9 @@ end
 
 section
 
-variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
+variable {γ : Type*} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
-variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
+variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
 theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : LowerSemicontinuousWithinAt f s x) (gmon : Monotone g) :
@@ -367,7 +367,7 @@ end
 
 section
 
-variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
+variable {ι : Type*} {γ : Type*} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
   [OrderTopology γ]
 
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an
@@ -545,7 +545,7 @@ end
 
 section
 
-variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
+variable {ι : Sort*} {δ δ' : Type*} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
 theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
@@ -629,7 +629,7 @@ end
 
 section
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
@@ -790,7 +790,7 @@ theorem UpperSemicontinuous.isOpen_preimage (hf : UpperSemicontinuous f) (y : β
 
 section
 
-variable {γ : Type _} [LinearOrder γ]
+variable {γ : Type*} [LinearOrder γ]
 
 theorem upperSemicontinuous_iff_isClosed_preimage {f : α → γ} :
     UpperSemicontinuous f ↔ ∀ y, IsClosed (f ⁻¹' Ici y) := by
@@ -828,9 +828,9 @@ end
 
 section
 
-variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
+variable {γ : Type*} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
-variable {δ : Type _} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
+variable {δ : Type*} [LinearOrder δ] [TopologicalSpace δ] [OrderTopology δ]
 
 theorem ContinuousAt.comp_upperSemicontinuousWithinAt {g : γ → δ} {f : α → γ}
     (hg : ContinuousAt g (f x)) (hf : UpperSemicontinuousWithinAt f s x) (gmon : Monotone g) :
@@ -882,7 +882,7 @@ end
 
 section
 
-variable {ι : Type _} {γ : Type _} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
+variable {ι : Type*} {γ : Type*} [LinearOrderedAddCommMonoid γ] [TopologicalSpace γ]
   [OrderTopology γ]
 
 /-- The sum of two upper semicontinuous functions is upper semicontinuous. Formulated with an
@@ -991,7 +991,7 @@ end
 
 section
 
-variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
+variable {ι : Sort*} {δ δ' : Type*} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
 theorem upperSemicontinuousWithinAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
@@ -1065,7 +1065,7 @@ end
 
 section
 
-variable {γ : Type _} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
+variable {γ : Type*} [LinearOrder γ] [TopologicalSpace γ] [OrderTopology γ]
 
 theorem continuousWithinAt_iff_lower_upperSemicontinuousWithinAt {f : α → γ} :
     ContinuousWithinAt f s x ↔

• 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 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.semicontinuous
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.IndicatorFunction
 import Mathlib.Topology.ContinuousOn
 import Mathlib.Topology.Instances.ENNReal
 
+#align_import topology.semicontinuous from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Semicontinuous maps
 

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

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

@@ -68,7 +68,7 @@ variable {α : Type _} [TopologicalSpace α] {β : Type _} [Preorder β] {f g :
 
 
 /-- A real function `f` is lower semicontinuous at `x` within a set `s` if, for any `ε > 0`, for all
-`x'` close enough to `x` in  `s`, then `f x'` is at least `f x - ε`. We formulate this in a general
+`x'` close enough to `x` in `s`, then `f x'` is at least `f x - ε`. We formulate this in a general
 preordered space, using an arbitrary `y < f x` instead of `f x - ε`. -/
 def LowerSemicontinuousWithinAt (f : α → β) (s : Set α) (x : α) :=
   ∀ y < f x, ∀ᶠ x' in 𝓝[s] x, y < f x'
@@ -96,7 +96,7 @@ def LowerSemicontinuous (f : α → β) :=
 #align lower_semicontinuous LowerSemicontinuous
 
 /-- A real function `f` is upper semicontinuous at `x` within a set `s` if, for any `ε > 0`, for all
-`x'` close enough to `x` in  `s`, then `f x'` is at most `f x + ε`. We formulate this in a general
+`x'` close enough to `x` in `s`, then `f x'` is at most `f x + ε`. We formulate this in a general
 preordered space, using an arbitrary `y > f x` instead of `f x + ε`. -/
 def UpperSemicontinuousWithinAt (f : α → β) (s : Set α) (x : α) :=
   ∀ y, f x < y → ∀ᶠ x' in 𝓝[s] x, f x' < y

Changes are of the form

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

@@ -327,7 +327,7 @@ theorem ContinuousAt.comp_lowerSemicontinuousWithinAt {g : γ → δ} {f : α 
 
 theorem ContinuousAt.comp_lowerSemicontinuousAt {g : γ → δ} {f : α → γ} (hg : ContinuousAt g (f x))
     (hf : LowerSemicontinuousAt f x) (gmon : Monotone g) : LowerSemicontinuousAt (g ∘ f) x := by
-  simp only [← lowerSemicontinuousWithinAt_univ_iff] at hf⊢
+  simp only [← lowerSemicontinuousWithinAt_univ_iff] at hf ⊢
   exact hg.comp_lowerSemicontinuousWithinAt hf gmon
 #align continuous_at.comp_lower_semicontinuous_at ContinuousAt.comp_lowerSemicontinuousAt
 

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>

@@ -550,80 +550,80 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-theorem lowerSemicontinuousWithinAt_csupᵢ {f : ι → α → δ'}
+theorem lowerSemicontinuousWithinAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x := by
   cases isEmpty_or_nonempty ι
-  · simpa only [supᵢ_of_empty'] using lowerSemicontinuousWithinAt_const
+  · simpa only [iSup_of_empty'] using lowerSemicontinuousWithinAt_const
   · intro y hy
-    rcases exists_lt_of_lt_csupᵢ hy with ⟨i, hi⟩
-    filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_csupᵢ hy' i)
-#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupᵢ
+    rcases exists_lt_of_lt_ciSup hy with ⟨i, hi⟩
+    filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_ciSup hy' i)
+#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_ciSup
 
-theorem lowerSemicontinuousWithinAt_supᵢ {f : ι → α → δ}
+theorem lowerSemicontinuousWithinAt_iSup {f : ι → α → δ}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
-  lowerSemicontinuousWithinAt_csupᵢ (by simp) h
-#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_supᵢ
+  lowerSemicontinuousWithinAt_ciSup (by simp) h
+#align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_iSup
 
-theorem lowerSemicontinuousWithinAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousWithinAt_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ (i) (hi), f i hi x') s x :=
-  lowerSemicontinuousWithinAt_supᵢ fun i => lowerSemicontinuousWithinAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupᵢ
+  lowerSemicontinuousWithinAt_iSup fun i => lowerSemicontinuousWithinAt_iSup fun hi => h i hi
+#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_biSup
 
-theorem lowerSemicontinuousAt_csupᵢ {f : ι → α → δ'}
+theorem lowerSemicontinuousAt_ciSup {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddAbove (range fun i => f i y)) (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x := by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
   rw [← nhdsWithin_univ] at bdd
-  exact lowerSemicontinuousWithinAt_csupᵢ bdd h
-#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupᵢ
+  exact lowerSemicontinuousWithinAt_ciSup bdd h
+#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_ciSup
 
-theorem lowerSemicontinuousAt_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
+theorem lowerSemicontinuousAt_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
-  lowerSemicontinuousAt_csupᵢ (by simp) h
-#align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢ
+  lowerSemicontinuousAt_ciSup (by simp) h
+#align lower_semicontinuous_at_supr lowerSemicontinuousAt_iSup
 
-theorem lowerSemicontinuousAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousAt_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
     LowerSemicontinuousAt (fun x' => ⨆ (i) (hi), f i hi x') x :=
-  lowerSemicontinuousAt_supᵢ fun i => lowerSemicontinuousAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupᵢ
+  lowerSemicontinuousAt_iSup fun i => lowerSemicontinuousAt_iSup fun hi => h i hi
+#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_biSup
 
-theorem lowerSemicontinuousOn_csupᵢ {f : ι → α → δ'}
+theorem lowerSemicontinuousOn_ciSup {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddAbove (range fun i => f i x)) (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s := fun x hx =>
-  lowerSemicontinuousWithinAt_csupᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupᵢ
+  lowerSemicontinuousWithinAt_ciSup (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_ciSup
 
-theorem lowerSemicontinuousOn_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
+theorem lowerSemicontinuousOn_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s :=
-  lowerSemicontinuousOn_csupᵢ (by simp) h
-#align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢ
+  lowerSemicontinuousOn_ciSup (by simp) h
+#align lower_semicontinuous_on_supr lowerSemicontinuousOn_iSup
 
-theorem lowerSemicontinuousOn_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousOn_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
     LowerSemicontinuousOn (fun x' => ⨆ (i) (hi), f i hi x') s :=
-  lowerSemicontinuousOn_supᵢ fun i => lowerSemicontinuousOn_supᵢ fun hi => h i hi
-#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupᵢ
+  lowerSemicontinuousOn_iSup fun i => lowerSemicontinuousOn_iSup fun hi => h i hi
+#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_biSup
 
-theorem lowerSemicontinuous_csupᵢ {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
+theorem lowerSemicontinuous_ciSup {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
     (h : ∀ i, LowerSemicontinuous (f i)) : LowerSemicontinuous fun x' => ⨆ i, f i x' := fun x =>
-  lowerSemicontinuousAt_csupᵢ (eventually_of_forall bdd) fun i => h i x
-#align lower_semicontinuous_csupr lowerSemicontinuous_csupᵢ
+  lowerSemicontinuousAt_ciSup (eventually_of_forall bdd) fun i => h i x
+#align lower_semicontinuous_csupr lowerSemicontinuous_ciSup
 
-theorem lowerSemicontinuous_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
+theorem lowerSemicontinuous_iSup {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ⨆ i, f i x' :=
-  lowerSemicontinuous_csupᵢ (by simp) h
-#align lower_semicontinuous_supr lowerSemicontinuous_supᵢ
+  lowerSemicontinuous_ciSup (by simp) h
+#align lower_semicontinuous_supr lowerSemicontinuous_iSup
 
-theorem lowerSemicontinuous_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuous_biSup {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
     LowerSemicontinuous fun x' => ⨆ (i) (hi), f i hi x' :=
-  lowerSemicontinuous_supᵢ fun i => lowerSemicontinuous_supᵢ fun hi => h i hi
-#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupᵢ
+  lowerSemicontinuous_iSup fun i => lowerSemicontinuous_iSup fun hi => h i hi
+#align lower_semicontinuous_bsupr lowerSemicontinuous_biSup
 
 end
 
@@ -637,8 +637,8 @@ variable {ι : Type _}
 theorem lowerSemicontinuousWithinAt_tsum {f : ι → α → ℝ≥0∞}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ∑' i, f i x') s x := by
-  simp_rw [ENNReal.tsum_eq_supᵢ_sum]
-  refine lowerSemicontinuousWithinAt_supᵢ fun b => ?_
+  simp_rw [ENNReal.tsum_eq_iSup_sum]
+  refine lowerSemicontinuousWithinAt_iSup fun b => ?_
   exact lowerSemicontinuousWithinAt_sum fun i _hi => h i
 #align lower_semicontinuous_within_at_tsum lowerSemicontinuousWithinAt_tsum
 
@@ -996,73 +996,73 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-theorem upperSemicontinuousWithinAt_cinfᵢ {f : ι → α → δ'}
+theorem upperSemicontinuousWithinAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
-  @lowerSemicontinuousWithinAt_csupᵢ α _ x s ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfᵢ
+  @lowerSemicontinuousWithinAt_ciSup α _ x s ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_ciInf
 
-theorem upperSemicontinuousWithinAt_infᵢ {f : ι → α → δ}
+theorem upperSemicontinuousWithinAt_iInf {f : ι → α → δ}
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
-  @lowerSemicontinuousWithinAt_supᵢ α _ x s ι δᵒᵈ _ f h
-#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_infᵢ
+  @lowerSemicontinuousWithinAt_iSup α _ x s ι δᵒᵈ _ f h
+#align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_iInf
 
-theorem upperSemicontinuousWithinAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousWithinAt_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ (i) (hi), f i hi x') s x :=
-  upperSemicontinuousWithinAt_infᵢ fun i => upperSemicontinuousWithinAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfᵢ
+  upperSemicontinuousWithinAt_iInf fun i => upperSemicontinuousWithinAt_iInf fun hi => h i hi
+#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_biInf
 
-theorem upperSemicontinuousAt_cinfᵢ {f : ι → α → δ'}
+theorem upperSemicontinuousAt_ciInf {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddBelow (range fun i => f i y)) (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
-  @lowerSemicontinuousAt_csupᵢ α _ x ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfᵢ
+  @lowerSemicontinuousAt_ciSup α _ x ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_ciInf
 
-theorem upperSemicontinuousAt_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
+theorem upperSemicontinuousAt_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
-  @lowerSemicontinuousAt_supᵢ α _ x ι δᵒᵈ _ f h
-#align upper_semicontinuous_at_infi upperSemicontinuousAt_infᵢ
+  @lowerSemicontinuousAt_iSup α _ x ι δᵒᵈ _ f h
+#align upper_semicontinuous_at_infi upperSemicontinuousAt_iInf
 
-theorem upperSemicontinuousAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousAt_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
     UpperSemicontinuousAt (fun x' => ⨅ (i) (hi), f i hi x') x :=
-  upperSemicontinuousAt_infᵢ fun i => upperSemicontinuousAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfᵢ
+  upperSemicontinuousAt_iInf fun i => upperSemicontinuousAt_iInf fun hi => h i hi
+#align upper_semicontinuous_at_binfi upperSemicontinuousAt_biInf
 
-theorem upperSemicontinuousOn_cinfᵢ {f : ι → α → δ'}
+theorem upperSemicontinuousOn_ciInf {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddBelow (range fun i => f i x)) (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
-  upperSemicontinuousWithinAt_cinfᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfᵢ
+  upperSemicontinuousWithinAt_ciInf (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_ciInf
 
-theorem upperSemicontinuousOn_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
+theorem upperSemicontinuousOn_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
-  upperSemicontinuousWithinAt_infᵢ fun i => h i x hx
-#align upper_semicontinuous_on_infi upperSemicontinuousOn_infᵢ
+  upperSemicontinuousWithinAt_iInf fun i => h i x hx
+#align upper_semicontinuous_on_infi upperSemicontinuousOn_iInf
 
-theorem upperSemicontinuousOn_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousOn_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
     UpperSemicontinuousOn (fun x' => ⨅ (i) (hi), f i hi x') s :=
-  upperSemicontinuousOn_infᵢ fun i => upperSemicontinuousOn_infᵢ fun hi => h i hi
-#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfᵢ
+  upperSemicontinuousOn_iInf fun i => upperSemicontinuousOn_iInf fun hi => h i hi
+#align upper_semicontinuous_on_binfi upperSemicontinuousOn_biInf
 
-theorem upperSemicontinuous_cinfᵢ {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
+theorem upperSemicontinuous_ciInf {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
     (h : ∀ i, UpperSemicontinuous (f i)) : UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x =>
-  upperSemicontinuousAt_cinfᵢ (eventually_of_forall bdd) fun i => h i x
-#align upper_semicontinuous_cinfi upperSemicontinuous_cinfᵢ
+  upperSemicontinuousAt_ciInf (eventually_of_forall bdd) fun i => h i x
+#align upper_semicontinuous_cinfi upperSemicontinuous_ciInf
 
-theorem upperSemicontinuous_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
-    UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_infᵢ fun i => h i x
-#align upper_semicontinuous_infi upperSemicontinuous_infᵢ
+theorem upperSemicontinuous_iInf {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
+    UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_iInf fun i => h i x
+#align upper_semicontinuous_infi upperSemicontinuous_iInf
 
-theorem upperSemicontinuous_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuous_biInf {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
     UpperSemicontinuous fun x' => ⨅ (i) (hi), f i hi x' :=
-  upperSemicontinuous_infᵢ fun i => upperSemicontinuous_infᵢ fun hi => h i hi
-#align upper_semicontinuous_binfi upperSemicontinuous_binfᵢ
+  upperSemicontinuous_iInf fun i => upperSemicontinuous_iInf fun hi => h i hi
+#align upper_semicontinuous_binfi upperSemicontinuous_biInf
 
 end
 

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -437,7 +437,6 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < f x + min (g z) (g x) := h this
         _ ≤ f z + g z := add_le_add (hx₁ (f z)) (min_le_left _ _)
-
     · simp only [not_exists, not_lt] at hx₁ hx₂
       apply Filter.eventually_of_forall
       intro z
@@ -445,7 +444,6 @@ theorem LowerSemicontinuousWithinAt.add' {f g : α → γ} (hf : LowerSemicontin
       calc
         y < f x + g x := h this
         _ ≤ f z + g z := add_le_add (hx₁ (f z)) (hx₂ (g z))
-
 #align lower_semicontinuous_within_at.add' LowerSemicontinuousWithinAt.add'
 
 /-- The sum of two lower semicontinuous functions is lower semicontinuous. Formulated with an

@@ -552,7 +552,7 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-theorem lowerSemicontinuousWithinAt_csupr {f : ι → α → δ'}
+theorem lowerSemicontinuousWithinAt_csupᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddAbove (range fun i => f i y))
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x := by
@@ -561,71 +561,71 @@ theorem lowerSemicontinuousWithinAt_csupr {f : ι → α → δ'}
   · intro y hy
     rcases exists_lt_of_lt_csupᵢ hy with ⟨i, hi⟩
     filter_upwards [h i y hi, bdd]with y hy hy' using hy.trans_le (le_csupᵢ hy' i)
-#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupr
+#align lower_semicontinuous_within_at_csupr lowerSemicontinuousWithinAt_csupᵢ
 
 theorem lowerSemicontinuousWithinAt_supᵢ {f : ι → α → δ}
     (h : ∀ i, LowerSemicontinuousWithinAt (f i) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ i, f i x') s x :=
-  lowerSemicontinuousWithinAt_csupr (by simp) h
+  lowerSemicontinuousWithinAt_csupᵢ (by simp) h
 #align lower_semicontinuous_within_at_supr lowerSemicontinuousWithinAt_supᵢ
 
-theorem lowerSemicontinuousWithinAt_bsupr {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousWithinAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousWithinAt (f i hi) s x) :
     LowerSemicontinuousWithinAt (fun x' => ⨆ (i) (hi), f i hi x') s x :=
   lowerSemicontinuousWithinAt_supᵢ fun i => lowerSemicontinuousWithinAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupr
+#align lower_semicontinuous_within_at_bsupr lowerSemicontinuousWithinAt_bsupᵢ
 
-theorem lowerSemicontinuousAt_csupr {f : ι → α → δ'}
+theorem lowerSemicontinuousAt_csupᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddAbove (range fun i => f i y)) (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x := by
   simp_rw [← lowerSemicontinuousWithinAt_univ_iff] at *
   rw [← nhdsWithin_univ] at bdd
-  exact lowerSemicontinuousWithinAt_csupr bdd h
-#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupr
+  exact lowerSemicontinuousWithinAt_csupᵢ bdd h
+#align lower_semicontinuous_at_csupr lowerSemicontinuousAt_csupᵢ
 
 theorem lowerSemicontinuousAt_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousAt (f i) x) :
     LowerSemicontinuousAt (fun x' => ⨆ i, f i x') x :=
-  lowerSemicontinuousAt_csupr (by simp) h
+  lowerSemicontinuousAt_csupᵢ (by simp) h
 #align lower_semicontinuous_at_supr lowerSemicontinuousAt_supᵢ
 
-theorem lowerSemicontinuousAt_bsupr {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousAt_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousAt (f i hi) x) :
     LowerSemicontinuousAt (fun x' => ⨆ (i) (hi), f i hi x') x :=
   lowerSemicontinuousAt_supᵢ fun i => lowerSemicontinuousAt_supᵢ fun hi => h i hi
-#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupr
+#align lower_semicontinuous_at_bsupr lowerSemicontinuousAt_bsupᵢ
 
-theorem lowerSemicontinuousOn_csupr {f : ι → α → δ'}
+theorem lowerSemicontinuousOn_csupᵢ {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddAbove (range fun i => f i x)) (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s := fun x hx =>
-  lowerSemicontinuousWithinAt_csupr (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupr
+  lowerSemicontinuousWithinAt_csupᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align lower_semicontinuous_on_csupr lowerSemicontinuousOn_csupᵢ
 
 theorem lowerSemicontinuousOn_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuousOn (f i) s) :
     LowerSemicontinuousOn (fun x' => ⨆ i, f i x') s :=
-  lowerSemicontinuousOn_csupr (by simp) h
+  lowerSemicontinuousOn_csupᵢ (by simp) h
 #align lower_semicontinuous_on_supr lowerSemicontinuousOn_supᵢ
 
-theorem lowerSemicontinuousOn_bsupr {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuousOn_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuousOn (f i hi) s) :
     LowerSemicontinuousOn (fun x' => ⨆ (i) (hi), f i hi x') s :=
   lowerSemicontinuousOn_supᵢ fun i => lowerSemicontinuousOn_supᵢ fun hi => h i hi
-#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupr
+#align lower_semicontinuous_on_bsupr lowerSemicontinuousOn_bsupᵢ
 
-theorem lowerSemicontinuous_csupr {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
+theorem lowerSemicontinuous_csupᵢ {f : ι → α → δ'} (bdd : ∀ x, BddAbove (range fun i => f i x))
     (h : ∀ i, LowerSemicontinuous (f i)) : LowerSemicontinuous fun x' => ⨆ i, f i x' := fun x =>
-  lowerSemicontinuousAt_csupr (eventually_of_forall bdd) fun i => h i x
-#align lower_semicontinuous_csupr lowerSemicontinuous_csupr
+  lowerSemicontinuousAt_csupᵢ (eventually_of_forall bdd) fun i => h i x
+#align lower_semicontinuous_csupr lowerSemicontinuous_csupᵢ
 
 theorem lowerSemicontinuous_supᵢ {f : ι → α → δ} (h : ∀ i, LowerSemicontinuous (f i)) :
     LowerSemicontinuous fun x' => ⨆ i, f i x' :=
-  lowerSemicontinuous_csupr (by simp) h
+  lowerSemicontinuous_csupᵢ (by simp) h
 #align lower_semicontinuous_supr lowerSemicontinuous_supᵢ
 
-theorem lowerSemicontinuous_bsupr {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem lowerSemicontinuous_bsupᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, LowerSemicontinuous (f i hi)) :
     LowerSemicontinuous fun x' => ⨆ (i) (hi), f i hi x' :=
   lowerSemicontinuous_supᵢ fun i => lowerSemicontinuous_supᵢ fun hi => h i hi
-#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupr
+#align lower_semicontinuous_bsupr lowerSemicontinuous_bsupᵢ
 
 end
 
@@ -998,12 +998,12 @@ section
 
 variable {ι : Sort _} {δ δ' : Type _} [CompleteLinearOrder δ] [ConditionallyCompleteLinearOrder δ']
 
-theorem upperSemicontinuousWithinAt_cinfi {f : ι → α → δ'}
+theorem upperSemicontinuousWithinAt_cinfᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝[s] x, BddBelow (range fun i => f i y))
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ i, f i x') s x :=
-  @lowerSemicontinuousWithinAt_csupr α _ x s ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfi
+  @lowerSemicontinuousWithinAt_csupᵢ α _ x s ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_within_at_cinfi upperSemicontinuousWithinAt_cinfᵢ
 
 theorem upperSemicontinuousWithinAt_infᵢ {f : ι → α → δ}
     (h : ∀ i, UpperSemicontinuousWithinAt (f i) s x) :
@@ -1011,60 +1011,60 @@ theorem upperSemicontinuousWithinAt_infᵢ {f : ι → α → δ}
   @lowerSemicontinuousWithinAt_supᵢ α _ x s ι δᵒᵈ _ f h
 #align upper_semicontinuous_within_at_infi upperSemicontinuousWithinAt_infᵢ
 
-theorem upperSemicontinuousWithinAt_binfi {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousWithinAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousWithinAt (f i hi) s x) :
     UpperSemicontinuousWithinAt (fun x' => ⨅ (i) (hi), f i hi x') s x :=
   upperSemicontinuousWithinAt_infᵢ fun i => upperSemicontinuousWithinAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfi
+#align upper_semicontinuous_within_at_binfi upperSemicontinuousWithinAt_binfᵢ
 
-theorem upperSemicontinuousAt_cinfi {f : ι → α → δ'}
+theorem upperSemicontinuousAt_cinfᵢ {f : ι → α → δ'}
     (bdd : ∀ᶠ y in 𝓝 x, BddBelow (range fun i => f i y)) (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
-  @lowerSemicontinuousAt_csupr α _ x ι δ'ᵒᵈ _ f bdd h
-#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfi
+  @lowerSemicontinuousAt_csupᵢ α _ x ι δ'ᵒᵈ _ f bdd h
+#align upper_semicontinuous_at_cinfi upperSemicontinuousAt_cinfᵢ
 
 theorem upperSemicontinuousAt_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousAt (f i) x) :
     UpperSemicontinuousAt (fun x' => ⨅ i, f i x') x :=
   @lowerSemicontinuousAt_supᵢ α _ x ι δᵒᵈ _ f h
 #align upper_semicontinuous_at_infi upperSemicontinuousAt_infᵢ
 
-theorem upperSemicontinuousAt_binfi {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousAt_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousAt (f i hi) x) :
     UpperSemicontinuousAt (fun x' => ⨅ (i) (hi), f i hi x') x :=
   upperSemicontinuousAt_infᵢ fun i => upperSemicontinuousAt_infᵢ fun hi => h i hi
-#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfi
+#align upper_semicontinuous_at_binfi upperSemicontinuousAt_binfᵢ
 
-theorem upperSemicontinuousOn_cinfi {f : ι → α → δ'}
+theorem upperSemicontinuousOn_cinfᵢ {f : ι → α → δ'}
     (bdd : ∀ x ∈ s, BddBelow (range fun i => f i x)) (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
-  upperSemicontinuousWithinAt_cinfi (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
-#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfi
+  upperSemicontinuousWithinAt_cinfᵢ (eventually_nhdsWithin_of_forall bdd) fun i => h i x hx
+#align upper_semicontinuous_on_cinfi upperSemicontinuousOn_cinfᵢ
 
 theorem upperSemicontinuousOn_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuousOn (f i) s) :
     UpperSemicontinuousOn (fun x' => ⨅ i, f i x') s := fun x hx =>
   upperSemicontinuousWithinAt_infᵢ fun i => h i x hx
 #align upper_semicontinuous_on_infi upperSemicontinuousOn_infᵢ
 
-theorem upperSemicontinuousOn_binfi {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuousOn_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuousOn (f i hi) s) :
     UpperSemicontinuousOn (fun x' => ⨅ (i) (hi), f i hi x') s :=
   upperSemicontinuousOn_infᵢ fun i => upperSemicontinuousOn_infᵢ fun hi => h i hi
-#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfi
+#align upper_semicontinuous_on_binfi upperSemicontinuousOn_binfᵢ
 
-theorem upperSemicontinuous_cinfi {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
+theorem upperSemicontinuous_cinfᵢ {f : ι → α → δ'} (bdd : ∀ x, BddBelow (range fun i => f i x))
     (h : ∀ i, UpperSemicontinuous (f i)) : UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x =>
-  upperSemicontinuousAt_cinfi (eventually_of_forall bdd) fun i => h i x
-#align upper_semicontinuous_cinfi upperSemicontinuous_cinfi
+  upperSemicontinuousAt_cinfᵢ (eventually_of_forall bdd) fun i => h i x
+#align upper_semicontinuous_cinfi upperSemicontinuous_cinfᵢ
 
 theorem upperSemicontinuous_infᵢ {f : ι → α → δ} (h : ∀ i, UpperSemicontinuous (f i)) :
     UpperSemicontinuous fun x' => ⨅ i, f i x' := fun x => upperSemicontinuousAt_infᵢ fun i => h i x
 #align upper_semicontinuous_infi upperSemicontinuous_infᵢ
 
-theorem upperSemicontinuous_binfi {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
+theorem upperSemicontinuous_binfᵢ {p : ι → Prop} {f : ∀ (i) (_h : p i), α → δ}
     (h : ∀ i hi, UpperSemicontinuous (f i hi)) :
     UpperSemicontinuous fun x' => ⨅ (i) (hi), f i hi x' :=
   upperSemicontinuous_infᵢ fun i => upperSemicontinuous_infᵢ fun hi => h i hi
-#align upper_semicontinuous_binfi upperSemicontinuous_binfi
+#align upper_semicontinuous_binfi upperSemicontinuous_binfᵢ
 
 end