order.conditionally_complete_lattice.basic ⟷ Mathlib.Order.ConditionallyCompleteLattice.Basic

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

@@ -5,7 +5,7 @@ Authors: Sébastien Gouëzel
 -/
 import Order.Bounds.Basic
 import Order.WellFounded
-import Data.Set.Intervals.Basic
+import Order.Interval.Set.Basic
 import Data.Set.Lattice
 
 #align_import order.conditionally_complete_lattice.basic from "leanprover-community/mathlib"@"29cb56a7b35f72758b05a30490e1f10bd62c35c1"

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

@@ -912,7 +912,7 @@ theorem csSup_Iic : sSup (Iic a) = a :=
 @[simp]
 theorem csSup_Iio [NoMinOrder α] [DenselyOrdered α] : sSup (Iio a) = a :=
   csSup_eq_of_forall_le_of_forall_lt_exists_gt nonempty_Iio (fun _ => le_of_lt) fun w hw => by
-    simpa [and_comm'] using exists_between hw
+    simpa [and_comm] using exists_between hw
 #align cSup_Iio csSup_Iio
 -/
 

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

@@ -568,28 +568,28 @@ theorem isGLB_ciInf_set {f : β → α} {s : Set β} (H : BddBelow (f '' s)) (Hn
 #print ciSup_le_iff /-
 theorem ciSup_le_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddAbove (range f)) :
     iSup f ≤ a ↔ ∀ i, f i ≤ a :=
-  (isLUB_le_iff <| isLUB_ciSup hf).trans forall_range_iff
+  (isLUB_le_iff <| isLUB_ciSup hf).trans forall_mem_range
 #align csupr_le_iff ciSup_le_iff
 -/
 
 #print le_ciInf_iff /-
 theorem le_ciInf_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddBelow (range f)) :
     a ≤ iInf f ↔ ∀ i, a ≤ f i :=
-  (le_isGLB_iff <| isGLB_ciInf hf).trans forall_range_iff
+  (le_isGLB_iff <| isGLB_ciInf hf).trans forall_mem_range
 #align le_cinfi_iff le_ciInf_iff
 -/
 
 #print ciSup_set_le_iff /-
 theorem ciSup_set_le_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddAbove (f '' s)) : (⨆ i : s, f i) ≤ a ↔ ∀ i ∈ s, f i ≤ a :=
-  (isLUB_le_iff <| isLUB_ciSup_set hf hs).trans ball_image_iff
+  (isLUB_le_iff <| isLUB_ciSup_set hf hs).trans forall_mem_image
 #align csupr_set_le_iff ciSup_set_le_iff
 -/
 
 #print le_ciInf_set_iff /-
 theorem le_ciInf_set_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddBelow (f '' s)) : (a ≤ ⨅ i : s, f i) ↔ ∀ i ∈ s, a ≤ f i :=
-  (le_isGLB_iff <| isGLB_ciInf_set hf hs).trans ball_image_iff
+  (le_isGLB_iff <| isGLB_ciInf_set hf hs).trans forall_mem_image
 #align le_cinfi_set_iff le_ciInf_set_iff
 -/
 
@@ -1052,7 +1052,7 @@ is larger than `f i` for all `i`, and that this is not the case of any `w<b`.
 See `supr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in complete lattices. -/
 theorem ciSup_eq_of_forall_le_of_forall_lt_exists_gt [Nonempty ι] {f : ι → α} (h₁ : ∀ i, f i ≤ b)
     (h₂ : ∀ w, w < b → ∃ i, w < f i) : (⨆ i : ι, f i) = b :=
-  csSup_eq_of_forall_le_of_forall_lt_exists_gt (range_nonempty f) (forall_range_iff.mpr h₁)
+  csSup_eq_of_forall_le_of_forall_lt_exists_gt (range_nonempty f) (forall_mem_range.mpr h₁)
     fun w hw => exists_range_iff.mpr <| h₂ w hw
 #align csupr_eq_of_forall_le_of_forall_lt_exists_gt ciSup_eq_of_forall_le_of_forall_lt_exists_gt
 -/
@@ -1110,12 +1110,12 @@ instance Pi.conditionallyCompleteLattice {ι : Type _} {α : ∀ i : ι, Type _}
   { Pi.lattice, Pi.supSet,
     Pi.infSet with
     le_cSup := fun s f ⟨g, hg⟩ hf i =>
-      le_csSup ⟨g i, Set.forall_range_iff.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
+      le_csSup ⟨g i, Set.forall_mem_range.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
     cSup_le := fun s f hs hf i =>
       csSup_le (by haveI := hs.to_subtype <;> apply range_nonempty) fun b ⟨⟨g, hg⟩, hb⟩ =>
         hb ▸ hf hg i
     cInf_le := fun s f ⟨g, hg⟩ hf i =>
-      csInf_le ⟨g i, Set.forall_range_iff.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
+      csInf_le ⟨g i, Set.forall_mem_range.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
     le_cInf := fun s f hs hf i =>
       le_csInf (by haveI := hs.to_subtype <;> apply range_nonempty) fun b ⟨⟨g, hg⟩, hb⟩ =>
         hb ▸ hf hg i }
@@ -1319,13 +1319,13 @@ theorem exists_lt_of_lt_csSup' {s : Set α} {a : α} (h : a < sSup s) : ∃ b 
 #print ciSup_le_iff' /-
 theorem ciSup_le_iff' {f : ι → α} (h : BddAbove (range f)) {a : α} :
     (⨆ i, f i) ≤ a ↔ ∀ i, f i ≤ a :=
-  (csSup_le_iff' h).trans forall_range_iff
+  (csSup_le_iff' h).trans forall_mem_range
 #align csupr_le_iff' ciSup_le_iff'
 -/
 
 #print ciSup_le' /-
 theorem ciSup_le' {f : ι → α} {a : α} (h : ∀ i, f i ≤ a) : (⨆ i, f i) ≤ a :=
-  csSup_le' <| forall_range_iff.2 h
+  csSup_le' <| forall_mem_range.2 h
 #align csupr_le' ciSup_le'
 -/
 
@@ -1543,7 +1543,7 @@ theorem l_ciSup (gc : GaloisConnection l u) {f : ι → α} (hf : BddAbove (rang
 #print GaloisConnection.l_ciSup_set /-
 theorem l_ciSup_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : l (⨆ i : s, f i) = ⨆ i : s, l (f i) := by haveI := hne.to_subtype;
-  rw [image_eq_range] at hf ; exact gc.l_csupr hf
+  rw [image_eq_range] at hf; exact gc.l_csupr hf
 #align galois_connection.l_csupr_set GaloisConnection.l_ciSup_set
 -/
 
@@ -1783,7 +1783,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
       cases' S.eq_empty_or_nonempty with h
       · show ite _ _ _ ≤ a
         split_ifs
-        · rw [h] at h_1 ; cases h_1
+        · rw [h] at h_1; cases h_1
         · convert bot_le; convert WithBot.csSup_empty; rw [h]; rfl
         · exfalso; apply h_2; use⊥; rw [h]; rintro b ⟨⟩
       · refine' (WithTop.isLUB_sSup' h).2 ha

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

@@ -210,7 +210,7 @@ class ConditionallyCompleteLattice (α : Type _) extends Lattice α, SupSet α,
 -/
 
 #print ConditionallyCompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:429:11: unsupported: advanced extends in structure -/
 /-- A conditionally complete linear order is a linear order in which
 every nonempty subset which is bounded above has a supremum, and
 every nonempty subset which is bounded below has an infimum.
@@ -221,7 +221,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrder (α : Type _) extends ConditionallyCompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:429:11: unsupported: advanced extends in structure"
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 -/
 

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

@@ -1429,7 +1429,12 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
     · rintro (⟨⟩ | a) ha
       · exfalso; apply h; intro b hb; exact Set.mem_singleton_iff.2 (top_le_iff.1 (ha hb))
       · refine' some_le_some.2 (le_csInf _ _)
-        · classical
+        ·
+          classical
+          contrapose! h
+          rintro (⟨⟩ | a) ha
+          · exact mem_singleton ⊤
+          · exact (h ⟨a, ha⟩).elim
         · intro b hb
           rw [← some_le_some]
           exact ha hb

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

@@ -1429,12 +1429,7 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
     · rintro (⟨⟩ | a) ha
       · exfalso; apply h; intro b hb; exact Set.mem_singleton_iff.2 (top_le_iff.1 (ha hb))
       · refine' some_le_some.2 (le_csInf _ _)
-        ·
-          classical
-          contrapose! h
-          rintro (⟨⟩ | a) ha
-          · exact mem_singleton ⊤
-          · exact (h ⟨a, ha⟩).elim
+        · classical
         · intro b hb
           rw [← some_le_some]
           exact ha hb

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

@@ -210,7 +210,7 @@ class ConditionallyCompleteLattice (α : Type _) extends Lattice α, SupSet α,
 -/
 
 #print ConditionallyCompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure -/
 /-- A conditionally complete linear order is a linear order in which
 every nonempty subset which is bounded above has a supremum, and
 every nonempty subset which is bounded below has an infimum.
@@ -221,7 +221,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrder (α : Type _) extends ConditionallyCompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:433:11: unsupported: advanced extends in structure"
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 -/
 

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

@@ -1067,29 +1067,29 @@ theorem ciInf_eq_of_forall_ge_of_forall_gt_exists_lt [Nonempty ι] {f : ι → 
 #align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt ciInf_eq_of_forall_ge_of_forall_gt_exists_lt
 -/
 
-#print Monotone.ciSup_mem_Inter_Icc_of_antitone /-
+#print Monotone.ciSup_mem_iInter_Icc_of_antitone /-
 /-- Nested intervals lemma: if `f` is a monotone sequence, `g` is an antitone sequence, and
 `f n ≤ g n` for all `n`, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
-theorem Monotone.ciSup_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β → α} (hf : Monotone f)
+theorem Monotone.ciSup_mem_iInter_Icc_of_antitone [SemilatticeSup β] {f g : β → α} (hf : Monotone f)
     (hg : Antitone g) (h : f ≤ g) : (⨆ n, f n) ∈ ⋂ n, Icc (f n) (g n) :=
   by
   refine' mem_Inter.2 fun n => _
   haveI : Nonempty β := ⟨n⟩
   have : ∀ m, f m ≤ g n := fun m => hf.forall_le_of_antitone hg h m n
   exact ⟨le_ciSup ⟨g <| n, forall_range_iff.2 this⟩ _, ciSup_le this⟩
-#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_Inter_Icc_of_antitone
+#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_iInter_Icc_of_antitone
 -/
 
-#print ciSup_mem_Inter_Icc_of_antitone_Icc /-
+#print ciSup_mem_iInter_Icc_of_antitone_Icc /-
 /-- Nested intervals lemma: if `[f n, g n]` is an antitone sequence of nonempty
 closed intervals, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
-theorem ciSup_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α}
+theorem ciSup_mem_iInter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α}
     (h : Antitone fun n => Icc (f n) (g n)) (h' : ∀ n, f n ≤ g n) :
     (⨆ n, f n) ∈ ⋂ n, Icc (f n) (g n) :=
-  Monotone.ciSup_mem_Inter_Icc_of_antitone
+  Monotone.ciSup_mem_iInter_Icc_of_antitone
     (fun m n hmn => ((Icc_subset_Icc_iff (h' n)).1 (h hmn)).1)
     (fun m n hmn => ((Icc_subset_Icc_iff (h' n)).1 (h hmn)).2) h'
-#align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_Inter_Icc_of_antitone_Icc
+#align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_iInter_Icc_of_antitone_Icc
 -/
 
 #print csSup_eq_of_is_forall_le_of_forall_le_imp_ge /-

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

@@ -3,10 +3,10 @@ Copyright (c) 2018 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Order.Bounds.Basic
-import Mathbin.Order.WellFounded
-import Mathbin.Data.Set.Intervals.Basic
-import Mathbin.Data.Set.Lattice
+import Order.Bounds.Basic
+import Order.WellFounded
+import Data.Set.Intervals.Basic
+import Data.Set.Lattice
 
 #align_import order.conditionally_complete_lattice.basic from "leanprover-community/mathlib"@"29cb56a7b35f72758b05a30490e1f10bd62c35c1"
 
@@ -210,7 +210,7 @@ class ConditionallyCompleteLattice (α : Type _) extends Lattice α, SupSet α,
 -/
 
 #print ConditionallyCompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
 /-- A conditionally complete linear order is a linear order in which
 every nonempty subset which is bounded above has a supremum, and
 every nonempty subset which is bounded below has an infimum.
@@ -221,7 +221,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrder (α : Type _) extends ConditionallyCompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -321,7 +321,7 @@ instance (α : Type _) [ConditionallyCompleteLattice α] : ConditionallyComplete
     cInf_le := @ConditionallyCompleteLattice.le_cSup α _ }
 
 instance (α : Type _) [ConditionallyCompleteLinearOrder α] : ConditionallyCompleteLinearOrder αᵒᵈ :=
-  { OrderDual.conditionallyCompleteLattice α, OrderDual.linearOrder α with }
+  { OrderDual.conditionallyCompleteLattice α, OrderDual.instLinearOrder α with }
 
 end OrderDual
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -1397,7 +1397,7 @@ theorem isLUB_sSup (s : Set (WithTop α)) : IsLUB s (sSup s) :=
     split_ifs
     · cases h
     · rw [preimage_empty, csSup_empty]; exact isLUB_empty
-    · exfalso; apply h_1; use ⊥; rintro a ⟨⟩
+    · exfalso; apply h_1; use⊥; rintro a ⟨⟩
   exact is_lub_Sup' hs
 #align with_top.is_lub_Sup WithTop.isLUB_sSup
 -/
@@ -1446,7 +1446,7 @@ theorem isGLB_sInf (s : Set (WithTop α)) : IsGLB s (sInf s) :=
   by
   by_cases hs : BddBelow s
   · exact is_glb_Inf' hs
-  · exfalso; apply hs; use ⊥; intro _ _; exact bot_le
+  · exfalso; apply hs; use⊥; intro _ _; exact bot_le
 #align with_top.is_glb_Inf WithTop.isGLB_sInf
 -/
 
@@ -1785,7 +1785,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
         split_ifs
         · rw [h] at h_1 ; cases h_1
         · convert bot_le; convert WithBot.csSup_empty; rw [h]; rfl
-        · exfalso; apply h_2; use ⊥; rw [h]; rintro b ⟨⟩
+        · exfalso; apply h_2; use⊥; rw [h]; rintro b ⟨⟩
       · refine' (WithTop.isLUB_sSup' h).2 ha
     inf_le := fun S a haS =>
       show ite _ _ _ ≤ a by
@@ -1794,7 +1794,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
           cases h haS <;> tauto
         · cases a
           · exact le_top
-          · apply WithTop.some_le_some.2; refine' csInf_le _ haS; use ⊥; intro b hb; exact bot_le
+          · apply WithTop.some_le_some.2; refine' csInf_le _ haS; use⊥; intro b hb; exact bot_le
     le_inf := fun S a haS => (WithTop.isGLB_sInf' ⟨a, haS⟩).2 haS }
 #align with_top.with_bot.complete_lattice WithTop.WithBot.completeLattice
 -/

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

@@ -2,17 +2,14 @@
 Copyright (c) 2018 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 order.conditionally_complete_lattice.basic
-! leanprover-community/mathlib commit 29cb56a7b35f72758b05a30490e1f10bd62c35c1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Order.Bounds.Basic
 import Mathbin.Order.WellFounded
 import Mathbin.Data.Set.Intervals.Basic
 import Mathbin.Data.Set.Lattice
 
+#align_import order.conditionally_complete_lattice.basic from "leanprover-community/mathlib"@"29cb56a7b35f72758b05a30490e1f10bd62c35c1"
+
 /-!
 # Theory of conditionally complete lattices.
 

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

@@ -77,15 +77,19 @@ theorem WithTop.sInf_eq [InfSet α] {s : Set (WithTop α)} (hs : ¬s ⊆ {⊤})
 #align with_top.Inf_eq WithTop.sInf_eq
 -/
 
+#print WithBot.sInf_eq /-
 theorem WithBot.sInf_eq [Preorder α] [InfSet α] {s : Set (WithBot α)} (hs : ⊥ ∉ s)
     (hs' : BddBelow (coe ⁻¹' s : Set α)) : sInf s = ↑(sInf (coe ⁻¹' s) : α) :=
   (if_neg hs).trans <| if_pos hs'
 #align with_bot.Inf_eq WithBot.sInf_eq
+-/
 
+#print WithBot.sSup_eq /-
 theorem WithBot.sSup_eq [SupSet α] {s : Set (WithBot α)} (hs : ¬s ⊆ {⊥}) :
     sSup s = ↑(sSup (coe ⁻¹' s) : α) :=
   if_neg hs
 #align with_bot.Sup_eq WithBot.sSup_eq
+-/
 
 #print WithTop.sInf_empty /-
 @[simp]
@@ -133,45 +137,59 @@ theorem WithTop.coe_sSup' [Preorder α] [SupSet α] {s : Set α} (hs : BddAbove
 #align with_top.coe_Sup' WithTop.coe_sSup'
 -/
 
+#print WithTop.coe_iSup /-
 @[norm_cast]
 theorem WithTop.coe_iSup [Preorder α] [SupSet α] (f : ι → α) (h : BddAbove (Set.range f)) :
     ↑(⨆ i, f i) = (⨆ i, f i : WithTop α) := by rw [iSup, iSup, WithTop.coe_sSup' h, range_comp]
 #align with_top.coe_supr WithTop.coe_iSup
+-/
 
+#print WithBot.csSup_empty /-
 @[simp]
 theorem WithBot.csSup_empty {α : Type _} [SupSet α] : sSup (∅ : Set (WithBot α)) = ⊥ :=
   if_pos <| Set.empty_subset _
 #align with_bot.cSup_empty WithBot.csSup_empty
+-/
 
+#print WithBot.ciSup_empty /-
 @[simp]
 theorem WithBot.ciSup_empty {α : Type _} [IsEmpty ι] [SupSet α] (f : ι → WithBot α) :
     (⨆ i, f i) = ⊥ :=
   @WithTop.iInf_empty _ αᵒᵈ _ _ _
 #align with_bot.csupr_empty WithBot.ciSup_empty
+-/
 
+#print WithBot.coe_sSup' /-
 @[norm_cast]
 theorem WithBot.coe_sSup' [SupSet α] {s : Set α} (hs : s.Nonempty) :
     ↑(sSup s) = (sSup (coe '' s) : WithBot α) :=
   @WithTop.coe_sInf' αᵒᵈ _ _ hs
 #align with_bot.coe_Sup' WithBot.coe_sSup'
+-/
 
+#print WithBot.coe_iSup /-
 @[norm_cast]
 theorem WithBot.coe_iSup [Nonempty ι] [SupSet α] (f : ι → α) :
     ↑(⨆ i, f i) = (⨆ i, f i : WithBot α) :=
   @WithTop.coe_iInf αᵒᵈ _ _ _ _
 #align with_bot.coe_supr WithBot.coe_iSup
+-/
 
+#print WithBot.coe_sInf' /-
 @[norm_cast]
 theorem WithBot.coe_sInf' [Preorder α] [InfSet α] {s : Set α} (hs : BddBelow s) :
     ↑(sInf s) = (sInf (coe '' s) : WithBot α) :=
   @WithTop.coe_sSup' αᵒᵈ _ _ _ hs
 #align with_bot.coe_Inf' WithBot.coe_sInf'
+-/
 
+#print WithBot.coe_iInf /-
 @[norm_cast]
 theorem WithBot.coe_iInf [Preorder α] [InfSet α] (f : ι → α) (h : BddBelow (Set.range f)) :
     ↑(⨅ i, f i) = (⨅ i, f i : WithBot α) :=
   @WithTop.coe_iSup αᵒᵈ _ _ _ _ h
 #align with_bot.coe_infi WithBot.coe_iInf
+-/
 
 end
 
@@ -195,7 +213,7 @@ class ConditionallyCompleteLattice (α : Type _) extends Lattice α, SupSet α,
 -/
 
 #print ConditionallyCompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- A conditionally complete linear order is a linear order in which
 every nonempty subset which is bounded above has a supremum, and
 every nonempty subset which is bounded below has an infimum.
@@ -206,7 +224,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrder (α : Type _) extends ConditionallyCompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 -/
 
@@ -450,168 +468,243 @@ section ConditionallyCompleteLattice
 
 variable [ConditionallyCompleteLattice α] {s t : Set α} {a b : α}
 
+#print le_csSup /-
 theorem le_csSup (h₁ : BddAbove s) (h₂ : a ∈ s) : a ≤ sSup s :=
   ConditionallyCompleteLattice.le_cSup s a h₁ h₂
 #align le_cSup le_csSup
+-/
 
+#print csSup_le /-
 theorem csSup_le (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, b ≤ a) : sSup s ≤ a :=
   ConditionallyCompleteLattice.cSup_le s a h₁ h₂
 #align cSup_le csSup_le
+-/
 
+#print csInf_le /-
 theorem csInf_le (h₁ : BddBelow s) (h₂ : a ∈ s) : sInf s ≤ a :=
   ConditionallyCompleteLattice.cInf_le s a h₁ h₂
 #align cInf_le csInf_le
+-/
 
+#print le_csInf /-
 theorem le_csInf (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, a ≤ b) : a ≤ sInf s :=
   ConditionallyCompleteLattice.le_cInf s a h₁ h₂
 #align le_cInf le_csInf
+-/
 
+#print le_csSup_of_le /-
 theorem le_csSup_of_le (hs : BddAbove s) (hb : b ∈ s) (h : a ≤ b) : a ≤ sSup s :=
   le_trans h (le_csSup hs hb)
 #align le_cSup_of_le le_csSup_of_le
+-/
 
+#print csInf_le_of_le /-
 theorem csInf_le_of_le (hs : BddBelow s) (hb : b ∈ s) (h : b ≤ a) : sInf s ≤ a :=
   le_trans (csInf_le hs hb) h
 #align cInf_le_of_le csInf_le_of_le
+-/
 
+#print csSup_le_csSup /-
 theorem csSup_le_csSup (ht : BddAbove t) (hs : s.Nonempty) (h : s ⊆ t) : sSup s ≤ sSup t :=
   csSup_le hs fun a ha => le_csSup ht (h ha)
 #align cSup_le_cSup csSup_le_csSup
+-/
 
+#print csInf_le_csInf /-
 theorem csInf_le_csInf (ht : BddBelow t) (hs : s.Nonempty) (h : s ⊆ t) : sInf t ≤ sInf s :=
   le_csInf hs fun a ha => csInf_le ht (h ha)
 #align cInf_le_cInf csInf_le_csInf
+-/
 
+#print le_csSup_iff /-
 theorem le_csSup_iff (h : BddAbove s) (hs : s.Nonempty) :
     a ≤ sSup s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
   ⟨fun h b hb => le_trans h (csSup_le hs hb), fun hb => hb _ fun x => le_csSup h⟩
 #align le_cSup_iff le_csSup_iff
+-/
 
+#print csInf_le_iff /-
 theorem csInf_le_iff (h : BddBelow s) (hs : s.Nonempty) : sInf s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
   ⟨fun h b hb => le_trans (le_csInf hs hb) h, fun hb => hb _ fun x => csInf_le h⟩
 #align cInf_le_iff csInf_le_iff
+-/
 
+#print isLUB_csSup /-
 theorem isLUB_csSup (ne : s.Nonempty) (H : BddAbove s) : IsLUB s (sSup s) :=
   ⟨fun x => le_csSup H, fun x => csSup_le Ne⟩
 #align is_lub_cSup isLUB_csSup
+-/
 
+#print isLUB_ciSup /-
 theorem isLUB_ciSup [Nonempty ι] {f : ι → α} (H : BddAbove (range f)) :
     IsLUB (range f) (⨆ i, f i) :=
   isLUB_csSup (range_nonempty f) H
 #align is_lub_csupr isLUB_ciSup
+-/
 
+#print isLUB_ciSup_set /-
 theorem isLUB_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) (Hne : s.Nonempty) :
     IsLUB (f '' s) (⨆ i : s, f i) := by rw [← sSup_image']; exact isLUB_csSup (Hne.image _) H
 #align is_lub_csupr_set isLUB_ciSup_set
+-/
 
+#print isGLB_csInf /-
 theorem isGLB_csInf (ne : s.Nonempty) (H : BddBelow s) : IsGLB s (sInf s) :=
   ⟨fun x => csInf_le H, fun x => le_csInf Ne⟩
 #align is_glb_cInf isGLB_csInf
+-/
 
+#print isGLB_ciInf /-
 theorem isGLB_ciInf [Nonempty ι] {f : ι → α} (H : BddBelow (range f)) :
     IsGLB (range f) (⨅ i, f i) :=
   isGLB_csInf (range_nonempty f) H
 #align is_glb_cinfi isGLB_ciInf
+-/
 
+#print isGLB_ciInf_set /-
 theorem isGLB_ciInf_set {f : β → α} {s : Set β} (H : BddBelow (f '' s)) (Hne : s.Nonempty) :
     IsGLB (f '' s) (⨅ i : s, f i) :=
   @isLUB_ciSup_set αᵒᵈ _ _ _ _ H Hne
 #align is_glb_cinfi_set isGLB_ciInf_set
+-/
 
+#print ciSup_le_iff /-
 theorem ciSup_le_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddAbove (range f)) :
     iSup f ≤ a ↔ ∀ i, f i ≤ a :=
   (isLUB_le_iff <| isLUB_ciSup hf).trans forall_range_iff
 #align csupr_le_iff ciSup_le_iff
+-/
 
+#print le_ciInf_iff /-
 theorem le_ciInf_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddBelow (range f)) :
     a ≤ iInf f ↔ ∀ i, a ≤ f i :=
   (le_isGLB_iff <| isGLB_ciInf hf).trans forall_range_iff
 #align le_cinfi_iff le_ciInf_iff
+-/
 
+#print ciSup_set_le_iff /-
 theorem ciSup_set_le_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddAbove (f '' s)) : (⨆ i : s, f i) ≤ a ↔ ∀ i ∈ s, f i ≤ a :=
   (isLUB_le_iff <| isLUB_ciSup_set hf hs).trans ball_image_iff
 #align csupr_set_le_iff ciSup_set_le_iff
+-/
 
+#print le_ciInf_set_iff /-
 theorem le_ciInf_set_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddBelow (f '' s)) : (a ≤ ⨅ i : s, f i) ↔ ∀ i ∈ s, a ≤ f i :=
   (le_isGLB_iff <| isGLB_ciInf_set hf hs).trans ball_image_iff
 #align le_cinfi_set_iff le_ciInf_set_iff
+-/
 
+#print IsLUB.csSup_eq /-
 theorem IsLUB.csSup_eq (H : IsLUB s a) (ne : s.Nonempty) : sSup s = a :=
   (isLUB_csSup Ne ⟨a, H.1⟩).unique H
 #align is_lub.cSup_eq IsLUB.csSup_eq
+-/
 
+#print IsLUB.ciSup_eq /-
 theorem IsLUB.ciSup_eq [Nonempty ι] {f : ι → α} (H : IsLUB (range f) a) : (⨆ i, f i) = a :=
   H.csSup_eq (range_nonempty f)
 #align is_lub.csupr_eq IsLUB.ciSup_eq
+-/
 
+#print IsLUB.ciSup_set_eq /-
 theorem IsLUB.ciSup_set_eq {s : Set β} {f : β → α} (H : IsLUB (f '' s) a) (Hne : s.Nonempty) :
     (⨆ i : s, f i) = a :=
   IsLUB.csSup_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
 #align is_lub.csupr_set_eq IsLUB.ciSup_set_eq
+-/
 
+#print IsGreatest.csSup_eq /-
 /-- A greatest element of a set is the supremum of this set. -/
 theorem IsGreatest.csSup_eq (H : IsGreatest s a) : sSup s = a :=
   H.IsLUB.csSup_eq H.Nonempty
 #align is_greatest.cSup_eq IsGreatest.csSup_eq
+-/
 
+#print IsGreatest.csSup_mem /-
 theorem IsGreatest.csSup_mem (H : IsGreatest s a) : sSup s ∈ s :=
   H.csSup_eq.symm ▸ H.1
 #align is_greatest.Sup_mem IsGreatest.csSup_mem
+-/
 
+#print IsGLB.csInf_eq /-
 theorem IsGLB.csInf_eq (H : IsGLB s a) (ne : s.Nonempty) : sInf s = a :=
   (isGLB_csInf Ne ⟨a, H.1⟩).unique H
 #align is_glb.cInf_eq IsGLB.csInf_eq
+-/
 
+#print IsGLB.ciInf_eq /-
 theorem IsGLB.ciInf_eq [Nonempty ι] {f : ι → α} (H : IsGLB (range f) a) : (⨅ i, f i) = a :=
   H.csInf_eq (range_nonempty f)
 #align is_glb.cinfi_eq IsGLB.ciInf_eq
+-/
 
+#print IsGLB.ciInf_set_eq /-
 theorem IsGLB.ciInf_set_eq {s : Set β} {f : β → α} (H : IsGLB (f '' s) a) (Hne : s.Nonempty) :
     (⨅ i : s, f i) = a :=
   IsGLB.csInf_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
 #align is_glb.cinfi_set_eq IsGLB.ciInf_set_eq
+-/
 
+#print IsLeast.csInf_eq /-
 /-- A least element of a set is the infimum of this set. -/
 theorem IsLeast.csInf_eq (H : IsLeast s a) : sInf s = a :=
   H.IsGLB.csInf_eq H.Nonempty
 #align is_least.cInf_eq IsLeast.csInf_eq
+-/
 
+#print IsLeast.csInf_mem /-
 theorem IsLeast.csInf_mem (H : IsLeast s a) : sInf s ∈ s :=
   H.csInf_eq.symm ▸ H.1
 #align is_least.Inf_mem IsLeast.csInf_mem
+-/
 
+#print subset_Icc_csInf_csSup /-
 theorem subset_Icc_csInf_csSup (hb : BddBelow s) (ha : BddAbove s) : s ⊆ Icc (sInf s) (sSup s) :=
   fun x hx => ⟨csInf_le hb hx, le_csSup ha hx⟩
 #align subset_Icc_cInf_cSup subset_Icc_csInf_csSup
+-/
 
+#print csSup_le_iff /-
 theorem csSup_le_iff (hb : BddAbove s) (hs : s.Nonempty) : sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
   isLUB_le_iff (isLUB_csSup hs hb)
 #align cSup_le_iff csSup_le_iff
+-/
 
+#print le_csInf_iff /-
 theorem le_csInf_iff (hb : BddBelow s) (hs : s.Nonempty) : a ≤ sInf s ↔ ∀ b ∈ s, a ≤ b :=
   le_isGLB_iff (isGLB_csInf hs hb)
 #align le_cInf_iff le_csInf_iff
+-/
 
+#print csSup_lower_bounds_eq_csInf /-
 theorem csSup_lower_bounds_eq_csInf {s : Set α} (h : BddBelow s) (hs : s.Nonempty) :
     sSup (lowerBounds s) = sInf s :=
   (isLUB_csSup h <| hs.mono fun x hx y hy => hy hx).unique (isGLB_csInf hs h).IsLUB
 #align cSup_lower_bounds_eq_cInf csSup_lower_bounds_eq_csInf
+-/
 
+#print csInf_upper_bounds_eq_csSup /-
 theorem csInf_upper_bounds_eq_csSup {s : Set α} (h : BddAbove s) (hs : s.Nonempty) :
     sInf (upperBounds s) = sSup s :=
   (isGLB_csInf h <| hs.mono fun x hx y hy => hy hx).unique (isLUB_csSup hs h).IsGLB
 #align cInf_upper_bounds_eq_cSup csInf_upper_bounds_eq_csSup
+-/
 
+#print not_mem_of_lt_csInf /-
 theorem not_mem_of_lt_csInf {x : α} {s : Set α} (h : x < sInf s) (hs : BddBelow s) : x ∉ s :=
   fun hx => lt_irrefl _ (h.trans_le (csInf_le hs hx))
 #align not_mem_of_lt_cInf not_mem_of_lt_csInf
+-/
 
+#print not_mem_of_csSup_lt /-
 theorem not_mem_of_csSup_lt {x : α} {s : Set α} (h : sSup s < x) (hs : BddAbove s) : x ∉ s :=
   @not_mem_of_lt_csInf αᵒᵈ _ x s h hs
 #align not_mem_of_cSup_lt not_mem_of_csSup_lt
+-/
 
+#print csSup_eq_of_forall_le_of_forall_lt_exists_gt /-
 /-- Introduction rule to prove that `b` is the supremum of `s`: it suffices to check that `b`
 is larger than all elements of `s`, and that this is not the case of any `w<b`.
 See `Sup_eq_of_forall_le_of_forall_lt_exists_gt` for a version in complete lattices. -/
@@ -621,7 +714,9 @@ theorem csSup_eq_of_forall_le_of_forall_lt_exists_gt (hs : s.Nonempty) (H : ∀
     let ⟨a, ha, ha'⟩ := H' _ hb
     lt_irrefl _ <| ha'.trans_le <| le_csSup ⟨b, H⟩ ha
 #align cSup_eq_of_forall_le_of_forall_lt_exists_gt csSup_eq_of_forall_le_of_forall_lt_exists_gt
+-/
 
+#print csInf_eq_of_forall_ge_of_forall_gt_exists_lt /-
 /-- Introduction rule to prove that `b` is the infimum of `s`: it suffices to check that `b`
 is smaller than all elements of `s`, and that this is not the case of any `w>b`.
 See `Inf_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in complete lattices. -/
@@ -629,7 +724,9 @@ theorem csInf_eq_of_forall_ge_of_forall_gt_exists_lt :
     s.Nonempty → (∀ a ∈ s, b ≤ a) → (∀ w, b < w → ∃ a ∈ s, a < w) → sInf s = b :=
   @csSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _
 #align cInf_eq_of_forall_ge_of_forall_gt_exists_lt csInf_eq_of_forall_ge_of_forall_gt_exists_lt
+-/
 
+#print lt_csSup_of_lt /-
 /-- b < Sup s when there is an element a in s with b < a, when s is bounded above.
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness above for one direction, nonemptiness and linear
@@ -638,7 +735,9 @@ the complete_lattice case.-/
 theorem lt_csSup_of_lt (hs : BddAbove s) (ha : a ∈ s) (h : b < a) : b < sSup s :=
   lt_of_lt_of_le h (le_csSup hs ha)
 #align lt_cSup_of_lt lt_csSup_of_lt
+-/
 
+#print csInf_lt_of_lt /-
 /-- Inf s < b when there is an element a in s with a < b, when s is bounded below.
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness below for one direction, nonemptiness and linear
@@ -647,158 +746,214 @@ the complete_lattice case.-/
 theorem csInf_lt_of_lt : BddBelow s → a ∈ s → a < b → sInf s < b :=
   @lt_csSup_of_lt αᵒᵈ _ _ _ _
 #align cInf_lt_of_lt csInf_lt_of_lt
+-/
 
+#print exists_between_of_forall_le /-
 /-- If all elements of a nonempty set `s` are less than or equal to all elements
 of a nonempty set `t`, then there exists an element between these sets. -/
 theorem exists_between_of_forall_le (sne : s.Nonempty) (tne : t.Nonempty)
     (hst : ∀ x ∈ s, ∀ y ∈ t, x ≤ y) : (upperBounds s ∩ lowerBounds t).Nonempty :=
   ⟨sInf t, fun x hx => le_csInf tne <| hst x hx, fun y hy => csInf_le (sne.mono hst) hy⟩
 #align exists_between_of_forall_le exists_between_of_forall_le
+-/
 
+#print csSup_singleton /-
 /-- The supremum of a singleton is the element of the singleton-/
 @[simp]
 theorem csSup_singleton (a : α) : sSup {a} = a :=
   isGreatest_singleton.csSup_eq
 #align cSup_singleton csSup_singleton
+-/
 
+#print csInf_singleton /-
 /-- The infimum of a singleton is the element of the singleton-/
 @[simp]
 theorem csInf_singleton (a : α) : sInf {a} = a :=
   isLeast_singleton.csInf_eq
 #align cInf_singleton csInf_singleton
+-/
 
+#print csSup_pair /-
 @[simp]
 theorem csSup_pair (a b : α) : sSup {a, b} = a ⊔ b :=
   (@isLUB_pair _ _ a b).csSup_eq (insert_nonempty _ _)
 #align cSup_pair csSup_pair
+-/
 
+#print csInf_pair /-
 @[simp]
 theorem csInf_pair (a b : α) : sInf {a, b} = a ⊓ b :=
   (@isGLB_pair _ _ a b).csInf_eq (insert_nonempty _ _)
 #align cInf_pair csInf_pair
+-/
 
+#print csInf_le_csSup /-
 /-- If a set is bounded below and above, and nonempty, its infimum is less than or equal to
 its supremum.-/
 theorem csInf_le_csSup (hb : BddBelow s) (ha : BddAbove s) (ne : s.Nonempty) : sInf s ≤ sSup s :=
   isGLB_le_isLUB (isGLB_csInf Ne hb) (isLUB_csSup Ne ha) Ne
 #align cInf_le_cSup csInf_le_csSup
+-/
 
+#print csSup_union /-
 /-- The sup of a union of two sets is the max of the suprema of each subset, under the assumptions
 that all sets are bounded above and nonempty.-/
 theorem csSup_union (hs : BddAbove s) (sne : s.Nonempty) (ht : BddAbove t) (tne : t.Nonempty) :
     sSup (s ∪ t) = sSup s ⊔ sSup t :=
   ((isLUB_csSup sne hs).union (isLUB_csSup tne ht)).csSup_eq sne.inl
 #align cSup_union csSup_union
+-/
 
+#print csInf_union /-
 /-- The inf of a union of two sets is the min of the infima of each subset, under the assumptions
 that all sets are bounded below and nonempty.-/
 theorem csInf_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tne : t.Nonempty) :
     sInf (s ∪ t) = sInf s ⊓ sInf t :=
   @csSup_union αᵒᵈ _ _ _ hs sne ht tne
 #align cInf_union csInf_union
+-/
 
+#print csSup_inter_le /-
 /-- The supremum of an intersection of two sets is bounded by the minimum of the suprema of each
 set, if all sets are bounded above and nonempty.-/
 theorem csSup_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).Nonempty) :
     sSup (s ∩ t) ≤ sSup s ⊓ sSup t :=
   csSup_le hst fun x hx => le_inf (le_csSup hs hx.1) (le_csSup ht hx.2)
 #align cSup_inter_le csSup_inter_le
+-/
 
+#print le_csInf_inter /-
 /-- The infimum of an intersection of two sets is bounded below by the maximum of the
 infima of each set, if all sets are bounded below and nonempty.-/
 theorem le_csInf_inter :
     BddBelow s → BddBelow t → (s ∩ t).Nonempty → sInf s ⊔ sInf t ≤ sInf (s ∩ t) :=
   @csSup_inter_le αᵒᵈ _ _ _
 #align le_cInf_inter le_csInf_inter
+-/
 
+#print csSup_insert /-
 /-- The supremum of insert a s is the maximum of a and the supremum of s, if s is
 nonempty and bounded above.-/
 theorem csSup_insert (hs : BddAbove s) (sne : s.Nonempty) : sSup (insert a s) = a ⊔ sSup s :=
   ((isLUB_csSup sne hs).insert a).csSup_eq (insert_nonempty a s)
 #align cSup_insert csSup_insert
+-/
 
+#print csInf_insert /-
 /-- The infimum of insert a s is the minimum of a and the infimum of s, if s is
 nonempty and bounded below.-/
 theorem csInf_insert (hs : BddBelow s) (sne : s.Nonempty) : sInf (insert a s) = a ⊓ sInf s :=
   @csSup_insert αᵒᵈ _ _ _ hs sne
 #align cInf_insert csInf_insert
+-/
 
+#print csInf_Icc /-
 @[simp]
 theorem csInf_Icc (h : a ≤ b) : sInf (Icc a b) = a :=
   (isGLB_Icc h).csInf_eq (nonempty_Icc.2 h)
 #align cInf_Icc csInf_Icc
+-/
 
+#print csInf_Ici /-
 @[simp]
 theorem csInf_Ici : sInf (Ici a) = a :=
   isLeast_Ici.csInf_eq
 #align cInf_Ici csInf_Ici
+-/
 
+#print csInf_Ico /-
 @[simp]
 theorem csInf_Ico (h : a < b) : sInf (Ico a b) = a :=
   (isGLB_Ico h).csInf_eq (nonempty_Ico.2 h)
 #align cInf_Ico csInf_Ico
+-/
 
+#print csInf_Ioc /-
 @[simp]
 theorem csInf_Ioc [DenselyOrdered α] (h : a < b) : sInf (Ioc a b) = a :=
   (isGLB_Ioc h).csInf_eq (nonempty_Ioc.2 h)
 #align cInf_Ioc csInf_Ioc
+-/
 
+#print csInf_Ioi /-
 @[simp]
 theorem csInf_Ioi [NoMaxOrder α] [DenselyOrdered α] : sInf (Ioi a) = a :=
   csInf_eq_of_forall_ge_of_forall_gt_exists_lt nonempty_Ioi (fun _ => le_of_lt) fun w hw => by
     simpa using exists_between hw
 #align cInf_Ioi csInf_Ioi
+-/
 
+#print csInf_Ioo /-
 @[simp]
 theorem csInf_Ioo [DenselyOrdered α] (h : a < b) : sInf (Ioo a b) = a :=
   (isGLB_Ioo h).csInf_eq (nonempty_Ioo.2 h)
 #align cInf_Ioo csInf_Ioo
+-/
 
+#print csSup_Icc /-
 @[simp]
 theorem csSup_Icc (h : a ≤ b) : sSup (Icc a b) = b :=
   (isLUB_Icc h).csSup_eq (nonempty_Icc.2 h)
 #align cSup_Icc csSup_Icc
+-/
 
+#print csSup_Ico /-
 @[simp]
 theorem csSup_Ico [DenselyOrdered α] (h : a < b) : sSup (Ico a b) = b :=
   (isLUB_Ico h).csSup_eq (nonempty_Ico.2 h)
 #align cSup_Ico csSup_Ico
+-/
 
+#print csSup_Iic /-
 @[simp]
 theorem csSup_Iic : sSup (Iic a) = a :=
   isGreatest_Iic.csSup_eq
 #align cSup_Iic csSup_Iic
+-/
 
+#print csSup_Iio /-
 @[simp]
 theorem csSup_Iio [NoMinOrder α] [DenselyOrdered α] : sSup (Iio a) = a :=
   csSup_eq_of_forall_le_of_forall_lt_exists_gt nonempty_Iio (fun _ => le_of_lt) fun w hw => by
     simpa [and_comm'] using exists_between hw
 #align cSup_Iio csSup_Iio
+-/
 
+#print csSup_Ioc /-
 @[simp]
 theorem csSup_Ioc (h : a < b) : sSup (Ioc a b) = b :=
   (isLUB_Ioc h).csSup_eq (nonempty_Ioc.2 h)
 #align cSup_Ioc csSup_Ioc
+-/
 
+#print csSup_Ioo /-
 @[simp]
 theorem csSup_Ioo [DenselyOrdered α] (h : a < b) : sSup (Ioo a b) = b :=
   (isLUB_Ioo h).csSup_eq (nonempty_Ioo.2 h)
 #align cSup_Ioo csSup_Ioo
+-/
 
+#print ciSup_le /-
 /-- The indexed supremum of a function is bounded above by a uniform bound-/
 theorem ciSup_le [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, f x ≤ c) : iSup f ≤ c :=
   csSup_le (range_nonempty f) (by rwa [forall_range_iff])
 #align csupr_le ciSup_le
+-/
 
+#print le_ciSup /-
 /-- The indexed supremum of a function is bounded below by the value taken at one point-/
 theorem le_ciSup {f : ι → α} (H : BddAbove (range f)) (c : ι) : f c ≤ iSup f :=
   le_csSup H (mem_range_self _)
 #align le_csupr le_ciSup
+-/
 
+#print le_ciSup_of_le /-
 theorem le_ciSup_of_le {f : ι → α} (H : BddAbove (range f)) (c : ι) (h : a ≤ f c) : a ≤ iSup f :=
   le_trans h (le_ciSup H c)
 #align le_csupr_of_le le_ciSup_of_le
+-/
 
+#print ciSup_mono /-
 /-- The indexed supremum of two functions are comparable if the functions are pointwise comparable-/
 theorem ciSup_mono {f g : ι → α} (B : BddAbove (range g)) (H : ∀ x, f x ≤ g x) : iSup f ≤ iSup g :=
   by
@@ -806,69 +961,95 @@ theorem ciSup_mono {f g : ι → α} (B : BddAbove (range g)) (H : ∀ x, f x 
   · rw [iSup_of_empty', iSup_of_empty']
   · exact ciSup_le fun x => le_ciSup_of_le B x (H x)
 #align csupr_mono ciSup_mono
+-/
 
+#print le_ciSup_set /-
 theorem le_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) {c : β} (hc : c ∈ s) :
     f c ≤ ⨆ i : s, f i :=
   (le_csSup H <| mem_image_of_mem f hc).trans_eq sSup_image'
 #align le_csupr_set le_ciSup_set
+-/
 
+#print ciInf_mono /-
 /-- The indexed infimum of two functions are comparable if the functions are pointwise comparable-/
 theorem ciInf_mono {f g : ι → α} (B : BddBelow (range f)) (H : ∀ x, f x ≤ g x) : iInf f ≤ iInf g :=
   @ciSup_mono αᵒᵈ _ _ _ _ B H
 #align cinfi_mono ciInf_mono
+-/
 
+#print le_ciInf /-
 /-- The indexed minimum of a function is bounded below by a uniform lower bound-/
 theorem le_ciInf [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, c ≤ f x) : c ≤ iInf f :=
   @ciSup_le αᵒᵈ _ _ _ _ _ H
 #align le_cinfi le_ciInf
+-/
 
+#print ciInf_le /-
 /-- The indexed infimum of a function is bounded above by the value taken at one point-/
 theorem ciInf_le {f : ι → α} (H : BddBelow (range f)) (c : ι) : iInf f ≤ f c :=
   @le_ciSup αᵒᵈ _ _ _ H c
 #align cinfi_le ciInf_le
+-/
 
+#print ciInf_le_of_le /-
 theorem ciInf_le_of_le {f : ι → α} (H : BddBelow (range f)) (c : ι) (h : f c ≤ a) : iInf f ≤ a :=
   @le_ciSup_of_le αᵒᵈ _ _ _ _ H c h
 #align cinfi_le_of_le ciInf_le_of_le
+-/
 
+#print ciInf_set_le /-
 theorem ciInf_set_le {f : β → α} {s : Set β} (H : BddBelow (f '' s)) {c : β} (hc : c ∈ s) :
     (⨅ i : s, f i) ≤ f c :=
   @le_ciSup_set αᵒᵈ _ _ _ _ H _ hc
 #align cinfi_set_le ciInf_set_le
+-/
 
+#print ciSup_const /-
 @[simp]
 theorem ciSup_const [hι : Nonempty ι] {a : α} : (⨆ b : ι, a) = a := by
   rw [iSup, range_const, csSup_singleton]
 #align csupr_const ciSup_const
+-/
 
+#print ciInf_const /-
 @[simp]
 theorem ciInf_const [hι : Nonempty ι] {a : α} : (⨅ b : ι, a) = a :=
   @ciSup_const αᵒᵈ _ _ _ _
 #align cinfi_const ciInf_const
+-/
 
+#print ciSup_unique /-
 @[simp]
 theorem ciSup_unique [Unique ι] {s : ι → α} : (⨆ i, s i) = s default :=
   by
   have : ∀ i, s i = s default := fun i => congr_arg s (Unique.eq_default i)
   simp only [this, ciSup_const]
 #align supr_unique ciSup_unique
+-/
 
+#print ciInf_unique /-
 @[simp]
 theorem ciInf_unique [Unique ι] {s : ι → α} : (⨅ i, s i) = s default :=
   @ciSup_unique αᵒᵈ _ _ _ _
 #align infi_unique ciInf_unique
+-/
 
+#print ciSup_pos /-
 @[simp]
 theorem ciSup_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
   haveI := uniqueProp hp
   ciSup_unique
 #align csupr_pos ciSup_pos
+-/
 
+#print ciInf_pos /-
 @[simp]
 theorem ciInf_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
   @ciSup_pos αᵒᵈ _ _ _ hp
 #align cinfi_pos ciInf_pos
+-/
 
+#print ciSup_eq_of_forall_le_of_forall_lt_exists_gt /-
 /-- Introduction rule to prove that `b` is the supremum of `f`: it suffices to check that `b`
 is larger than `f i` for all `i`, and that this is not the case of any `w<b`.
 See `supr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in complete lattices. -/
@@ -877,7 +1058,9 @@ theorem ciSup_eq_of_forall_le_of_forall_lt_exists_gt [Nonempty ι] {f : ι → 
   csSup_eq_of_forall_le_of_forall_lt_exists_gt (range_nonempty f) (forall_range_iff.mpr h₁)
     fun w hw => exists_range_iff.mpr <| h₂ w hw
 #align csupr_eq_of_forall_le_of_forall_lt_exists_gt ciSup_eq_of_forall_le_of_forall_lt_exists_gt
+-/
 
+#print ciInf_eq_of_forall_ge_of_forall_gt_exists_lt /-
 /-- Introduction rule to prove that `b` is the infimum of `f`: it suffices to check that `b`
 is smaller than `f i` for all `i`, and that this is not the case of any `w>b`.
 See `infi_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in complete lattices. -/
@@ -885,7 +1068,9 @@ theorem ciInf_eq_of_forall_ge_of_forall_gt_exists_lt [Nonempty ι] {f : ι → 
     (h₂ : ∀ w, b < w → ∃ i, f i < w) : (⨅ i : ι, f i) = b :=
   @ciSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _ ‹_› ‹_› ‹_›
 #align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt ciInf_eq_of_forall_ge_of_forall_gt_exists_lt
+-/
 
+#print Monotone.ciSup_mem_Inter_Icc_of_antitone /-
 /-- Nested intervals lemma: if `f` is a monotone sequence, `g` is an antitone sequence, and
 `f n ≤ g n` for all `n`, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
 theorem Monotone.ciSup_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β → α} (hf : Monotone f)
@@ -896,7 +1081,9 @@ theorem Monotone.ciSup_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β 
   have : ∀ m, f m ≤ g n := fun m => hf.forall_le_of_antitone hg h m n
   exact ⟨le_ciSup ⟨g <| n, forall_range_iff.2 this⟩ _, ciSup_le this⟩
 #align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_Inter_Icc_of_antitone
+-/
 
+#print ciSup_mem_Inter_Icc_of_antitone_Icc /-
 /-- Nested intervals lemma: if `[f n, g n]` is an antitone sequence of nonempty
 closed intervals, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
 theorem ciSup_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α}
@@ -906,7 +1093,9 @@ theorem ciSup_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α
     (fun m n hmn => ((Icc_subset_Icc_iff (h' n)).1 (h hmn)).1)
     (fun m n hmn => ((Icc_subset_Icc_iff (h' n)).1 (h hmn)).2) h'
 #align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_Inter_Icc_of_antitone_Icc
+-/
 
+#print csSup_eq_of_is_forall_le_of_forall_le_imp_ge /-
 /-- Introduction rule to prove that b is the supremum of s: it suffices to check that
 1) b is an upper bound
 2) every other upper bound b' satisfies b ≤ b'.-/
@@ -914,6 +1103,7 @@ theorem csSup_eq_of_is_forall_le_of_forall_le_imp_ge (hs : s.Nonempty) (h_is_ub
     (h_b_le_ub : ∀ ub, (∀ a ∈ s, a ≤ ub) → b ≤ ub) : sSup s = b :=
   (csSup_le hs h_is_ub).antisymm (h_b_le_ub _ fun a => le_csSup ⟨b, h_is_ub⟩)
 #align cSup_eq_of_is_forall_le_of_forall_le_imp_ge csSup_eq_of_is_forall_le_of_forall_le_imp_ge
+-/
 
 end ConditionallyCompleteLattice
 
@@ -939,12 +1129,15 @@ section ConditionallyCompleteLinearOrder
 
 variable [ConditionallyCompleteLinearOrder α] {s t : Set α} {a b : α}
 
+#print exists_lt_of_lt_csSup /-
 /-- When b < Sup s, there is an element a in s with b < a, if s is nonempty and the order is
 a linear order. -/
 theorem exists_lt_of_lt_csSup (hs : s.Nonempty) (hb : b < sSup s) : ∃ a ∈ s, b < a := by
   contrapose! hb; exact csSup_le hs hb
 #align exists_lt_of_lt_cSup exists_lt_of_lt_csSup
+-/
 
+#print exists_lt_of_lt_ciSup /-
 /-- Indexed version of the above lemma `exists_lt_of_lt_cSup`.
 When `b < supr f`, there is an element `i` such that `b < f i`.
 -/
@@ -952,54 +1145,73 @@ theorem exists_lt_of_lt_ciSup [Nonempty ι] {f : ι → α} (h : b < iSup f) : 
   let ⟨_, ⟨i, rfl⟩, h⟩ := exists_lt_of_lt_csSup (range_nonempty f) h
   ⟨i, h⟩
 #align exists_lt_of_lt_csupr exists_lt_of_lt_ciSup
+-/
 
+#print exists_lt_of_csInf_lt /-
 /-- When Inf s < b, there is an element a in s with a < b, if s is nonempty and the order is
 a linear order.-/
 theorem exists_lt_of_csInf_lt (hs : s.Nonempty) (hb : sInf s < b) : ∃ a ∈ s, a < b :=
   @exists_lt_of_lt_csSup αᵒᵈ _ _ _ hs hb
 #align exists_lt_of_cInf_lt exists_lt_of_csInf_lt
+-/
 
+#print exists_lt_of_ciInf_lt /-
 /-- Indexed version of the above lemma `exists_lt_of_cInf_lt`
 When `infi f < a`, there is an element `i` such that `f i < a`.
 -/
 theorem exists_lt_of_ciInf_lt [Nonempty ι] {f : ι → α} (h : iInf f < a) : ∃ i, f i < a :=
   @exists_lt_of_lt_ciSup αᵒᵈ _ _ _ _ _ h
 #align exists_lt_of_cinfi_lt exists_lt_of_ciInf_lt
+-/
 
 open Function
 
 variable [IsWellOrder α (· < ·)]
 
+#print sInf_eq_argmin_on /-
 theorem sInf_eq_argmin_on (hs : s.Nonempty) :
     sInf s = argminOn id (@IsWellFounded.wf α (· < ·) _) s hs :=
   IsLeast.csInf_eq ⟨argminOn_mem _ _ _ _, fun a ha => argminOn_le id _ _ ha⟩
 #align Inf_eq_argmin_on sInf_eq_argmin_on
+-/
 
+#print isLeast_csInf /-
 theorem isLeast_csInf (hs : s.Nonempty) : IsLeast s (sInf s) := by rw [sInf_eq_argmin_on hs];
   exact ⟨argmin_on_mem _ _ _ _, fun a ha => argmin_on_le id _ _ ha⟩
 #align is_least_Inf isLeast_csInf
+-/
 
+#print le_csInf_iff' /-
 theorem le_csInf_iff' (hs : s.Nonempty) : b ≤ sInf s ↔ b ∈ lowerBounds s :=
   le_isGLB_iff (isLeast_csInf hs).IsGLB
 #align le_cInf_iff' le_csInf_iff'
+-/
 
+#print csInf_mem /-
 theorem csInf_mem (hs : s.Nonempty) : sInf s ∈ s :=
   (isLeast_csInf hs).1
 #align Inf_mem csInf_mem
+-/
 
+#print ciInf_mem /-
 theorem ciInf_mem [Nonempty ι] (f : ι → α) : iInf f ∈ range f :=
   csInf_mem (range_nonempty f)
 #align infi_mem ciInf_mem
+-/
 
+#print MonotoneOn.map_csInf /-
 theorem MonotoneOn.map_csInf {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : MonotoneOn f s) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
   (hf.map_isLeast (isLeast_csInf hs)).csInf_eq.symm
 #align monotone_on.map_Inf MonotoneOn.map_csInf
+-/
 
+#print Monotone.map_csInf /-
 theorem Monotone.map_csInf {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : Monotone f) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
   (hf.map_isLeast (isLeast_csInf hs)).csInf_eq.symm
 #align monotone.map_Inf Monotone.map_csInf
+-/
 
 end ConditionallyCompleteLinearOrder
 
@@ -1014,92 +1226,130 @@ section ConditionallyCompleteLinearOrderBot
 
 variable [ConditionallyCompleteLinearOrderBot α]
 
+#print csSup_empty /-
 @[simp]
 theorem csSup_empty : (sSup ∅ : α) = ⊥ :=
   ConditionallyCompleteLinearOrderBot.cSup_empty
 #align cSup_empty csSup_empty
+-/
 
+#print ciSup_of_empty /-
 @[simp]
 theorem ciSup_of_empty [IsEmpty ι] (f : ι → α) : (⨆ i, f i) = ⊥ := by
   rw [iSup_of_empty', csSup_empty]
 #align csupr_of_empty ciSup_of_empty
+-/
 
+#print ciSup_false /-
 @[simp]
 theorem ciSup_false (f : False → α) : (⨆ i, f i) = ⊥ :=
   ciSup_of_empty f
 #align csupr_false ciSup_false
+-/
 
+#print csInf_univ /-
 @[simp]
 theorem csInf_univ : sInf (univ : Set α) = ⊥ :=
   isLeast_univ.csInf_eq
 #align cInf_univ csInf_univ
+-/
 
+#print isLUB_csSup' /-
 theorem isLUB_csSup' {s : Set α} (hs : BddAbove s) : IsLUB s (sSup s) :=
   by
   rcases eq_empty_or_nonempty s with (rfl | hne)
   · simp only [csSup_empty, isLUB_empty]
   · exact isLUB_csSup hne hs
 #align is_lub_cSup' isLUB_csSup'
+-/
 
+#print csSup_le_iff' /-
 theorem csSup_le_iff' {s : Set α} (hs : BddAbove s) {a : α} : sSup s ≤ a ↔ ∀ x ∈ s, x ≤ a :=
   isLUB_le_iff (isLUB_csSup' hs)
 #align cSup_le_iff' csSup_le_iff'
+-/
 
+#print csSup_le' /-
 theorem csSup_le' {s : Set α} {a : α} (h : a ∈ upperBounds s) : sSup s ≤ a :=
   (csSup_le_iff' ⟨a, h⟩).2 h
 #align cSup_le' csSup_le'
+-/
 
+#print le_csSup_iff' /-
 theorem le_csSup_iff' {s : Set α} {a : α} (h : BddAbove s) :
     a ≤ sSup s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
   ⟨fun h b hb => le_trans h (csSup_le' hb), fun hb => hb _ fun x => le_csSup h⟩
 #align le_cSup_iff' le_csSup_iff'
+-/
 
+#print le_ciSup_iff' /-
 theorem le_ciSup_iff' {s : ι → α} {a : α} (h : BddAbove (range s)) :
     a ≤ iSup s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by simp [iSup, h, le_csSup_iff', upperBounds]
 #align le_csupr_iff' le_ciSup_iff'
+-/
 
+#print le_csInf_iff'' /-
 theorem le_csInf_iff'' {s : Set α} {a : α} (ne : s.Nonempty) :
     a ≤ sInf s ↔ ∀ b : α, b ∈ s → a ≤ b :=
   le_csInf_iff ⟨⊥, fun a _ => bot_le⟩ Ne
 #align le_cInf_iff'' le_csInf_iff''
+-/
 
+#print le_ciInf_iff' /-
 theorem le_ciInf_iff' [Nonempty ι] {f : ι → α} {a : α} : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
   le_ciInf_iff ⟨⊥, fun a _ => bot_le⟩
 #align le_cinfi_iff' le_ciInf_iff'
+-/
 
+#print csInf_le' /-
 theorem csInf_le' {s : Set α} {a : α} (h : a ∈ s) : sInf s ≤ a :=
   csInf_le ⟨⊥, fun a _ => bot_le⟩ h
 #align cInf_le' csInf_le'
+-/
 
+#print ciInf_le' /-
 theorem ciInf_le' (f : ι → α) (i : ι) : iInf f ≤ f i :=
   ciInf_le ⟨⊥, fun a _ => bot_le⟩ _
 #align cinfi_le' ciInf_le'
+-/
 
+#print exists_lt_of_lt_csSup' /-
 theorem exists_lt_of_lt_csSup' {s : Set α} {a : α} (h : a < sSup s) : ∃ b ∈ s, a < b := by
   contrapose! h; exact csSup_le' h
 #align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'
+-/
 
+#print ciSup_le_iff' /-
 theorem ciSup_le_iff' {f : ι → α} (h : BddAbove (range f)) {a : α} :
     (⨆ i, f i) ≤ a ↔ ∀ i, f i ≤ a :=
   (csSup_le_iff' h).trans forall_range_iff
 #align csupr_le_iff' ciSup_le_iff'
+-/
 
+#print ciSup_le' /-
 theorem ciSup_le' {f : ι → α} {a : α} (h : ∀ i, f i ≤ a) : (⨆ i, f i) ≤ a :=
   csSup_le' <| forall_range_iff.2 h
 #align csupr_le' ciSup_le'
+-/
 
+#print exists_lt_of_lt_ciSup' /-
 theorem exists_lt_of_lt_ciSup' {f : ι → α} {a : α} (h : a < ⨆ i, f i) : ∃ i, a < f i := by
   contrapose! h; exact ciSup_le' h
 #align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'
+-/
 
+#print ciSup_mono' /-
 theorem ciSup_mono' {ι'} {f : ι → α} {g : ι' → α} (hg : BddAbove (range g))
     (h : ∀ i, ∃ i', f i ≤ g i') : iSup f ≤ iSup g :=
   ciSup_le' fun i => Exists.elim (h i) (le_ciSup_of_le hg)
 #align csupr_mono' ciSup_mono'
+-/
 
+#print csInf_le_csInf' /-
 theorem csInf_le_csInf' {s t : Set α} (h₁ : t.Nonempty) (h₂ : t ⊆ s) : sInf s ≤ sInf t :=
   csInf_le_csInf (OrderBot.bddBelow s) h₁ h₂
 #align cInf_le_cInf' csInf_le_csInf'
+-/
 
 end ConditionallyCompleteLinearOrderBot
 
@@ -1109,6 +1359,7 @@ open scoped Classical
 
 variable [ConditionallyCompleteLinearOrderBot α]
 
+#print WithTop.isLUB_sSup' /-
 /-- The Sup of a non-empty set is its least upper bound for a conditionally
 complete lattice with a top. -/
 theorem isLUB_sSup' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
@@ -1138,7 +1389,9 @@ theorem isLUB_sSup' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
       · exact le_rfl
       · exfalso; apply h_1; use b; intro a ha; exact some_le_some.1 (hb ha)
 #align with_top.is_lub_Sup' WithTop.isLUB_sSup'
+-/
 
+#print WithTop.isLUB_sSup /-
 theorem isLUB_sSup (s : Set (WithTop α)) : IsLUB s (sSup s) :=
   by
   cases' s.eq_empty_or_nonempty with hs hs
@@ -1150,7 +1403,9 @@ theorem isLUB_sSup (s : Set (WithTop α)) : IsLUB s (sSup s) :=
     · exfalso; apply h_1; use ⊥; rintro a ⟨⟩
   exact is_lub_Sup' hs
 #align with_top.is_lub_Sup WithTop.isLUB_sSup
+-/
 
+#print WithTop.isGLB_sInf' /-
 /-- The Inf of a bounded-below set is its greatest lower bound for a conditionally
 complete lattice with a top. -/
 theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
@@ -1187,13 +1442,16 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
           rw [← some_le_some]
           exact ha hb
 #align with_top.is_glb_Inf' WithTop.isGLB_sInf'
+-/
 
+#print WithTop.isGLB_sInf /-
 theorem isGLB_sInf (s : Set (WithTop α)) : IsGLB s (sInf s) :=
   by
   by_cases hs : BddBelow s
   · exact is_glb_Inf' hs
   · exfalso; apply hs; use ⊥; intro _ _; exact bot_le
 #align with_top.is_glb_Inf WithTop.isGLB_sInf
+-/
 
 noncomputable instance : CompleteLinearOrder (WithTop α) :=
   { WithTop.linearOrder, WithTop.lattice, WithTop.orderTop,
@@ -1205,17 +1463,21 @@ noncomputable instance : CompleteLinearOrder (WithTop α) :=
     le_inf := fun s => (isGLB_sInf s).2
     inf_le := fun s => (isGLB_sInf s).1 }
 
+#print WithTop.coe_sSup /-
 /-- A version of `with_top.coe_Sup'` with a more convenient but less general statement. -/
 @[norm_cast]
 theorem coe_sSup {s : Set α} (hb : BddAbove s) : ↑(sSup s) = (⨆ a ∈ s, ↑a : WithTop α) := by
   rw [coe_Sup' hb, sSup_image]
 #align with_top.coe_Sup WithTop.coe_sSup
+-/
 
+#print WithTop.coe_sInf /-
 /-- A version of `with_top.coe_Inf'` with a more convenient but less general statement. -/
 @[norm_cast]
 theorem coe_sInf {s : Set α} (hs : s.Nonempty) : ↑(sInf s) = (⨅ a ∈ s, ↑a : WithTop α) := by
   rw [coe_Inf' hs, sInf_image]
 #align with_top.coe_Inf WithTop.coe_sInf
+-/
 
 end WithTop
 
@@ -1227,25 +1489,33 @@ variable [Preorder α] [ConditionallyCompleteLattice β] {f : α → β} (h_mono
 `Sup` and `Inf`. -/
 
 
+#print Monotone.le_csSup_image /-
 theorem le_csSup_image {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddAbove s) :
     f c ≤ sSup (f '' s) :=
   le_csSup (map_bddAbove h_mono h_bdd) (mem_image_of_mem f hcs)
 #align monotone.le_cSup_image Monotone.le_csSup_image
+-/
 
+#print Monotone.csSup_image_le /-
 theorem csSup_image_le {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ upperBounds s) :
     sSup (f '' s) ≤ f B :=
   csSup_le (Nonempty.image f hs) (h_mono.mem_upperBounds_image hB)
 #align monotone.cSup_image_le Monotone.csSup_image_le
+-/
 
+#print Monotone.csInf_image_le /-
 theorem csInf_image_le {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddBelow s) :
     sInf (f '' s) ≤ f c :=
   @le_csSup_image αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ _ hcs h_bdd
 #align monotone.cInf_image_le Monotone.csInf_image_le
+-/
 
+#print Monotone.le_csInf_image /-
 theorem le_csInf_image {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ lowerBounds s) :
     f B ≤ sInf (f '' s) :=
   @csSup_image_le αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ hs _ hB
 #align monotone.le_cInf_image Monotone.le_csInf_image
+-/
 
 end Monotone
 
@@ -1254,43 +1524,59 @@ namespace GaloisConnection
 variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [Nonempty ι] {l : α → β}
   {u : β → α}
 
+#print GaloisConnection.l_csSup /-
 theorem l_csSup (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     l (sSup s) = ⨆ x : s, l x :=
   Eq.symm <| IsLUB.ciSup_set_eq (gc.isLUB_l_image <| isLUB_csSup hne hbdd) hne
 #align galois_connection.l_cSup GaloisConnection.l_csSup
+-/
 
+#print GaloisConnection.l_csSup' /-
 theorem l_csSup' (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     l (sSup s) = sSup (l '' s) := by rw [gc.l_cSup hne hbdd, sSup_image']
 #align galois_connection.l_cSup' GaloisConnection.l_csSup'
+-/
 
+#print GaloisConnection.l_ciSup /-
 theorem l_ciSup (gc : GaloisConnection l u) {f : ι → α} (hf : BddAbove (range f)) :
     l (⨆ i, f i) = ⨆ i, l (f i) := by rw [iSup, gc.l_cSup (range_nonempty _) hf, iSup_range']
 #align galois_connection.l_csupr GaloisConnection.l_ciSup
+-/
 
+#print GaloisConnection.l_ciSup_set /-
 theorem l_ciSup_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : l (⨆ i : s, f i) = ⨆ i : s, l (f i) := by haveI := hne.to_subtype;
   rw [image_eq_range] at hf ; exact gc.l_csupr hf
 #align galois_connection.l_csupr_set GaloisConnection.l_ciSup_set
+-/
 
+#print GaloisConnection.u_csInf /-
 theorem u_csInf (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
     u (sInf s) = ⨅ x : s, u x :=
   gc.dual.l_csSup hne hbdd
 #align galois_connection.u_cInf GaloisConnection.u_csInf
+-/
 
+#print GaloisConnection.u_csInf' /-
 theorem u_csInf' (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
     u (sInf s) = sInf (u '' s) :=
   gc.dual.l_csSup' hne hbdd
 #align galois_connection.u_cInf' GaloisConnection.u_csInf'
+-/
 
+#print GaloisConnection.u_ciInf /-
 theorem u_ciInf (gc : GaloisConnection l u) {f : ι → β} (hf : BddBelow (range f)) :
     u (⨅ i, f i) = ⨅ i, u (f i) :=
   gc.dual.l_ciSup hf
 #align galois_connection.u_cinfi GaloisConnection.u_ciInf
+-/
 
+#print GaloisConnection.u_ciInf_set /-
 theorem u_ciInf_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → β} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : u (⨅ i : s, f i) = ⨅ i : s, u (f i) :=
   gc.dual.l_ciSup_set hf hne
 #align galois_connection.u_cinfi_set GaloisConnection.u_ciInf_set
+-/
 
 end GaloisConnection
 
@@ -1298,45 +1584,61 @@ namespace OrderIso
 
 variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [Nonempty ι]
 
+#print OrderIso.map_csSup /-
 theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = ⨆ x : s, e x :=
   e.to_galoisConnection.l_csSup hne hbdd
 #align order_iso.map_cSup OrderIso.map_csSup
+-/
 
+#print OrderIso.map_csSup' /-
 theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = sSup (e '' s) :=
   e.to_galoisConnection.l_csSup' hne hbdd
 #align order_iso.map_cSup' OrderIso.map_csSup'
+-/
 
+#print OrderIso.map_ciSup /-
 theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
     e (⨆ i, f i) = ⨆ i, e (f i) :=
   e.to_galoisConnection.l_ciSup hf
 #align order_iso.map_csupr OrderIso.map_ciSup
+-/
 
+#print OrderIso.map_ciSup_set /-
 theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : e (⨆ i : s, f i) = ⨆ i : s, e (f i) :=
   e.to_galoisConnection.l_ciSup_set hf hne
 #align order_iso.map_csupr_set OrderIso.map_ciSup_set
+-/
 
+#print OrderIso.map_csInf /-
 theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = ⨅ x : s, e x :=
   e.dual.map_csSup hne hbdd
 #align order_iso.map_cInf OrderIso.map_csInf
+-/
 
+#print OrderIso.map_csInf' /-
 theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = sInf (e '' s) :=
   e.dual.map_csSup' hne hbdd
 #align order_iso.map_cInf' OrderIso.map_csInf'
+-/
 
+#print OrderIso.map_ciInf /-
 theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
     e (⨅ i, f i) = ⨅ i, e (f i) :=
   e.dual.map_ciSup hf
 #align order_iso.map_cinfi OrderIso.map_ciInf
+-/
 
+#print OrderIso.map_ciInf_set /-
 theorem map_ciInf_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : e (⨅ i : s, f i) = ⨅ i : s, e (f i) :=
   e.dual.map_ciSup_set hf hne
 #align order_iso.map_cinfi_set OrderIso.map_ciInf_set
+-/
 
 end OrderIso
 
@@ -1355,6 +1657,7 @@ variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β]
 
 variable {l u : α → β → γ} {l₁ u₁ : β → γ → α} {l₂ u₂ : α → γ → β}
 
+#print csSup_image2_eq_csSup_csSup /-
 theorem csSup_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) (hs₀ : s.Nonempty) (hs₁ : BddAbove s)
     (ht₀ : t.Nonempty) (ht₁ : BddAbove t) : sSup (image2 l s t) = l (sSup s) (sSup t) :=
@@ -1365,49 +1668,64 @@ theorem csSup_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (swap l b) (
     forall_image2_iff, forall₂_swap, (h₂ _).le_iff_le, csSup_le_iff ht₁ ht₀]
   simp_rw [← (h₂ _).le_iff_le, (h₁ _).le_iff_le, csSup_le_iff hs₁ hs₀]
 #align cSup_image2_eq_cSup_cSup csSup_image2_eq_csSup_csSup
+-/
 
+#print csSup_image2_eq_csSup_csInf /-
 theorem csSup_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
     s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → sSup (image2 l s t) = l (sSup s) (sInf t) :=
   @csSup_image2_eq_csSup_csSup _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cSup_image2_eq_cSup_cInf csSup_image2_eq_csSup_csInf
+-/
 
+#print csSup_image2_eq_csInf_csSup /-
 theorem csSup_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → sSup (image2 l s t) = l (sInf s) (sSup t) :=
   @csSup_image2_eq_csSup_csSup αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cSup_image2_eq_cInf_cSup csSup_image2_eq_csInf_csSup
+-/
 
+#print csSup_image2_eq_csInf_csInf /-
 theorem csSup_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → sSup (image2 l s t) = l (sInf s) (sInf t) :=
   @csSup_image2_eq_csSup_csSup αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cSup_image2_eq_cInf_cInf csSup_image2_eq_csInf_csInf
+-/
 
+#print csInf_image2_eq_csInf_csInf /-
 theorem csInf_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → sInf (image2 u s t) = u (sInf s) (sInf t) :=
   @csSup_image2_eq_csSup_csSup αᵒᵈ βᵒᵈ γᵒᵈ _ _ _ _ _ _ l₁ l₂ (fun _ => (h₁ _).dual) fun _ =>
     (h₂ _).dual
 #align cInf_image2_eq_cInf_cInf csInf_image2_eq_csInf_csInf
+-/
 
+#print csInf_image2_eq_csInf_csSup /-
 theorem csInf_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → sInf (image2 u s t) = u (sInf s) (sSup t) :=
   @csInf_image2_eq_csInf_csInf _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cInf_image2_eq_cInf_cSup csInf_image2_eq_csInf_csSup
+-/
 
+#print csInf_image2_eq_csSup_csInf /-
 theorem csInf_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
     s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → sInf (image2 u s t) = u (sSup s) (sInf t) :=
   @csInf_image2_eq_csInf_csInf αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cInf_image2_eq_cSup_cInf csInf_image2_eq_csSup_csInf
+-/
 
+#print csInf_image2_eq_csSup_csSup /-
 theorem csInf_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
     s.Nonempty → BddAbove s → t.Nonempty → BddAbove t → sInf (image2 u s t) = u (sSup s) (sSup t) :=
   @csInf_image2_eq_csInf_csInf αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cInf_image2_eq_cSup_cSup csInf_image2_eq_csSup_csSup
+-/
 
 end
 
@@ -1510,6 +1828,7 @@ noncomputable instance WithBot.WithTop.completeLinearOrder {α : Type _}
 #align with_bot.with_top.complete_linear_order WithBot.WithTop.completeLinearOrder
 -/
 
+#print WithTop.iSup_coe_eq_top /-
 theorem WithTop.iSup_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) = ⊤ ↔ ¬BddAbove (Set.range f) :=
   by
@@ -1520,11 +1839,14 @@ theorem WithTop.iSup_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyComple
   · rcases hf (a.untop ha.ne) with ⟨-, ⟨i, rfl⟩, hi⟩
     exact ⟨i, by simpa only [WithTop.coe_untop _ ha.ne] using with_top.coe_lt_coe.mpr hi⟩
 #align with_top.supr_coe_eq_top WithTop.iSup_coe_eq_top
+-/
 
+#print WithTop.iSup_coe_lt_top /-
 theorem WithTop.iSup_coe_lt_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) < ⊤ ↔ BddAbove (Set.range f) :=
   lt_top_iff_ne_top.trans <| (WithTop.iSup_coe_eq_top f).Not.trans Classical.not_not
 #align with_top.supr_coe_lt_top WithTop.iSup_coe_lt_top
+-/
 
 end WithTopBot
 

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

@@ -195,7 +195,7 @@ class ConditionallyCompleteLattice (α : Type _) extends Lattice α, SupSet α,
 -/
 
 #print ConditionallyCompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure -/
 /-- A conditionally complete linear order is a linear order in which
 every nonempty subset which is bounded above has a supremum, and
 every nonempty subset which is bounded below has an infimum.
@@ -206,7 +206,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrder (α : Type _) extends ConditionallyCompleteLattice α,
-    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:423:11: unsupported: advanced extends in structure"
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 -/
 
@@ -1179,10 +1179,10 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
       · refine' some_le_some.2 (le_csInf _ _)
         ·
           classical
-            contrapose! h
-            rintro (⟨⟩ | a) ha
-            · exact mem_singleton ⊤
-            · exact (h ⟨a, ha⟩).elim
+          contrapose! h
+          rintro (⟨⟩ | a) ha
+          · exact mem_singleton ⊤
+          · exact (h ⟨a, ha⟩).elim
         · intro b hb
           rw [← some_le_some]
           exact ha hb

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

@@ -206,7 +206,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrder (α : Type _) extends ConditionallyCompleteLattice α,
-  "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
+    "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 -/
 
@@ -220,7 +220,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrderBot (α : Type _) extends ConditionallyCompleteLinearOrder α,
-  Bot α where
+    Bot α where
   bot_le : ∀ x : α, ⊥ ≤ x
   csSup_empty : Sup ∅ = ⊥
 #align conditionally_complete_linear_order_bot ConditionallyCompleteLinearOrderBot
@@ -1269,7 +1269,7 @@ theorem l_ciSup (gc : GaloisConnection l u) {f : ι → α} (hf : BddAbove (rang
 
 theorem l_ciSup_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : l (⨆ i : s, f i) = ⨆ i : s, l (f i) := by haveI := hne.to_subtype;
-  rw [image_eq_range] at hf; exact gc.l_csupr hf
+  rw [image_eq_range] at hf ; exact gc.l_csupr hf
 #align galois_connection.l_csupr_set GaloisConnection.l_ciSup_set
 
 theorem u_csInf (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
@@ -1468,7 +1468,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
       cases' S.eq_empty_or_nonempty with h
       · show ite _ _ _ ≤ a
         split_ifs
-        · rw [h] at h_1; cases h_1
+        · rw [h] at h_1 ; cases h_1
         · convert bot_le; convert WithBot.csSup_empty; rw [h]; rfl
         · exfalso; apply h_2; use ⊥; rw [h]; rintro b ⟨⟩
       · refine' (WithTop.isLUB_sSup' h).2 ha

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

@@ -48,7 +48,7 @@ Extension of Sup and Inf from a preorder `α` to `with_top α` and `with_bot α`
 -/
 
 
-open Classical
+open scoped Classical
 
 noncomputable instance {α : Type _} [Preorder α] [SupSet α] : SupSet (WithTop α) :=
   ⟨fun S =>
@@ -226,11 +226,13 @@ class ConditionallyCompleteLinearOrderBot (α : Type _) extends ConditionallyCom
 #align conditionally_complete_linear_order_bot ConditionallyCompleteLinearOrderBot
 -/
 
+#print ConditionallyCompleteLinearOrderBot.toOrderBot /-
 -- see Note [lower instance priority]
 instance (priority := 100) ConditionallyCompleteLinearOrderBot.toOrderBot
     [h : ConditionallyCompleteLinearOrderBot α] : OrderBot α :=
   { h with }
 #align conditionally_complete_linear_order_bot.to_order_bot ConditionallyCompleteLinearOrderBot.toOrderBot
+-/
 
 #print CompleteLattice.toConditionallyCompleteLattice /-
 -- see Note [lower instance priority]
@@ -259,8 +261,9 @@ instance (priority := 100) CompleteLinearOrder.toConditionallyCompleteLinearOrde
 
 section
 
-open Classical
+open scoped Classical
 
+#print IsWellOrder.conditionallyCompleteLinearOrderBot /-
 /-- A well founded linear order is conditionally complete, with a bottom element. -/
 @[reducible]
 noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _) [i₁ : LinearOrder α]
@@ -287,6 +290,7 @@ noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _)
       simpa using h.wf.not_lt_min _ h's has
     csSup_empty := by simpa using eq_bot_iff.2 (not_lt.1 <| h.wf.not_lt_min _ _ <| mem_univ ⊥) }
 #align is_well_order.conditionally_complete_linear_order_bot IsWellOrder.conditionallyCompleteLinearOrderBot
+-/
 
 end
 
@@ -1101,7 +1105,7 @@ end ConditionallyCompleteLinearOrderBot
 
 namespace WithTop
 
-open Classical
+open scoped Classical
 
 variable [ConditionallyCompleteLinearOrderBot α]
 
@@ -1424,7 +1428,7 @@ This result can be used to show that the extended reals `[-∞, ∞]` are a comp
 -/
 
 
-open Classical
+open scoped Classical
 
 #print WithTop.conditionallyCompleteLattice /-
 /-- Adding a top element to a conditionally complete lattice

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

@@ -77,23 +77,11 @@ theorem WithTop.sInf_eq [InfSet α] {s : Set (WithTop α)} (hs : ¬s ⊆ {⊤})
 #align with_top.Inf_eq WithTop.sInf_eq
 -/
 
-/- warning: with_bot.Inf_eq -> WithBot.sInf_eq is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (Membership.Mem.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.hasMem.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α)) s)) -> (BddBelow.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)) -> (Eq.{succ u1} (WithBot.{u1} α) (InfSet.sInf.{u1} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (InfSet.sInf.{u1} α _inst_2 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align with_bot.Inf_eq WithBot.sInf_eqₓ'. -/
 theorem WithBot.sInf_eq [Preorder α] [InfSet α] {s : Set (WithBot α)} (hs : ⊥ ∉ s)
     (hs' : BddBelow (coe ⁻¹' s : Set α)) : sInf s = ↑(sInf (coe ⁻¹' s) : α) :=
   (if_neg hs).trans <| if_pos hs'
 #align with_bot.Inf_eq WithBot.sInf_eq
 
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 theorem WithBot.sSup_eq [SupSet α] {s : Set (WithBot α)} (hs : ¬s ⊆ {⊥}) :
     sSup s = ↑(sSup (coe ⁻¹' s) : α) :=
   if_neg hs
@@ -145,82 +133,40 @@ theorem WithTop.coe_sSup' [Preorder α] [SupSet α] {s : Set α} (hs : BddAbove
 #align with_top.coe_Sup' WithTop.coe_sSup'
 -/
 
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 @[norm_cast]
 theorem WithTop.coe_iSup [Preorder α] [SupSet α] (f : ι → α) (h : BddAbove (Set.range f)) :
     ↑(⨆ i, f i) = (⨆ i, f i : WithTop α) := by rw [iSup, iSup, WithTop.coe_sSup' h, range_comp]
 #align with_top.coe_supr WithTop.coe_iSup
 
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 @[simp]
 theorem WithBot.csSup_empty {α : Type _} [SupSet α] : sSup (∅ : Set (WithBot α)) = ⊥ :=
   if_pos <| Set.empty_subset _
 #align with_bot.cSup_empty WithBot.csSup_empty
 
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 @[simp]
 theorem WithBot.ciSup_empty {α : Type _} [IsEmpty ι] [SupSet α] (f : ι → WithBot α) :
     (⨆ i, f i) = ⊥ :=
   @WithTop.iInf_empty _ αᵒᵈ _ _ _
 #align with_bot.csupr_empty WithBot.ciSup_empty
 
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 @[norm_cast]
 theorem WithBot.coe_sSup' [SupSet α] {s : Set α} (hs : s.Nonempty) :
     ↑(sSup s) = (sSup (coe '' s) : WithBot α) :=
   @WithTop.coe_sInf' αᵒᵈ _ _ hs
 #align with_bot.coe_Sup' WithBot.coe_sSup'
 
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 @[norm_cast]
 theorem WithBot.coe_iSup [Nonempty ι] [SupSet α] (f : ι → α) :
     ↑(⨆ i, f i) = (⨆ i, f i : WithBot α) :=
   @WithTop.coe_iInf αᵒᵈ _ _ _ _
 #align with_bot.coe_supr WithBot.coe_iSup
 
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 @[norm_cast]
 theorem WithBot.coe_sInf' [Preorder α] [InfSet α] {s : Set α} (hs : BddBelow s) :
     ↑(sInf s) = (sInf (coe '' s) : WithBot α) :=
   @WithTop.coe_sSup' αᵒᵈ _ _ _ hs
 #align with_bot.coe_Inf' WithBot.coe_sInf'
 
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 @[norm_cast]
 theorem WithBot.coe_iInf [Preorder α] [InfSet α] (f : ι → α) (h : BddBelow (Set.range f)) :
     ↑(⨅ i, f i) = (⨅ i, f i : WithBot α) :=
@@ -280,12 +226,6 @@ class ConditionallyCompleteLinearOrderBot (α : Type _) extends ConditionallyCom
 #align conditionally_complete_linear_order_bot ConditionallyCompleteLinearOrderBot
 -/
 
-/- warning: conditionally_complete_linear_order_bot.to_order_bot -> ConditionallyCompleteLinearOrderBot.toOrderBot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align conditionally_complete_linear_order_bot.to_order_bot ConditionallyCompleteLinearOrderBot.toOrderBotₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) ConditionallyCompleteLinearOrderBot.toOrderBot
     [h : ConditionallyCompleteLinearOrderBot α] : OrderBot α :=
@@ -321,12 +261,6 @@ section
 
 open Classical
 
-/- warning: is_well_order.conditionally_complete_linear_order_bot -> IsWellOrder.conditionallyCompleteLinearOrderBot is a dubious translation:
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-  forall (α : Type.{u1}) [i₁ : LinearOrder.{u1} α] [i₂ : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α i₁)))))] [h : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α i₁))))))], ConditionallyCompleteLinearOrderBot.{u1} α
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-Case conversion may be inaccurate. Consider using '#align is_well_order.conditionally_complete_linear_order_bot IsWellOrder.conditionallyCompleteLinearOrderBotₓ'. -/
 /-- A well founded linear order is conditionally complete, with a bottom element. -/
 @[reducible]
 noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _) [i₁ : LinearOrder α]
@@ -512,396 +446,168 @@ section ConditionallyCompleteLattice
 
 variable [ConditionallyCompleteLattice α] {s t : Set α} {a b : α}
 
-/- warning: le_cSup -> le_csSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_cSup le_csSupₓ'. -/
 theorem le_csSup (h₁ : BddAbove s) (h₂ : a ∈ s) : a ≤ sSup s :=
   ConditionallyCompleteLattice.le_cSup s a h₁ h₂
 #align le_cSup le_csSup
 
-/- warning: cSup_le -> csSup_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cSup_le csSup_leₓ'. -/
 theorem csSup_le (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, b ≤ a) : sSup s ≤ a :=
   ConditionallyCompleteLattice.cSup_le s a h₁ h₂
 #align cSup_le csSup_le
 
-/- warning: cInf_le -> csInf_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cInf_le csInf_leₓ'. -/
 theorem csInf_le (h₁ : BddBelow s) (h₂ : a ∈ s) : sInf s ≤ a :=
   ConditionallyCompleteLattice.cInf_le s a h₁ h₂
 #align cInf_le csInf_le
 
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-Case conversion may be inaccurate. Consider using '#align le_cInf le_csInfₓ'. -/
 theorem le_csInf (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, a ≤ b) : a ≤ sInf s :=
   ConditionallyCompleteLattice.le_cInf s a h₁ h₂
 #align le_cInf le_csInf
 
-/- warning: le_cSup_of_le -> le_csSup_of_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_cSup_of_le le_csSup_of_leₓ'. -/
 theorem le_csSup_of_le (hs : BddAbove s) (hb : b ∈ s) (h : a ≤ b) : a ≤ sSup s :=
   le_trans h (le_csSup hs hb)
 #align le_cSup_of_le le_csSup_of_le
 
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-Case conversion may be inaccurate. Consider using '#align cInf_le_of_le csInf_le_of_leₓ'. -/
 theorem csInf_le_of_le (hs : BddBelow s) (hb : b ∈ s) (h : b ≤ a) : sInf s ≤ a :=
   le_trans (csInf_le hs hb) h
 #align cInf_le_of_le csInf_le_of_le
 
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 theorem csSup_le_csSup (ht : BddAbove t) (hs : s.Nonempty) (h : s ⊆ t) : sSup s ≤ sSup t :=
   csSup_le hs fun a ha => le_csSup ht (h ha)
 #align cSup_le_cSup csSup_le_csSup
 
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 theorem csInf_le_csInf (ht : BddBelow t) (hs : s.Nonempty) (h : s ⊆ t) : sInf t ≤ sInf s :=
   le_csInf hs fun a ha => csInf_le ht (h ha)
 #align cInf_le_cInf csInf_le_csInf
 
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 theorem le_csSup_iff (h : BddAbove s) (hs : s.Nonempty) :
     a ≤ sSup s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
   ⟨fun h b hb => le_trans h (csSup_le hs hb), fun hb => hb _ fun x => le_csSup h⟩
 #align le_cSup_iff le_csSup_iff
 
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 theorem csInf_le_iff (h : BddBelow s) (hs : s.Nonempty) : sInf s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
   ⟨fun h b hb => le_trans (le_csInf hs hb) h, fun hb => hb _ fun x => csInf_le h⟩
 #align cInf_le_iff csInf_le_iff
 
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 theorem isLUB_csSup (ne : s.Nonempty) (H : BddAbove s) : IsLUB s (sSup s) :=
   ⟨fun x => le_csSup H, fun x => csSup_le Ne⟩
 #align is_lub_cSup isLUB_csSup
 
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 theorem isLUB_ciSup [Nonempty ι] {f : ι → α} (H : BddAbove (range f)) :
     IsLUB (range f) (⨆ i, f i) :=
   isLUB_csSup (range_nonempty f) H
 #align is_lub_csupr isLUB_ciSup
 
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 theorem isLUB_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) (Hne : s.Nonempty) :
     IsLUB (f '' s) (⨆ i : s, f i) := by rw [← sSup_image']; exact isLUB_csSup (Hne.image _) H
 #align is_lub_csupr_set isLUB_ciSup_set
 
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 theorem isGLB_csInf (ne : s.Nonempty) (H : BddBelow s) : IsGLB s (sInf s) :=
   ⟨fun x => csInf_le H, fun x => le_csInf Ne⟩
 #align is_glb_cInf isGLB_csInf
 
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 theorem isGLB_ciInf [Nonempty ι] {f : ι → α} (H : BddBelow (range f)) :
     IsGLB (range f) (⨅ i, f i) :=
   isGLB_csInf (range_nonempty f) H
 #align is_glb_cinfi isGLB_ciInf
 
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 theorem isGLB_ciInf_set {f : β → α} {s : Set β} (H : BddBelow (f '' s)) (Hne : s.Nonempty) :
     IsGLB (f '' s) (⨅ i : s, f i) :=
   @isLUB_ciSup_set αᵒᵈ _ _ _ _ H Hne
 #align is_glb_cinfi_set isGLB_ciInf_set
 
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 theorem ciSup_le_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddAbove (range f)) :
     iSup f ≤ a ↔ ∀ i, f i ≤ a :=
   (isLUB_le_iff <| isLUB_ciSup hf).trans forall_range_iff
 #align csupr_le_iff ciSup_le_iff
 
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 theorem le_ciInf_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddBelow (range f)) :
     a ≤ iInf f ↔ ∀ i, a ≤ f i :=
   (le_isGLB_iff <| isGLB_ciInf hf).trans forall_range_iff
 #align le_cinfi_iff le_ciInf_iff
 
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 theorem ciSup_set_le_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddAbove (f '' s)) : (⨆ i : s, f i) ≤ a ↔ ∀ i ∈ s, f i ≤ a :=
   (isLUB_le_iff <| isLUB_ciSup_set hf hs).trans ball_image_iff
 #align csupr_set_le_iff ciSup_set_le_iff
 
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 theorem le_ciInf_set_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddBelow (f '' s)) : (a ≤ ⨅ i : s, f i) ↔ ∀ i ∈ s, a ≤ f i :=
   (le_isGLB_iff <| isGLB_ciInf_set hf hs).trans ball_image_iff
 #align le_cinfi_set_iff le_ciInf_set_iff
 
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 theorem IsLUB.csSup_eq (H : IsLUB s a) (ne : s.Nonempty) : sSup s = a :=
   (isLUB_csSup Ne ⟨a, H.1⟩).unique H
 #align is_lub.cSup_eq IsLUB.csSup_eq
 
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 theorem IsLUB.ciSup_eq [Nonempty ι] {f : ι → α} (H : IsLUB (range f) a) : (⨆ i, f i) = a :=
   H.csSup_eq (range_nonempty f)
 #align is_lub.csupr_eq IsLUB.ciSup_eq
 
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 theorem IsLUB.ciSup_set_eq {s : Set β} {f : β → α} (H : IsLUB (f '' s) a) (Hne : s.Nonempty) :
     (⨆ i : s, f i) = a :=
   IsLUB.csSup_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
 #align is_lub.csupr_set_eq IsLUB.ciSup_set_eq
 
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 /-- A greatest element of a set is the supremum of this set. -/
 theorem IsGreatest.csSup_eq (H : IsGreatest s a) : sSup s = a :=
   H.IsLUB.csSup_eq H.Nonempty
 #align is_greatest.cSup_eq IsGreatest.csSup_eq
 
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 theorem IsGreatest.csSup_mem (H : IsGreatest s a) : sSup s ∈ s :=
   H.csSup_eq.symm ▸ H.1
 #align is_greatest.Sup_mem IsGreatest.csSup_mem
 
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 theorem IsGLB.csInf_eq (H : IsGLB s a) (ne : s.Nonempty) : sInf s = a :=
   (isGLB_csInf Ne ⟨a, H.1⟩).unique H
 #align is_glb.cInf_eq IsGLB.csInf_eq
 
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 theorem IsGLB.ciInf_eq [Nonempty ι] {f : ι → α} (H : IsGLB (range f) a) : (⨅ i, f i) = a :=
   H.csInf_eq (range_nonempty f)
 #align is_glb.cinfi_eq IsGLB.ciInf_eq
 
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 theorem IsGLB.ciInf_set_eq {s : Set β} {f : β → α} (H : IsGLB (f '' s) a) (Hne : s.Nonempty) :
     (⨅ i : s, f i) = a :=
   IsGLB.csInf_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
 #align is_glb.cinfi_set_eq IsGLB.ciInf_set_eq
 
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 /-- A least element of a set is the infimum of this set. -/
 theorem IsLeast.csInf_eq (H : IsLeast s a) : sInf s = a :=
   H.IsGLB.csInf_eq H.Nonempty
 #align is_least.cInf_eq IsLeast.csInf_eq
 
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 theorem IsLeast.csInf_mem (H : IsLeast s a) : sInf s ∈ s :=
   H.csInf_eq.symm ▸ H.1
 #align is_least.Inf_mem IsLeast.csInf_mem
 
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 theorem subset_Icc_csInf_csSup (hb : BddBelow s) (ha : BddAbove s) : s ⊆ Icc (sInf s) (sSup s) :=
   fun x hx => ⟨csInf_le hb hx, le_csSup ha hx⟩
 #align subset_Icc_cInf_cSup subset_Icc_csInf_csSup
 
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 theorem csSup_le_iff (hb : BddAbove s) (hs : s.Nonempty) : sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
   isLUB_le_iff (isLUB_csSup hs hb)
 #align cSup_le_iff csSup_le_iff
 
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 theorem le_csInf_iff (hb : BddBelow s) (hs : s.Nonempty) : a ≤ sInf s ↔ ∀ b ∈ s, a ≤ b :=
   le_isGLB_iff (isGLB_csInf hs hb)
 #align le_cInf_iff le_csInf_iff
 
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 theorem csSup_lower_bounds_eq_csInf {s : Set α} (h : BddBelow s) (hs : s.Nonempty) :
     sSup (lowerBounds s) = sInf s :=
   (isLUB_csSup h <| hs.mono fun x hx y hy => hy hx).unique (isGLB_csInf hs h).IsLUB
 #align cSup_lower_bounds_eq_cInf csSup_lower_bounds_eq_csInf
 
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-Case conversion may be inaccurate. Consider using '#align cInf_upper_bounds_eq_cSup csInf_upper_bounds_eq_csSupₓ'. -/
 theorem csInf_upper_bounds_eq_csSup {s : Set α} (h : BddAbove s) (hs : s.Nonempty) :
     sInf (upperBounds s) = sSup s :=
   (isGLB_csInf h <| hs.mono fun x hx y hy => hy hx).unique (isLUB_csSup hs h).IsGLB
 #align cInf_upper_bounds_eq_cSup csInf_upper_bounds_eq_csSup
 
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-Case conversion may be inaccurate. Consider using '#align not_mem_of_lt_cInf not_mem_of_lt_csInfₓ'. -/
 theorem not_mem_of_lt_csInf {x : α} {s : Set α} (h : x < sInf s) (hs : BddBelow s) : x ∉ s :=
   fun hx => lt_irrefl _ (h.trans_le (csInf_le hs hx))
 #align not_mem_of_lt_cInf not_mem_of_lt_csInf
 
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-Case conversion may be inaccurate. Consider using '#align not_mem_of_cSup_lt not_mem_of_csSup_ltₓ'. -/
 theorem not_mem_of_csSup_lt {x : α} {s : Set α} (h : sSup s < x) (hs : BddAbove s) : x ∉ s :=
   @not_mem_of_lt_csInf αᵒᵈ _ x s h hs
 #align not_mem_of_cSup_lt not_mem_of_csSup_lt
 
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-Case conversion may be inaccurate. Consider using '#align cSup_eq_of_forall_le_of_forall_lt_exists_gt csSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
 /-- Introduction rule to prove that `b` is the supremum of `s`: it suffices to check that `b`
 is larger than all elements of `s`, and that this is not the case of any `w<b`.
 See `Sup_eq_of_forall_le_of_forall_lt_exists_gt` for a version in complete lattices. -/
@@ -912,12 +618,6 @@ theorem csSup_eq_of_forall_le_of_forall_lt_exists_gt (hs : s.Nonempty) (H : ∀
     lt_irrefl _ <| ha'.trans_le <| le_csSup ⟨b, H⟩ ha
 #align cSup_eq_of_forall_le_of_forall_lt_exists_gt csSup_eq_of_forall_le_of_forall_lt_exists_gt
 
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-Case conversion may be inaccurate. Consider using '#align cInf_eq_of_forall_ge_of_forall_gt_exists_lt csInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
 /-- Introduction rule to prove that `b` is the infimum of `s`: it suffices to check that `b`
 is smaller than all elements of `s`, and that this is not the case of any `w>b`.
 See `Inf_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in complete lattices. -/
@@ -926,12 +626,6 @@ theorem csInf_eq_of_forall_ge_of_forall_gt_exists_lt :
   @csSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _
 #align cInf_eq_of_forall_ge_of_forall_gt_exists_lt csInf_eq_of_forall_ge_of_forall_gt_exists_lt
 
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-Case conversion may be inaccurate. Consider using '#align lt_cSup_of_lt lt_csSup_of_ltₓ'. -/
 /-- b < Sup s when there is an element a in s with b < a, when s is bounded above.
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness above for one direction, nonemptiness and linear
@@ -941,12 +635,6 @@ theorem lt_csSup_of_lt (hs : BddAbove s) (ha : a ∈ s) (h : b < a) : b < sSup s
   lt_of_lt_of_le h (le_csSup hs ha)
 #align lt_cSup_of_lt lt_csSup_of_lt
 
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-Case conversion may be inaccurate. Consider using '#align cInf_lt_of_lt csInf_lt_of_ltₓ'. -/
 /-- Inf s < b when there is an element a in s with a < b, when s is bounded below.
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness below for one direction, nonemptiness and linear
@@ -956,12 +644,6 @@ theorem csInf_lt_of_lt : BddBelow s → a ∈ s → a < b → sInf s < b :=
   @lt_csSup_of_lt αᵒᵈ _ _ _ _
 #align cInf_lt_of_lt csInf_lt_of_lt
 
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-Case conversion may be inaccurate. Consider using '#align exists_between_of_forall_le exists_between_of_forall_leₓ'. -/
 /-- If all elements of a nonempty set `s` are less than or equal to all elements
 of a nonempty set `t`, then there exists an element between these sets. -/
 theorem exists_between_of_forall_le (sne : s.Nonempty) (tne : t.Nonempty)
@@ -969,70 +651,34 @@ theorem exists_between_of_forall_le (sne : s.Nonempty) (tne : t.Nonempty)
   ⟨sInf t, fun x hx => le_csInf tne <| hst x hx, fun y hy => csInf_le (sne.mono hst) hy⟩
 #align exists_between_of_forall_le exists_between_of_forall_le
 
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 /-- The supremum of a singleton is the element of the singleton-/
 @[simp]
 theorem csSup_singleton (a : α) : sSup {a} = a :=
   isGreatest_singleton.csSup_eq
 #align cSup_singleton csSup_singleton
 
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 /-- The infimum of a singleton is the element of the singleton-/
 @[simp]
 theorem csInf_singleton (a : α) : sInf {a} = a :=
   isLeast_singleton.csInf_eq
 #align cInf_singleton csInf_singleton
 
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 @[simp]
 theorem csSup_pair (a b : α) : sSup {a, b} = a ⊔ b :=
   (@isLUB_pair _ _ a b).csSup_eq (insert_nonempty _ _)
 #align cSup_pair csSup_pair
 
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 @[simp]
 theorem csInf_pair (a b : α) : sInf {a, b} = a ⊓ b :=
   (@isGLB_pair _ _ a b).csInf_eq (insert_nonempty _ _)
 #align cInf_pair csInf_pair
 
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 /-- If a set is bounded below and above, and nonempty, its infimum is less than or equal to
 its supremum.-/
 theorem csInf_le_csSup (hb : BddBelow s) (ha : BddAbove s) (ne : s.Nonempty) : sInf s ≤ sSup s :=
   isGLB_le_isLUB (isGLB_csInf Ne hb) (isLUB_csSup Ne ha) Ne
 #align cInf_le_cSup csInf_le_csSup
 
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 /-- The sup of a union of two sets is the max of the suprema of each subset, under the assumptions
 that all sets are bounded above and nonempty.-/
 theorem csSup_union (hs : BddAbove s) (sne : s.Nonempty) (ht : BddAbove t) (tne : t.Nonempty) :
@@ -1040,12 +686,6 @@ theorem csSup_union (hs : BddAbove s) (sne : s.Nonempty) (ht : BddAbove t) (tne
   ((isLUB_csSup sne hs).union (isLUB_csSup tne ht)).csSup_eq sne.inl
 #align cSup_union csSup_union
 
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 /-- The inf of a union of two sets is the min of the infima of each subset, under the assumptions
 that all sets are bounded below and nonempty.-/
 theorem csInf_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tne : t.Nonempty) :
@@ -1053,12 +693,6 @@ theorem csInf_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tne
   @csSup_union αᵒᵈ _ _ _ hs sne ht tne
 #align cInf_union csInf_union
 
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 /-- The supremum of an intersection of two sets is bounded by the minimum of the suprema of each
 set, if all sets are bounded above and nonempty.-/
 theorem csSup_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).Nonempty) :
@@ -1066,12 +700,6 @@ theorem csSup_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).None
   csSup_le hst fun x hx => le_inf (le_csSup hs hx.1) (le_csSup ht hx.2)
 #align cSup_inter_le csSup_inter_le
 
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 /-- The infimum of an intersection of two sets is bounded below by the maximum of the
 infima of each set, if all sets are bounded below and nonempty.-/
 theorem le_csInf_inter :
@@ -1079,202 +707,94 @@ theorem le_csInf_inter :
   @csSup_inter_le αᵒᵈ _ _ _
 #align le_cInf_inter le_csInf_inter
 
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 /-- The supremum of insert a s is the maximum of a and the supremum of s, if s is
 nonempty and bounded above.-/
 theorem csSup_insert (hs : BddAbove s) (sne : s.Nonempty) : sSup (insert a s) = a ⊔ sSup s :=
   ((isLUB_csSup sne hs).insert a).csSup_eq (insert_nonempty a s)
 #align cSup_insert csSup_insert
 
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 /-- The infimum of insert a s is the minimum of a and the infimum of s, if s is
 nonempty and bounded below.-/
 theorem csInf_insert (hs : BddBelow s) (sne : s.Nonempty) : sInf (insert a s) = a ⊓ sInf s :=
   @csSup_insert αᵒᵈ _ _ _ hs sne
 #align cInf_insert csInf_insert
 
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 @[simp]
 theorem csInf_Icc (h : a ≤ b) : sInf (Icc a b) = a :=
   (isGLB_Icc h).csInf_eq (nonempty_Icc.2 h)
 #align cInf_Icc csInf_Icc
 
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 @[simp]
 theorem csInf_Ici : sInf (Ici a) = a :=
   isLeast_Ici.csInf_eq
 #align cInf_Ici csInf_Ici
 
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 @[simp]
 theorem csInf_Ico (h : a < b) : sInf (Ico a b) = a :=
   (isGLB_Ico h).csInf_eq (nonempty_Ico.2 h)
 #align cInf_Ico csInf_Ico
 
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 @[simp]
 theorem csInf_Ioc [DenselyOrdered α] (h : a < b) : sInf (Ioc a b) = a :=
   (isGLB_Ioc h).csInf_eq (nonempty_Ioc.2 h)
 #align cInf_Ioc csInf_Ioc
 
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 @[simp]
 theorem csInf_Ioi [NoMaxOrder α] [DenselyOrdered α] : sInf (Ioi a) = a :=
   csInf_eq_of_forall_ge_of_forall_gt_exists_lt nonempty_Ioi (fun _ => le_of_lt) fun w hw => by
     simpa using exists_between hw
 #align cInf_Ioi csInf_Ioi
 
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 @[simp]
 theorem csInf_Ioo [DenselyOrdered α] (h : a < b) : sInf (Ioo a b) = a :=
   (isGLB_Ioo h).csInf_eq (nonempty_Ioo.2 h)
 #align cInf_Ioo csInf_Ioo
 
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 @[simp]
 theorem csSup_Icc (h : a ≤ b) : sSup (Icc a b) = b :=
   (isLUB_Icc h).csSup_eq (nonempty_Icc.2 h)
 #align cSup_Icc csSup_Icc
 
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 @[simp]
 theorem csSup_Ico [DenselyOrdered α] (h : a < b) : sSup (Ico a b) = b :=
   (isLUB_Ico h).csSup_eq (nonempty_Ico.2 h)
 #align cSup_Ico csSup_Ico
 
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 @[simp]
 theorem csSup_Iic : sSup (Iic a) = a :=
   isGreatest_Iic.csSup_eq
 #align cSup_Iic csSup_Iic
 
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 @[simp]
 theorem csSup_Iio [NoMinOrder α] [DenselyOrdered α] : sSup (Iio a) = a :=
   csSup_eq_of_forall_le_of_forall_lt_exists_gt nonempty_Iio (fun _ => le_of_lt) fun w hw => by
     simpa [and_comm'] using exists_between hw
 #align cSup_Iio csSup_Iio
 
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 @[simp]
 theorem csSup_Ioc (h : a < b) : sSup (Ioc a b) = b :=
   (isLUB_Ioc h).csSup_eq (nonempty_Ioc.2 h)
 #align cSup_Ioc csSup_Ioc
 
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 @[simp]
 theorem csSup_Ioo [DenselyOrdered α] (h : a < b) : sSup (Ioo a b) = b :=
   (isLUB_Ioo h).csSup_eq (nonempty_Ioo.2 h)
 #align cSup_Ioo csSup_Ioo
 
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 /-- The indexed supremum of a function is bounded above by a uniform bound-/
 theorem ciSup_le [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, f x ≤ c) : iSup f ≤ c :=
   csSup_le (range_nonempty f) (by rwa [forall_range_iff])
 #align csupr_le ciSup_le
 
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 /-- The indexed supremum of a function is bounded below by the value taken at one point-/
 theorem le_ciSup {f : ι → α} (H : BddAbove (range f)) (c : ι) : f c ≤ iSup f :=
   le_csSup H (mem_range_self _)
 #align le_csupr le_ciSup
 
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 theorem le_ciSup_of_le {f : ι → α} (H : BddAbove (range f)) (c : ι) (h : a ≤ f c) : a ≤ iSup f :=
   le_trans h (le_ciSup H c)
 #align le_csupr_of_le le_ciSup_of_le
 
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 /-- The indexed supremum of two functions are comparable if the functions are pointwise comparable-/
 theorem ciSup_mono {f g : ι → α} (B : BddAbove (range g)) (H : ∀ x, f x ≤ g x) : iSup f ≤ iSup g :=
   by
@@ -1283,99 +803,45 @@ theorem ciSup_mono {f g : ι → α} (B : BddAbove (range g)) (H : ∀ x, f x 
   · exact ciSup_le fun x => le_ciSup_of_le B x (H x)
 #align csupr_mono ciSup_mono
 
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 theorem le_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) {c : β} (hc : c ∈ s) :
     f c ≤ ⨆ i : s, f i :=
   (le_csSup H <| mem_image_of_mem f hc).trans_eq sSup_image'
 #align le_csupr_set le_ciSup_set
 
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 /-- The indexed infimum of two functions are comparable if the functions are pointwise comparable-/
 theorem ciInf_mono {f g : ι → α} (B : BddBelow (range f)) (H : ∀ x, f x ≤ g x) : iInf f ≤ iInf g :=
   @ciSup_mono αᵒᵈ _ _ _ _ B H
 #align cinfi_mono ciInf_mono
 
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 /-- The indexed minimum of a function is bounded below by a uniform lower bound-/
 theorem le_ciInf [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, c ≤ f x) : c ≤ iInf f :=
   @ciSup_le αᵒᵈ _ _ _ _ _ H
 #align le_cinfi le_ciInf
 
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 /-- The indexed infimum of a function is bounded above by the value taken at one point-/
 theorem ciInf_le {f : ι → α} (H : BddBelow (range f)) (c : ι) : iInf f ≤ f c :=
   @le_ciSup αᵒᵈ _ _ _ H c
 #align cinfi_le ciInf_le
 
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 theorem ciInf_le_of_le {f : ι → α} (H : BddBelow (range f)) (c : ι) (h : f c ≤ a) : iInf f ≤ a :=
   @le_ciSup_of_le αᵒᵈ _ _ _ _ H c h
 #align cinfi_le_of_le ciInf_le_of_le
 
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 theorem ciInf_set_le {f : β → α} {s : Set β} (H : BddBelow (f '' s)) {c : β} (hc : c ∈ s) :
     (⨅ i : s, f i) ≤ f c :=
   @le_ciSup_set αᵒᵈ _ _ _ _ H _ hc
 #align cinfi_set_le ciInf_set_le
 
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 @[simp]
 theorem ciSup_const [hι : Nonempty ι] {a : α} : (⨆ b : ι, a) = a := by
   rw [iSup, range_const, csSup_singleton]
 #align csupr_const ciSup_const
 
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 @[simp]
 theorem ciInf_const [hι : Nonempty ι] {a : α} : (⨅ b : ι, a) = a :=
   @ciSup_const αᵒᵈ _ _ _ _
 #align cinfi_const ciInf_const
 
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 @[simp]
 theorem ciSup_unique [Unique ι] {s : ι → α} : (⨆ i, s i) = s default :=
   by
@@ -1383,46 +849,22 @@ theorem ciSup_unique [Unique ι] {s : ι → α} : (⨆ i, s i) = s default :=
   simp only [this, ciSup_const]
 #align supr_unique ciSup_unique
 
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 @[simp]
 theorem ciInf_unique [Unique ι] {s : ι → α} : (⨅ i, s i) = s default :=
   @ciSup_unique αᵒᵈ _ _ _ _
 #align infi_unique ciInf_unique
 
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 @[simp]
 theorem ciSup_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
   haveI := uniqueProp hp
   ciSup_unique
 #align csupr_pos ciSup_pos
 
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 @[simp]
 theorem ciInf_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
   @ciSup_pos αᵒᵈ _ _ _ hp
 #align cinfi_pos ciInf_pos
 
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 /-- Introduction rule to prove that `b` is the supremum of `f`: it suffices to check that `b`
 is larger than `f i` for all `i`, and that this is not the case of any `w<b`.
 See `supr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in complete lattices. -/
@@ -1432,12 +874,6 @@ theorem ciSup_eq_of_forall_le_of_forall_lt_exists_gt [Nonempty ι] {f : ι → 
     fun w hw => exists_range_iff.mpr <| h₂ w hw
 #align csupr_eq_of_forall_le_of_forall_lt_exists_gt ciSup_eq_of_forall_le_of_forall_lt_exists_gt
 
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 /-- Introduction rule to prove that `b` is the infimum of `f`: it suffices to check that `b`
 is smaller than `f i` for all `i`, and that this is not the case of any `w>b`.
 See `infi_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in complete lattices. -/
@@ -1446,12 +882,6 @@ theorem ciInf_eq_of_forall_ge_of_forall_gt_exists_lt [Nonempty ι] {f : ι → 
   @ciSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _ ‹_› ‹_› ‹_›
 #align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt ciInf_eq_of_forall_ge_of_forall_gt_exists_lt
 
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-Case conversion may be inaccurate. Consider using '#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_Inter_Icc_of_antitoneₓ'. -/
 /-- Nested intervals lemma: if `f` is a monotone sequence, `g` is an antitone sequence, and
 `f n ≤ g n` for all `n`, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
 theorem Monotone.ciSup_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β → α} (hf : Monotone f)
@@ -1463,12 +893,6 @@ theorem Monotone.ciSup_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β 
   exact ⟨le_ciSup ⟨g <| n, forall_range_iff.2 this⟩ _, ciSup_le this⟩
 #align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_Inter_Icc_of_antitone
 
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-Case conversion may be inaccurate. Consider using '#align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_Inter_Icc_of_antitone_Iccₓ'. -/
 /-- Nested intervals lemma: if `[f n, g n]` is an antitone sequence of nonempty
 closed intervals, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
 theorem ciSup_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α}
@@ -1479,12 +903,6 @@ theorem ciSup_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α
     (fun m n hmn => ((Icc_subset_Icc_iff (h' n)).1 (h hmn)).2) h'
 #align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_Inter_Icc_of_antitone_Icc
 
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-Case conversion may be inaccurate. Consider using '#align cSup_eq_of_is_forall_le_of_forall_le_imp_ge csSup_eq_of_is_forall_le_of_forall_le_imp_geₓ'. -/
 /-- Introduction rule to prove that b is the supremum of s: it suffices to check that
 1) b is an upper bound
 2) every other upper bound b' satisfies b ≤ b'.-/
@@ -1517,24 +935,12 @@ section ConditionallyCompleteLinearOrder
 
 variable [ConditionallyCompleteLinearOrder α] {s t : Set α} {a b : α}
 
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 /-- When b < Sup s, there is an element a in s with b < a, if s is nonempty and the order is
 a linear order. -/
 theorem exists_lt_of_lt_csSup (hs : s.Nonempty) (hb : b < sSup s) : ∃ a ∈ s, b < a := by
   contrapose! hb; exact csSup_le hs hb
 #align exists_lt_of_lt_cSup exists_lt_of_lt_csSup
 
-/- warning: exists_lt_of_lt_csupr -> exists_lt_of_lt_ciSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr exists_lt_of_lt_ciSupₓ'. -/
 /-- Indexed version of the above lemma `exists_lt_of_lt_cSup`.
 When `b < supr f`, there is an element `i` such that `b < f i`.
 -/
@@ -1543,24 +949,12 @@ theorem exists_lt_of_lt_ciSup [Nonempty ι] {f : ι → α} (h : b < iSup f) : 
   ⟨i, h⟩
 #align exists_lt_of_lt_csupr exists_lt_of_lt_ciSup
 
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-Case conversion may be inaccurate. Consider using '#align exists_lt_of_cInf_lt exists_lt_of_csInf_ltₓ'. -/
 /-- When Inf s < b, there is an element a in s with a < b, if s is nonempty and the order is
 a linear order.-/
 theorem exists_lt_of_csInf_lt (hs : s.Nonempty) (hb : sInf s < b) : ∃ a ∈ s, a < b :=
   @exists_lt_of_lt_csSup αᵒᵈ _ _ _ hs hb
 #align exists_lt_of_cInf_lt exists_lt_of_csInf_lt
 
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-Case conversion may be inaccurate. Consider using '#align exists_lt_of_cinfi_lt exists_lt_of_ciInf_ltₓ'. -/
 /-- Indexed version of the above lemma `exists_lt_of_cInf_lt`
 When `infi f < a`, there is an element `i` such that `f i < a`.
 -/
@@ -1572,74 +966,32 @@ open Function
 
 variable [IsWellOrder α (· < ·)]
 
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-Case conversion may be inaccurate. Consider using '#align Inf_eq_argmin_on sInf_eq_argmin_onₓ'. -/
 theorem sInf_eq_argmin_on (hs : s.Nonempty) :
     sInf s = argminOn id (@IsWellFounded.wf α (· < ·) _) s hs :=
   IsLeast.csInf_eq ⟨argminOn_mem _ _ _ _, fun a ha => argminOn_le id _ _ ha⟩
 #align Inf_eq_argmin_on sInf_eq_argmin_on
 
-/- warning: is_least_Inf -> isLeast_csInf is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_csInfₓ'. -/
 theorem isLeast_csInf (hs : s.Nonempty) : IsLeast s (sInf s) := by rw [sInf_eq_argmin_on hs];
   exact ⟨argmin_on_mem _ _ _ _, fun a ha => argmin_on_le id _ _ ha⟩
 #align is_least_Inf isLeast_csInf
 
-/- warning: le_cInf_iff' -> le_csInf_iff' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_cInf_iff' le_csInf_iff'ₓ'. -/
 theorem le_csInf_iff' (hs : s.Nonempty) : b ≤ sInf s ↔ b ∈ lowerBounds s :=
   le_isGLB_iff (isLeast_csInf hs).IsGLB
 #align le_cInf_iff' le_csInf_iff'
 
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-Case conversion may be inaccurate. Consider using '#align Inf_mem csInf_memₓ'. -/
 theorem csInf_mem (hs : s.Nonempty) : sInf s ∈ s :=
   (isLeast_csInf hs).1
 #align Inf_mem csInf_mem
 
-/- warning: infi_mem -> ciInf_mem is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align infi_mem ciInf_memₓ'. -/
 theorem ciInf_mem [Nonempty ι] (f : ι → α) : iInf f ∈ range f :=
   csInf_mem (range_nonempty f)
 #align infi_mem ciInf_mem
 
-/- warning: monotone_on.map_Inf -> MonotoneOn.map_csInf is a dubious translation:
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 theorem MonotoneOn.map_csInf {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : MonotoneOn f s) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
   (hf.map_isLeast (isLeast_csInf hs)).csInf_eq.symm
 #align monotone_on.map_Inf MonotoneOn.map_csInf
 
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-Case conversion may be inaccurate. Consider using '#align monotone.map_Inf Monotone.map_csInfₓ'. -/
 theorem Monotone.map_csInf {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : Monotone f) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
   (hf.map_isLeast (isLeast_csInf hs)).csInf_eq.symm
@@ -1658,56 +1010,26 @@ section ConditionallyCompleteLinearOrderBot
 
 variable [ConditionallyCompleteLinearOrderBot α]
 
-/- warning: cSup_empty -> csSup_empty is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align cSup_empty csSup_emptyₓ'. -/
 @[simp]
 theorem csSup_empty : (sSup ∅ : α) = ⊥ :=
   ConditionallyCompleteLinearOrderBot.cSup_empty
 #align cSup_empty csSup_empty
 
-/- warning: csupr_of_empty -> ciSup_of_empty is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align csupr_of_empty ciSup_of_emptyₓ'. -/
 @[simp]
 theorem ciSup_of_empty [IsEmpty ι] (f : ι → α) : (⨆ i, f i) = ⊥ := by
   rw [iSup_of_empty', csSup_empty]
 #align csupr_of_empty ciSup_of_empty
 
-/- warning: csupr_false -> ciSup_false is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align csupr_false ciSup_falseₓ'. -/
 @[simp]
 theorem ciSup_false (f : False → α) : (⨆ i, f i) = ⊥ :=
   ciSup_of_empty f
 #align csupr_false ciSup_false
 
-/- warning: cInf_univ -> csInf_univ is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cInf_univ csInf_univₓ'. -/
 @[simp]
 theorem csInf_univ : sInf (univ : Set α) = ⊥ :=
   isLeast_univ.csInf_eq
 #align cInf_univ csInf_univ
 
-/- warning: is_lub_cSup' -> isLUB_csSup' is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align is_lub_cSup' isLUB_csSup'ₓ'. -/
 theorem isLUB_csSup' {s : Set α} (hs : BddAbove s) : IsLUB s (sSup s) :=
   by
   rcases eq_empty_or_nonempty s with (rfl | hne)
@@ -1715,146 +1037,62 @@ theorem isLUB_csSup' {s : Set α} (hs : BddAbove s) : IsLUB s (sSup s) :=
   · exact isLUB_csSup hne hs
 #align is_lub_cSup' isLUB_csSup'
 
-/- warning: cSup_le_iff' -> csSup_le_iff' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cSup_le_iff' csSup_le_iff'ₓ'. -/
 theorem csSup_le_iff' {s : Set α} (hs : BddAbove s) {a : α} : sSup s ≤ a ↔ ∀ x ∈ s, x ≤ a :=
   isLUB_le_iff (isLUB_csSup' hs)
 #align cSup_le_iff' csSup_le_iff'
 
-/- warning: cSup_le' -> csSup_le' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cSup_le' csSup_le'ₓ'. -/
 theorem csSup_le' {s : Set α} {a : α} (h : a ∈ upperBounds s) : sSup s ≤ a :=
   (csSup_le_iff' ⟨a, h⟩).2 h
 #align cSup_le' csSup_le'
 
-/- warning: le_cSup_iff' -> le_csSup_iff' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_cSup_iff' le_csSup_iff'ₓ'. -/
 theorem le_csSup_iff' {s : Set α} {a : α} (h : BddAbove s) :
     a ≤ sSup s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
   ⟨fun h b hb => le_trans h (csSup_le' hb), fun hb => hb _ fun x => le_csSup h⟩
 #align le_cSup_iff' le_csSup_iff'
 
-/- warning: le_csupr_iff' -> le_ciSup_iff' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_csupr_iff' le_ciSup_iff'ₓ'. -/
 theorem le_ciSup_iff' {s : ι → α} {a : α} (h : BddAbove (range s)) :
     a ≤ iSup s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by simp [iSup, h, le_csSup_iff', upperBounds]
 #align le_csupr_iff' le_ciSup_iff'
 
-/- warning: le_cInf_iff'' -> le_csInf_iff'' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align le_cInf_iff'' le_csInf_iff''ₓ'. -/
 theorem le_csInf_iff'' {s : Set α} {a : α} (ne : s.Nonempty) :
     a ≤ sInf s ↔ ∀ b : α, b ∈ s → a ≤ b :=
   le_csInf_iff ⟨⊥, fun a _ => bot_le⟩ Ne
 #align le_cInf_iff'' le_csInf_iff''
 
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-Case conversion may be inaccurate. Consider using '#align le_cinfi_iff' le_ciInf_iff'ₓ'. -/
 theorem le_ciInf_iff' [Nonempty ι] {f : ι → α} {a : α} : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
   le_ciInf_iff ⟨⊥, fun a _ => bot_le⟩
 #align le_cinfi_iff' le_ciInf_iff'
 
-/- warning: cInf_le' -> csInf_le' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cInf_le' csInf_le'ₓ'. -/
 theorem csInf_le' {s : Set α} {a : α} (h : a ∈ s) : sInf s ≤ a :=
   csInf_le ⟨⊥, fun a _ => bot_le⟩ h
 #align cInf_le' csInf_le'
 
-/- warning: cinfi_le' -> ciInf_le' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cinfi_le' ciInf_le'ₓ'. -/
 theorem ciInf_le' (f : ι → α) (i : ι) : iInf f ≤ f i :=
   ciInf_le ⟨⊥, fun a _ => bot_le⟩ _
 #align cinfi_le' ciInf_le'
 
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-Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'ₓ'. -/
 theorem exists_lt_of_lt_csSup' {s : Set α} {a : α} (h : a < sSup s) : ∃ b ∈ s, a < b := by
   contrapose! h; exact csSup_le' h
 #align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'
 
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-Case conversion may be inaccurate. Consider using '#align csupr_le_iff' ciSup_le_iff'ₓ'. -/
 theorem ciSup_le_iff' {f : ι → α} (h : BddAbove (range f)) {a : α} :
     (⨆ i, f i) ≤ a ↔ ∀ i, f i ≤ a :=
   (csSup_le_iff' h).trans forall_range_iff
 #align csupr_le_iff' ciSup_le_iff'
 
-/- warning: csupr_le' -> ciSup_le' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align csupr_le' ciSup_le'ₓ'. -/
 theorem ciSup_le' {f : ι → α} {a : α} (h : ∀ i, f i ≤ a) : (⨆ i, f i) ≤ a :=
   csSup_le' <| forall_range_iff.2 h
 #align csupr_le' ciSup_le'
 
-/- warning: exists_lt_of_lt_csupr' -> exists_lt_of_lt_ciSup' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'ₓ'. -/
 theorem exists_lt_of_lt_ciSup' {f : ι → α} {a : α} (h : a < ⨆ i, f i) : ∃ i, a < f i := by
   contrapose! h; exact ciSup_le' h
 #align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'
 
-/- warning: csupr_mono' -> ciSup_mono' is a dubious translation:
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-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι' g))
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-Case conversion may be inaccurate. Consider using '#align csupr_mono' ciSup_mono'ₓ'. -/
 theorem ciSup_mono' {ι'} {f : ι → α} {g : ι' → α} (hg : BddAbove (range g))
     (h : ∀ i, ∃ i', f i ≤ g i') : iSup f ≤ iSup g :=
   ciSup_le' fun i => Exists.elim (h i) (le_ciSup_of_le hg)
 #align csupr_mono' ciSup_mono'
 
-/- warning: cInf_le_cInf' -> csInf_le_csInf' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
-Case conversion may be inaccurate. Consider using '#align cInf_le_cInf' csInf_le_csInf'ₓ'. -/
 theorem csInf_le_csInf' {s t : Set α} (h₁ : t.Nonempty) (h₂ : t ⊆ s) : sInf s ≤ sInf t :=
   csInf_le_csInf (OrderBot.bddBelow s) h₁ h₂
 #align cInf_le_cInf' csInf_le_csInf'
@@ -1867,12 +1105,6 @@ open Classical
 
 variable [ConditionallyCompleteLinearOrderBot α]
 
-/- warning: with_top.is_lub_Sup' -> WithTop.isLUB_sSup' is a dubious translation:
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-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (Set.Nonempty.{u1} (WithTop.{u1} β) s) -> (IsLUB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (SupSet.sSup.{u1} (WithTop.{u1} β) (WithTop.hasSup.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (ConditionallyCompleteLattice.toHasSup.{u1} β _inst_2)) s))
-but is expected to have type
-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (Set.Nonempty.{u1} (WithTop.{u1} β) s) -> (IsLUB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (SupSet.sSup.{u1} (WithTop.{u1} β) (instSupSetWithTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align with_top.is_lub_Sup' WithTop.isLUB_sSup'ₓ'. -/
 /-- The Sup of a non-empty set is its least upper bound for a conditionally
 complete lattice with a top. -/
 theorem isLUB_sSup' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
@@ -1903,12 +1135,6 @@ theorem isLUB_sSup' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
       · exfalso; apply h_1; use b; intro a ha; exact some_le_some.1 (hb ha)
 #align with_top.is_lub_Sup' WithTop.isLUB_sSup'
 
-/- warning: with_top.is_lub_Sup -> WithTop.isLUB_sSup is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsLUB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (SupSet.sSup.{u1} (WithTop.{u1} α) (WithTop.hasSup.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsLUB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (SupSet.sSup.{u1} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
-Case conversion may be inaccurate. Consider using '#align with_top.is_lub_Sup WithTop.isLUB_sSupₓ'. -/
 theorem isLUB_sSup (s : Set (WithTop α)) : IsLUB s (sSup s) :=
   by
   cases' s.eq_empty_or_nonempty with hs hs
@@ -1921,12 +1147,6 @@ theorem isLUB_sSup (s : Set (WithTop α)) : IsLUB s (sSup s) :=
   exact is_lub_Sup' hs
 #align with_top.is_lub_Sup WithTop.isLUB_sSup
 
-/- warning: with_top.is_glb_Inf' -> WithTop.isGLB_sInf' is a dubious translation:
-lean 3 declaration is
-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (BddBelow.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s) -> (IsGLB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (InfSet.sInf.{u1} (WithTop.{u1} β) (WithTop.hasInf.{u1} β (ConditionallyCompleteLattice.toHasInf.{u1} β _inst_2)) s))
-but is expected to have type
-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (BddBelow.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s) -> (IsGLB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (InfSet.sInf.{u1} (WithTop.{u1} β) (instInfSetWithTop.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align with_top.is_glb_Inf' WithTop.isGLB_sInf'ₓ'. -/
 /-- The Inf of a bounded-below set is its greatest lower bound for a conditionally
 complete lattice with a top. -/
 theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
@@ -1964,12 +1184,6 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
           exact ha hb
 #align with_top.is_glb_Inf' WithTop.isGLB_sInf'
 
-/- warning: with_top.is_glb_Inf -> WithTop.isGLB_sInf is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsGLB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (InfSet.sInf.{u1} (WithTop.{u1} α) (WithTop.hasInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsGLB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (InfSet.sInf.{u1} (WithTop.{u1} α) (instInfSetWithTop.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
-Case conversion may be inaccurate. Consider using '#align with_top.is_glb_Inf WithTop.isGLB_sInfₓ'. -/
 theorem isGLB_sInf (s : Set (WithTop α)) : IsGLB s (sInf s) :=
   by
   by_cases hs : BddBelow s
@@ -1987,24 +1201,12 @@ noncomputable instance : CompleteLinearOrder (WithTop α) :=
     le_inf := fun s => (isGLB_sInf s).2
     inf_le := fun s => (isGLB_sInf s).1 }
 
-/- warning: with_top.coe_Sup -> WithTop.coe_sSup is a dubious translation:
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 /-- A version of `with_top.coe_Sup'` with a more convenient but less general statement. -/
 @[norm_cast]
 theorem coe_sSup {s : Set α} (hb : BddAbove s) : ↑(sSup s) = (⨆ a ∈ s, ↑a : WithTop α) := by
   rw [coe_Sup' hb, sSup_image]
 #align with_top.coe_Sup WithTop.coe_sSup
 
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 /-- A version of `with_top.coe_Inf'` with a more convenient but less general statement. -/
 @[norm_cast]
 theorem coe_sInf {s : Set α} (hs : s.Nonempty) : ↑(sInf s) = (⨅ a ∈ s, ↑a : WithTop α) := by
@@ -2021,45 +1223,21 @@ variable [Preorder α] [ConditionallyCompleteLattice β] {f : α → β} (h_mono
 `Sup` and `Inf`. -/
 
 
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 theorem le_csSup_image {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddAbove s) :
     f c ≤ sSup (f '' s) :=
   le_csSup (map_bddAbove h_mono h_bdd) (mem_image_of_mem f hcs)
 #align monotone.le_cSup_image Monotone.le_csSup_image
 
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 theorem csSup_image_le {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ upperBounds s) :
     sSup (f '' s) ≤ f B :=
   csSup_le (Nonempty.image f hs) (h_mono.mem_upperBounds_image hB)
 #align monotone.cSup_image_le Monotone.csSup_image_le
 
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 theorem csInf_image_le {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddBelow s) :
     sInf (f '' s) ≤ f c :=
   @le_csSup_image αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ _ hcs h_bdd
 #align monotone.cInf_image_le Monotone.csInf_image_le
 
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 theorem le_csInf_image {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ lowerBounds s) :
     f B ≤ sInf (f '' s) :=
   @csSup_image_le αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ hs _ hB
@@ -2072,87 +1250,39 @@ namespace GaloisConnection
 variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [Nonempty ι] {l : α → β}
   {u : β → α}
 
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 theorem l_csSup (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     l (sSup s) = ⨆ x : s, l x :=
   Eq.symm <| IsLUB.ciSup_set_eq (gc.isLUB_l_image <| isLUB_csSup hne hbdd) hne
 #align galois_connection.l_cSup GaloisConnection.l_csSup
 
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 theorem l_csSup' (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     l (sSup s) = sSup (l '' s) := by rw [gc.l_cSup hne hbdd, sSup_image']
 #align galois_connection.l_cSup' GaloisConnection.l_csSup'
 
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 theorem l_ciSup (gc : GaloisConnection l u) {f : ι → α} (hf : BddAbove (range f)) :
     l (⨆ i, f i) = ⨆ i, l (f i) := by rw [iSup, gc.l_cSup (range_nonempty _) hf, iSup_range']
 #align galois_connection.l_csupr GaloisConnection.l_ciSup
 
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 theorem l_ciSup_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : l (⨆ i : s, f i) = ⨆ i : s, l (f i) := by haveI := hne.to_subtype;
   rw [image_eq_range] at hf; exact gc.l_csupr hf
 #align galois_connection.l_csupr_set GaloisConnection.l_ciSup_set
 
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 theorem u_csInf (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
     u (sInf s) = ⨅ x : s, u x :=
   gc.dual.l_csSup hne hbdd
 #align galois_connection.u_cInf GaloisConnection.u_csInf
 
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 theorem u_csInf' (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
     u (sInf s) = sInf (u '' s) :=
   gc.dual.l_csSup' hne hbdd
 #align galois_connection.u_cInf' GaloisConnection.u_csInf'
 
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 theorem u_ciInf (gc : GaloisConnection l u) {f : ι → β} (hf : BddBelow (range f)) :
     u (⨅ i, f i) = ⨅ i, u (f i) :=
   gc.dual.l_ciSup hf
 #align galois_connection.u_cinfi GaloisConnection.u_ciInf
 
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 theorem u_ciInf_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → β} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : u (⨅ i : s, f i) = ⨅ i : s, u (f i) :=
   gc.dual.l_ciSup_set hf hne
@@ -2164,65 +1294,41 @@ namespace OrderIso
 
 variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [Nonempty ι]
 
-/- warning: order_iso.map_cSup -> OrderIso.map_csSup is a dubious translation:
-<too large>
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 theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = ⨆ x : s, e x :=
   e.to_galoisConnection.l_csSup hne hbdd
 #align order_iso.map_cSup OrderIso.map_csSup
 
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 theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = sSup (e '' s) :=
   e.to_galoisConnection.l_csSup' hne hbdd
 #align order_iso.map_cSup' OrderIso.map_csSup'
 
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 theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
     e (⨆ i, f i) = ⨆ i, e (f i) :=
   e.to_galoisConnection.l_ciSup hf
 #align order_iso.map_csupr OrderIso.map_ciSup
 
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 theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : e (⨆ i : s, f i) = ⨆ i : s, e (f i) :=
   e.to_galoisConnection.l_ciSup_set hf hne
 #align order_iso.map_csupr_set OrderIso.map_ciSup_set
 
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-<too large>
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 theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = ⨅ x : s, e x :=
   e.dual.map_csSup hne hbdd
 #align order_iso.map_cInf OrderIso.map_csInf
 
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 theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = sInf (e '' s) :=
   e.dual.map_csSup' hne hbdd
 #align order_iso.map_cInf' OrderIso.map_csInf'
 
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-<too large>
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 theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
     e (⨅ i, f i) = ⨅ i, e (f i) :=
   e.dual.map_ciSup hf
 #align order_iso.map_cinfi OrderIso.map_ciInf
 
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 theorem map_ciInf_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : e (⨅ i : s, f i) = ⨅ i : s, e (f i) :=
   e.dual.map_ciSup_set hf hne
@@ -2245,12 +1351,6 @@ variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β]
 
 variable {l u : α → β → γ} {l₁ u₁ : β → γ → α} {l₂ u₂ : α → γ → β}
 
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-Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cSup_cSup csSup_image2_eq_csSup_csSupₓ'. -/
 theorem csSup_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) (hs₀ : s.Nonempty) (hs₁ : BddAbove s)
     (ht₀ : t.Nonempty) (ht₁ : BddAbove t) : sSup (image2 l s t) = l (sSup s) (sSup t) :=
@@ -2262,48 +1362,24 @@ theorem csSup_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (swap l b) (
   simp_rw [← (h₂ _).le_iff_le, (h₁ _).le_iff_le, csSup_le_iff hs₁ hs₀]
 #align cSup_image2_eq_cSup_cSup csSup_image2_eq_csSup_csSup
 
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 theorem csSup_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
     s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → sSup (image2 l s t) = l (sSup s) (sInf t) :=
   @csSup_image2_eq_csSup_csSup _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cSup_image2_eq_cSup_cInf csSup_image2_eq_csSup_csInf
 
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 theorem csSup_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → sSup (image2 l s t) = l (sInf s) (sSup t) :=
   @csSup_image2_eq_csSup_csSup αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cSup_image2_eq_cInf_cSup csSup_image2_eq_csInf_csSup
 
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-Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cInf csSup_image2_eq_csInf_csInfₓ'. -/
 theorem csSup_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → sSup (image2 l s t) = l (sInf s) (sInf t) :=
   @csSup_image2_eq_csSup_csSup αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cSup_image2_eq_cInf_cInf csSup_image2_eq_csInf_csInf
 
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-Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cInf_cInf csInf_image2_eq_csInf_csInfₓ'. -/
 theorem csInf_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → sInf (image2 u s t) = u (sInf s) (sInf t) :=
@@ -2311,36 +1387,18 @@ theorem csInf_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (l₁ b) (sw
     (h₂ _).dual
 #align cInf_image2_eq_cInf_cInf csInf_image2_eq_csInf_csInf
 
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 theorem csInf_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
     s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → sInf (image2 u s t) = u (sInf s) (sSup t) :=
   @csInf_image2_eq_csInf_csInf _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cInf_image2_eq_cInf_cSup csInf_image2_eq_csInf_csSup
 
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-Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cInf csInf_image2_eq_csSup_csInfₓ'. -/
 theorem csInf_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
     s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → sInf (image2 u s t) = u (sSup s) (sInf t) :=
   @csInf_image2_eq_csInf_csInf αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
 #align cInf_image2_eq_cSup_cInf csInf_image2_eq_csSup_csInf
 
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-Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cSup csInf_image2_eq_csSup_csSupₓ'. -/
 theorem csInf_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
     s.Nonempty → BddAbove s → t.Nonempty → BddAbove t → sInf (image2 u s t) = u (sSup s) (sSup t) :=
@@ -2448,12 +1506,6 @@ noncomputable instance WithBot.WithTop.completeLinearOrder {α : Type _}
 #align with_bot.with_top.complete_linear_order WithBot.WithTop.completeLinearOrder
 -/
 
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-Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_eq_top WithTop.iSup_coe_eq_topₓ'. -/
 theorem WithTop.iSup_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) = ⊤ ↔ ¬BddAbove (Set.range f) :=
   by
@@ -2465,12 +1517,6 @@ theorem WithTop.iSup_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyComple
     exact ⟨i, by simpa only [WithTop.coe_untop _ ha.ne] using with_top.coe_lt_coe.mpr hi⟩
 #align with_top.supr_coe_eq_top WithTop.iSup_coe_eq_top
 
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-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (LT.lt.{u2} (WithTop.{u2} α) (Preorder.toHasLt.{u2} (WithTop.{u2} α) (WithTop.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))))) (iSup.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f))
-but is expected to have type
-  forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (LT.lt.{u1} (WithTop.{u1} α) (Preorder.toLT.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))))) (iSup.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f))
-Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_lt_top WithTop.iSup_coe_lt_topₓ'. -/
 theorem WithTop.iSup_coe_lt_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) < ⊤ ↔ BddAbove (Set.range f) :=
   lt_top_iff_ne_top.trans <| (WithTop.iSup_coe_eq_top f).Not.trans Classical.not_not

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

@@ -641,9 +641,7 @@ but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))))
 Case conversion may be inaccurate. Consider using '#align is_lub_csupr_set isLUB_ciSup_setₓ'. -/
 theorem isLUB_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) (Hne : s.Nonempty) :
-    IsLUB (f '' s) (⨆ i : s, f i) := by
-  rw [← sSup_image']
-  exact isLUB_csSup (Hne.image _) H
+    IsLUB (f '' s) (⨆ i : s, f i) := by rw [← sSup_image']; exact isLUB_csSup (Hne.image _) H
 #align is_lub_csupr_set isLUB_ciSup_set
 
 /- warning: is_glb_cInf -> isGLB_csInf is a dubious translation:
@@ -1527,10 +1525,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup exists_lt_of_lt_csSupₓ'. -/
 /-- When b < Sup s, there is an element a in s with b < a, if s is nonempty and the order is
 a linear order. -/
-theorem exists_lt_of_lt_csSup (hs : s.Nonempty) (hb : b < sSup s) : ∃ a ∈ s, b < a :=
-  by
-  contrapose! hb
-  exact csSup_le hs hb
+theorem exists_lt_of_lt_csSup (hs : s.Nonempty) (hb : b < sSup s) : ∃ a ∈ s, b < a := by
+  contrapose! hb; exact csSup_le hs hb
 #align exists_lt_of_lt_cSup exists_lt_of_lt_csSup
 
 /- warning: exists_lt_of_lt_csupr -> exists_lt_of_lt_ciSup is a dubious translation:
@@ -1593,9 +1589,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_csInfₓ'. -/
-theorem isLeast_csInf (hs : s.Nonempty) : IsLeast s (sInf s) :=
-  by
-  rw [sInf_eq_argmin_on hs]
+theorem isLeast_csInf (hs : s.Nonempty) : IsLeast s (sInf s) := by rw [sInf_eq_argmin_on hs];
   exact ⟨argmin_on_mem _ _ _ _, fun a ha => argmin_on_le id _ _ ha⟩
 #align is_least_Inf isLeast_csInf
 
@@ -1809,10 +1803,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'ₓ'. -/
-theorem exists_lt_of_lt_csSup' {s : Set α} {a : α} (h : a < sSup s) : ∃ b ∈ s, a < b :=
-  by
-  contrapose! h
-  exact csSup_le' h
+theorem exists_lt_of_lt_csSup' {s : Set α} {a : α} (h : a < sSup s) : ∃ b ∈ s, a < b := by
+  contrapose! h; exact csSup_le' h
 #align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'
 
 /- warning: csupr_le_iff' -> ciSup_le_iff' is a dubious translation:
@@ -1842,10 +1834,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α} {a : α}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (f i)))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'ₓ'. -/
-theorem exists_lt_of_lt_ciSup' {f : ι → α} {a : α} (h : a < ⨆ i, f i) : ∃ i, a < f i :=
-  by
-  contrapose! h
-  exact ciSup_le' h
+theorem exists_lt_of_lt_ciSup' {f : ι → α} {a : α} (h : a < ⨆ i, f i) : ∃ i, a < f i := by
+  contrapose! h; exact ciSup_le' h
 #align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'
 
 /- warning: csupr_mono' -> ciSup_mono' is a dubious translation:
@@ -1890,14 +1880,12 @@ theorem isLUB_sSup' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
   constructor
   · show ite _ _ _ ∈ _
     split_ifs
-    · intro _ _
-      exact le_top
+    · intro _ _; exact le_top
     · rintro (⟨⟩ | a) ha
       · contradiction
       apply some_le_some.2
       exact le_csSup h_1 ha
-    · intro _ _
-      exact le_top
+    · intro _ _; exact le_top
   · show ite _ _ _ ∈ _
     split_ifs
     · rintro (⟨⟩ | a) ha
@@ -1909,15 +1897,10 @@ theorem isLUB_sSup' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
       · rcases hs with ⟨⟨⟩ | b, hb⟩
         · exact absurd hb h
         · exact ⟨b, hb⟩
-      · intro a ha
-        exact some_le_some.1 (hb ha)
+      · intro a ha; exact some_le_some.1 (hb ha)
     · rintro (⟨⟩ | b) hb
       · exact le_rfl
-      · exfalso
-        apply h_1
-        use b
-        intro a ha
-        exact some_le_some.1 (hb ha)
+      · exfalso; apply h_1; use b; intro a ha; exact some_le_some.1 (hb ha)
 #align with_top.is_lub_Sup' WithTop.isLUB_sSup'
 
 /- warning: with_top.is_lub_Sup -> WithTop.isLUB_sSup is a dubious translation:
@@ -1933,12 +1916,8 @@ theorem isLUB_sSup (s : Set (WithTop α)) : IsLUB s (sSup s) :=
     show IsLUB ∅ (ite _ _ _)
     split_ifs
     · cases h
-    · rw [preimage_empty, csSup_empty]
-      exact isLUB_empty
-    · exfalso
-      apply h_1
-      use ⊥
-      rintro a ⟨⟩
+    · rw [preimage_empty, csSup_empty]; exact isLUB_empty
+    · exfalso; apply h_1; use ⊥; rintro a ⟨⟩
   exact is_lub_Sup' hs
 #align with_top.is_lub_Sup WithTop.isLUB_sSup
 
@@ -1955,8 +1934,7 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
   constructor
   · show ite _ _ _ ∈ _
     split_ifs
-    · intro a ha
-      exact top_le_iff.2 (Set.mem_singleton_iff.1 (h ha))
+    · intro a ha; exact top_le_iff.2 (Set.mem_singleton_iff.1 (h ha))
     · rintro (⟨⟩ | a) ha
       · exact le_top
       refine' some_le_some.2 (csInf_le _ ha)
@@ -1971,13 +1949,9 @@ theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (Wi
       exact some_le_some.1 (hb hc)
   · show ite _ _ _ ∈ _
     split_ifs
-    · intro _ _
-      exact le_top
+    · intro _ _; exact le_top
     · rintro (⟨⟩ | a) ha
-      · exfalso
-        apply h
-        intro b hb
-        exact Set.mem_singleton_iff.2 (top_le_iff.1 (ha hb))
+      · exfalso; apply h; intro b hb; exact Set.mem_singleton_iff.2 (top_le_iff.1 (ha hb))
       · refine' some_le_some.2 (le_csInf _ _)
         ·
           classical
@@ -2000,11 +1974,7 @@ theorem isGLB_sInf (s : Set (WithTop α)) : IsGLB s (sInf s) :=
   by
   by_cases hs : BddBelow s
   · exact is_glb_Inf' hs
-  · exfalso
-    apply hs
-    use ⊥
-    intro _ _
-    exact bot_le
+  · exfalso; apply hs; use ⊥; intro _ _; exact bot_le
 #align with_top.is_glb_Inf WithTop.isGLB_sInf
 
 noncomputable instance : CompleteLinearOrder (WithTop α) :=
@@ -2140,11 +2110,8 @@ but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (l (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => l (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i))))))
 Case conversion may be inaccurate. Consider using '#align galois_connection.l_csupr_set GaloisConnection.l_ciSup_setₓ'. -/
 theorem l_ciSup_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
-    (hne : s.Nonempty) : l (⨆ i : s, f i) = ⨆ i : s, l (f i) :=
-  by
-  haveI := hne.to_subtype
-  rw [image_eq_range] at hf
-  exact gc.l_csupr hf
+    (hne : s.Nonempty) : l (⨆ i : s, f i) = ⨆ i : s, l (f i) := by haveI := hne.to_subtype;
+  rw [image_eq_range] at hf; exact gc.l_csupr hf
 #align galois_connection.l_csupr_set GaloisConnection.l_ciSup_set
 
 /- warning: galois_connection.u_cInf -> GaloisConnection.u_csInf is a dubious translation:
@@ -2439,31 +2406,18 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
       cases' S.eq_empty_or_nonempty with h
       · show ite _ _ _ ≤ a
         split_ifs
-        · rw [h] at h_1
-          cases h_1
-        · convert bot_le
-          convert WithBot.csSup_empty
-          rw [h]
-          rfl
-        · exfalso
-          apply h_2
-          use ⊥
-          rw [h]
-          rintro b ⟨⟩
+        · rw [h] at h_1; cases h_1
+        · convert bot_le; convert WithBot.csSup_empty; rw [h]; rfl
+        · exfalso; apply h_2; use ⊥; rw [h]; rintro b ⟨⟩
       · refine' (WithTop.isLUB_sSup' h).2 ha
     inf_le := fun S a haS =>
       show ite _ _ _ ≤ a by
         split_ifs
-        · cases' a with a
-          exact le_rfl
+        · cases' a with a; exact le_rfl
           cases h haS <;> tauto
         · cases a
           · exact le_top
-          · apply WithTop.some_le_some.2
-            refine' csInf_le _ haS
-            use ⊥
-            intro b hb
-            exact bot_le
+          · apply WithTop.some_le_some.2; refine' csInf_le _ haS; use ⊥; intro b hb; exact bot_le
     le_inf := fun S a haS => (WithTop.isGLB_sInf' ⟨a, haS⟩).2 haS }
 #align with_top.with_bot.complete_lattice WithTop.WithBot.completeLattice
 -/

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

@@ -2198,10 +2198,7 @@ namespace OrderIso
 variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [Nonempty ι]
 
 /- warning: order_iso.map_cSup -> OrderIso.map_csSup is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup OrderIso.map_csSupₓ'. -/
 theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = ⨆ x : s, e x :=
@@ -2209,10 +2206,7 @@ theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAb
 #align order_iso.map_cSup OrderIso.map_csSup
 
 /- warning: order_iso.map_cSup' -> OrderIso.map_csSup' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup' OrderIso.map_csSup'ₓ'. -/
 theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = sSup (e '' s) :=
@@ -2220,10 +2214,7 @@ theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddA
 #align order_iso.map_cSup' OrderIso.map_csSup'
 
 /- warning: order_iso.map_csupr -> OrderIso.map_ciSup is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr OrderIso.map_ciSupₓ'. -/
 theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
     e (⨆ i, f i) = ⨆ i, e (f i) :=
@@ -2231,10 +2222,7 @@ theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
 #align order_iso.map_csupr OrderIso.map_ciSup
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr_set OrderIso.map_ciSup_setₓ'. -/
 theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : e (⨆ i : s, f i) = ⨆ i : s, e (f i) :=
@@ -2242,10 +2230,7 @@ theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbo
 #align order_iso.map_csupr_set OrderIso.map_ciSup_set
 
 /- warning: order_iso.map_cInf -> OrderIso.map_csInf is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf OrderIso.map_csInfₓ'. -/
 theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = ⨅ x : s, e x :=
@@ -2253,10 +2238,7 @@ theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBe
 #align order_iso.map_cInf OrderIso.map_csInf
 
 /- warning: order_iso.map_cInf' -> OrderIso.map_csInf' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf' OrderIso.map_csInf'ₓ'. -/
 theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = sInf (e '' s) :=
@@ -2264,10 +2246,7 @@ theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddB
 #align order_iso.map_cInf' OrderIso.map_csInf'
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi OrderIso.map_ciInfₓ'. -/
 theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
     e (⨅ i, f i) = ⨅ i, e (f i) :=
@@ -2275,10 +2254,7 @@ theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
 #align order_iso.map_cinfi OrderIso.map_ciInf
 
 /- warning: order_iso.map_cinfi_set -> OrderIso.map_ciInf_set is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi_set OrderIso.map_ciInf_setₓ'. -/
 theorem map_ciInf_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : e (⨅ i : s, f i) = ⨅ i : s, e (f i) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -2201,7 +2201,7 @@ variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [No
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (iSup.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (iSup.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup OrderIso.map_csSupₓ'. -/
 theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = ⨆ x : s, e x :=
@@ -2212,7 +2212,7 @@ theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAb
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e) s)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup' OrderIso.map_csSup'ₓ'. -/
 theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (sSup s) = sSup (e '' s) :=
@@ -2223,7 +2223,7 @@ theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddA
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iSup.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (iSup.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (f i))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr OrderIso.map_ciSupₓ'. -/
 theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
     e (⨆ i, f i) = ⨆ i, e (f i) :=
@@ -2234,7 +2234,7 @@ theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u3} γ} {f : γ -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr_set OrderIso.map_ciSup_setₓ'. -/
 theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : e (⨆ i : s, f i) = ⨆ i : s, e (f i) :=
@@ -2245,7 +2245,7 @@ theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbo
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (iInf.{u1, succ u2} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (iInf.{u1, succ u2} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf OrderIso.map_csInfₓ'. -/
 theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = ⨅ x : s, e x :=
@@ -2256,7 +2256,7 @@ theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBe
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e) s)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf' OrderIso.map_csInf'ₓ'. -/
 theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (sInf s) = sInf (e '' s) :=
@@ -2267,7 +2267,7 @@ theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddB
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iInf.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (iInf.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (f i))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi OrderIso.map_ciInfₓ'. -/
 theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
     e (⨅ i, f i) = ⨅ i, e (f i) :=
@@ -2278,7 +2278,7 @@ theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u3} γ} {f : γ -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iInf.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (iInf.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi_set OrderIso.map_ciInf_setₓ'. -/
 theorem map_ciInf_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : e (⨅ i : s, f i) = ⨅ i : s, e (f i) :=
@@ -2323,7 +2323,7 @@ theorem csSup_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (swap l b) (
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} α γ (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.sSup.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.sSup.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.sSup.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cSup_cInf csSup_image2_eq_csSup_csInfₓ'. -/
 theorem csSup_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
@@ -2335,7 +2335,7 @@ theorem csSup_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (swap l b) (
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.sSup.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.sInf.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.sInf.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cSup csSup_image2_eq_csInf_csSupₓ'. -/
 theorem csSup_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) :
@@ -2347,7 +2347,7 @@ theorem csSup_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (swap l b 
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.sSup.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.sInf.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.sInf.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cInf csSup_image2_eq_csInf_csInfₓ'. -/
 theorem csSup_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
@@ -2372,7 +2372,7 @@ theorem csInf_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (l₁ b) (sw
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (l₁ b) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cInf_cSup csInf_image2_eq_csInf_csSupₓ'. -/
 theorem csInf_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
@@ -2384,7 +2384,7 @@ theorem csInf_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (l₁ b) (sw
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cInf csInf_image2_eq_csSup_csInfₓ'. -/
 theorem csInf_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
@@ -2396,7 +2396,7 @@ theorem csInf_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (toDual ∘
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cSup csInf_image2_eq_csSup_csSupₓ'. -/
 theorem csInf_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :

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

@@ -280,13 +280,17 @@ class ConditionallyCompleteLinearOrderBot (α : Type _) extends ConditionallyCom
 #align conditionally_complete_linear_order_bot ConditionallyCompleteLinearOrderBot
 -/
 
-#print ConditionallyCompleteLinearOrderBot.toOrderBot /-
+/- warning: conditionally_complete_linear_order_bot.to_order_bot -> ConditionallyCompleteLinearOrderBot.toOrderBot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [h : ConditionallyCompleteLinearOrderBot.{u1} α], OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α h)))))))
+but is expected to have type
+  forall {α : Type.{u1}} [h : ConditionallyCompleteLinearOrderBot.{u1} α], OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α h)))))))
+Case conversion may be inaccurate. Consider using '#align conditionally_complete_linear_order_bot.to_order_bot ConditionallyCompleteLinearOrderBot.toOrderBotₓ'. -/
 -- see Note [lower instance priority]
 instance (priority := 100) ConditionallyCompleteLinearOrderBot.toOrderBot
     [h : ConditionallyCompleteLinearOrderBot α] : OrderBot α :=
   { h with }
 #align conditionally_complete_linear_order_bot.to_order_bot ConditionallyCompleteLinearOrderBot.toOrderBot
--/
 
 #print CompleteLattice.toConditionallyCompleteLattice /-
 -- see Note [lower instance priority]
@@ -317,7 +321,12 @@ section
 
 open Classical
 
-#print IsWellOrder.conditionallyCompleteLinearOrderBot /-
+/- warning: is_well_order.conditionally_complete_linear_order_bot -> IsWellOrder.conditionallyCompleteLinearOrderBot is a dubious translation:
+lean 3 declaration is
+  forall (α : Type.{u1}) [i₁ : LinearOrder.{u1} α] [i₂ : OrderBot.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α i₁)))))] [h : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α i₁))))))], ConditionallyCompleteLinearOrderBot.{u1} α
+but is expected to have type
+  forall (α : Type.{u1}) [i₁ : LinearOrder.{u1} α] [i₂ : OrderBot.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α i₁))))))] [h : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.2073 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.2075 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (DistribLattice.toLattice.{u1} α (instDistribLattice.{u1} α i₁)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.2073 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.2075)], ConditionallyCompleteLinearOrderBot.{u1} α
+Case conversion may be inaccurate. Consider using '#align is_well_order.conditionally_complete_linear_order_bot IsWellOrder.conditionallyCompleteLinearOrderBotₓ'. -/
 /-- A well founded linear order is conditionally complete, with a bottom element. -/
 @[reducible]
 noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _) [i₁ : LinearOrder α]
@@ -344,7 +353,6 @@ noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _)
       simpa using h.wf.not_lt_min _ h's has
     csSup_empty := by simpa using eq_bot_iff.2 (not_lt.1 <| h.wf.not_lt_min _ _ <| mem_univ ⊥) }
 #align is_well_order.conditionally_complete_linear_order_bot IsWellOrder.conditionallyCompleteLinearOrderBot
--/
 
 end
 
@@ -506,7 +514,7 @@ variable [ConditionallyCompleteLattice α] {s t : Set α} {a b : α}
 
 /- warning: le_cSup -> le_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align le_cSup le_csSupₓ'. -/
@@ -516,7 +524,7 @@ theorem le_csSup (h₁ : BddAbove s) (h₂ : a ∈ s) : a ≤ sSup s :=
 
 /- warning: cSup_le -> csSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align cSup_le csSup_leₓ'. -/
@@ -526,7 +534,7 @@ theorem csSup_le (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, b ≤ a) : sSup s ≤
 
 /- warning: cInf_le -> csInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align cInf_le csInf_leₓ'. -/
@@ -536,7 +544,7 @@ theorem csInf_le (h₁ : BddBelow s) (h₂ : a ∈ s) : sInf s ≤ a :=
 
 /- warning: le_cInf -> le_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align le_cInf le_csInfₓ'. -/
@@ -546,7 +554,7 @@ theorem le_csInf (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, a ≤ b) : a ≤ sInf
 
 /- warning: le_cSup_of_le -> le_csSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align le_cSup_of_le le_csSup_of_leₓ'. -/
@@ -556,7 +564,7 @@ theorem le_csSup_of_le (hs : BddAbove s) (hb : b ∈ s) (h : a ≤ b) : a ≤ sS
 
 /- warning: cInf_le_of_le -> csInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
 Case conversion may be inaccurate. Consider using '#align cInf_le_of_le csInf_le_of_leₓ'. -/
@@ -566,7 +574,7 @@ theorem csInf_le_of_le (hs : BddBelow s) (hb : b ∈ s) (h : b ≤ a) : sInf s 
 
 /- warning: cSup_le_cSup -> csSup_le_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t))
 Case conversion may be inaccurate. Consider using '#align cSup_le_cSup csSup_le_csSupₓ'. -/
@@ -576,7 +584,7 @@ theorem csSup_le_csSup (ht : BddAbove t) (hs : s.Nonempty) (h : s ⊆ t) : sSup
 
 /- warning: cInf_le_cInf -> csInf_le_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align cInf_le_cInf csInf_le_csInfₓ'. -/
@@ -586,7 +594,7 @@ theorem csInf_le_csInf (ht : BddBelow t) (hs : s.Nonempty) (h : s ⊆ t) : sInf
 
 /- warning: le_cSup_iff -> le_csSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
 Case conversion may be inaccurate. Consider using '#align le_cSup_iff le_csSup_iffₓ'. -/
@@ -597,7 +605,7 @@ theorem le_csSup_iff (h : BddAbove s) (hs : s.Nonempty) :
 
 /- warning: cInf_le_iff -> csInf_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
 Case conversion may be inaccurate. Consider using '#align cInf_le_iff csInf_le_iffₓ'. -/
@@ -672,7 +680,7 @@ theorem isGLB_ciInf_set {f : β → α} {s : Set β} (H : BddBelow (f '' s)) (Hn
 
 /- warning: csupr_le_iff -> ciSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a))
 Case conversion may be inaccurate. Consider using '#align csupr_le_iff ciSup_le_iffₓ'. -/
@@ -683,7 +691,7 @@ theorem ciSup_le_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddAbove (rang
 
 /- warning: le_cinfi_iff -> le_ciInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i)))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i)))
 Case conversion may be inaccurate. Consider using '#align le_cinfi_iff le_ciInf_iffₓ'. -/
@@ -694,7 +702,7 @@ theorem le_ciInf_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddBelow (rang
 
 /- warning: csupr_set_le_iff -> ciSup_set_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) a) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) a) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i))) a) (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a)))
 Case conversion may be inaccurate. Consider using '#align csupr_set_le_iff ciSup_set_le_iffₓ'. -/
@@ -705,7 +713,7 @@ theorem ciSup_set_le_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs
 
 /- warning: le_cinfi_set_iff -> le_ciInf_set_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i)))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i)))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i)))) (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i))))
 Case conversion may be inaccurate. Consider using '#align le_cinfi_set_iff le_ciInf_set_iffₓ'. -/
@@ -830,7 +838,7 @@ theorem subset_Icc_csInf_csSup (hb : BddBelow s) (ha : BddAbove s) : s ⊆ Icc (
 
 /- warning: cSup_le_iff -> csSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
 Case conversion may be inaccurate. Consider using '#align cSup_le_iff csSup_le_iffₓ'. -/
@@ -840,7 +848,7 @@ theorem csSup_le_iff (hb : BddAbove s) (hs : s.Nonempty) : sSup s ≤ a ↔ ∀
 
 /- warning: le_cInf_iff -> le_csInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_iff le_csInf_iffₓ'. -/
@@ -872,7 +880,7 @@ theorem csInf_upper_bounds_eq_csSup {s : Set α} (h : BddAbove s) (hs : s.Nonemp
 
 /- warning: not_mem_of_lt_cInf -> not_mem_of_lt_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))
 Case conversion may be inaccurate. Consider using '#align not_mem_of_lt_cInf not_mem_of_lt_csInfₓ'. -/
@@ -882,7 +890,7 @@ theorem not_mem_of_lt_csInf {x : α} {s : Set α} (h : x < sInf s) (hs : BddBelo
 
 /- warning: not_mem_of_cSup_lt -> not_mem_of_csSup_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) x) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) x) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) x) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))
 Case conversion may be inaccurate. Consider using '#align not_mem_of_cSup_lt not_mem_of_csSup_ltₓ'. -/
@@ -892,7 +900,7 @@ theorem not_mem_of_csSup_lt {x : α} {s : Set α} (h : sSup s < x) (hs : BddAbov
 
 /- warning: cSup_eq_of_forall_le_of_forall_lt_exists_gt -> csSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) b)
 Case conversion may be inaccurate. Consider using '#align cSup_eq_of_forall_le_of_forall_lt_exists_gt csSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
@@ -908,7 +916,7 @@ theorem csSup_eq_of_forall_le_of_forall_lt_exists_gt (hs : s.Nonempty) (H : ∀
 
 /- warning: cInf_eq_of_forall_ge_of_forall_gt_exists_lt -> csInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) b)
 Case conversion may be inaccurate. Consider using '#align cInf_eq_of_forall_ge_of_forall_gt_exists_lt csInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
@@ -922,7 +930,7 @@ theorem csInf_eq_of_forall_ge_of_forall_gt_exists_lt :
 
 /- warning: lt_cSup_of_lt -> lt_csSup_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align lt_cSup_of_lt lt_csSup_of_ltₓ'. -/
@@ -937,7 +945,7 @@ theorem lt_csSup_of_lt (hs : BddAbove s) (ha : a ∈ s) (h : b < a) : b < sSup s
 
 /- warning: cInf_lt_of_lt -> csInf_lt_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) b)
 Case conversion may be inaccurate. Consider using '#align cInf_lt_of_lt csInf_lt_of_ltₓ'. -/
@@ -952,7 +960,7 @@ theorem csInf_lt_of_lt : BddBelow s → a ∈ s → a < b → sInf s < b :=
 
 /- warning: exists_between_of_forall_le -> exists_between_of_forall_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Set.Nonempty.{u1} α t) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x y))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Set.Nonempty.{u1} α t) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x y))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Set.Nonempty.{u1} α t) -> (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x y))) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t)))
 Case conversion may be inaccurate. Consider using '#align exists_between_of_forall_le exists_between_of_forall_leₓ'. -/
@@ -1011,7 +1019,7 @@ theorem csInf_pair (a b : α) : sInf {a, b} = a ⊓ b :=
 
 /- warning: cInf_le_cSup -> csInf_le_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
 Case conversion may be inaccurate. Consider using '#align cInf_le_cSup csInf_le_csSupₓ'. -/
@@ -1049,7 +1057,7 @@ theorem csInf_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tne
 
 /- warning: cSup_inter_le -> csSup_inter_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_inter_le csSup_inter_leₓ'. -/
@@ -1062,7 +1070,7 @@ theorem csSup_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).None
 
 /- warning: le_cInf_inter -> le_csInf_inter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_inter le_csInf_interₓ'. -/
@@ -1099,7 +1107,7 @@ theorem csInf_insert (hs : BddBelow s) (sne : s.Nonempty) : sInf (insert a s) =
 
 /- warning: cInf_Icc -> csInf_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 Case conversion may be inaccurate. Consider using '#align cInf_Icc csInf_Iccₓ'. -/
@@ -1121,7 +1129,7 @@ theorem csInf_Ici : sInf (Ici a) = a :=
 
 /- warning: cInf_Ico -> csInf_Ico is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 Case conversion may be inaccurate. Consider using '#align cInf_Ico csInf_Icoₓ'. -/
@@ -1132,7 +1140,7 @@ theorem csInf_Ico (h : a < b) : sInf (Ico a b) = a :=
 
 /- warning: cInf_Ioc -> csInf_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 Case conversion may be inaccurate. Consider using '#align cInf_Ioc csInf_Iocₓ'. -/
@@ -1143,7 +1151,7 @@ theorem csInf_Ioc [DenselyOrdered α] (h : a < b) : sInf (Ioc a b) = a :=
 
 /- warning: cInf_Ioi -> csInf_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMaxOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 Case conversion may be inaccurate. Consider using '#align cInf_Ioi csInf_Ioiₓ'. -/
@@ -1155,7 +1163,7 @@ theorem csInf_Ioi [NoMaxOrder α] [DenselyOrdered α] : sInf (Ioi a) = a :=
 
 /- warning: cInf_Ioo -> csInf_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 Case conversion may be inaccurate. Consider using '#align cInf_Ioo csInf_Iooₓ'. -/
@@ -1166,7 +1174,7 @@ theorem csInf_Ioo [DenselyOrdered α] (h : a < b) : sInf (Ioo a b) = a :=
 
 /- warning: cSup_Icc -> csSup_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 Case conversion may be inaccurate. Consider using '#align cSup_Icc csSup_Iccₓ'. -/
@@ -1177,7 +1185,7 @@ theorem csSup_Icc (h : a ≤ b) : sSup (Icc a b) = b :=
 
 /- warning: cSup_Ico -> csSup_Ico is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 Case conversion may be inaccurate. Consider using '#align cSup_Ico csSup_Icoₓ'. -/
@@ -1199,7 +1207,7 @@ theorem csSup_Iic : sSup (Iic a) = a :=
 
 /- warning: cSup_Iio -> csSup_Iio is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMinOrder.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 Case conversion may be inaccurate. Consider using '#align cSup_Iio csSup_Iioₓ'. -/
@@ -1211,7 +1219,7 @@ theorem csSup_Iio [NoMinOrder α] [DenselyOrdered α] : sSup (Iio a) = a :=
 
 /- warning: cSup_Ioc -> csSup_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 Case conversion may be inaccurate. Consider using '#align cSup_Ioc csSup_Iocₓ'. -/
@@ -1222,7 +1230,7 @@ theorem csSup_Ioc (h : a < b) : sSup (Ioc a b) = b :=
 
 /- warning: cSup_Ioo -> csSup_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 Case conversion may be inaccurate. Consider using '#align cSup_Ioo csSup_Iooₓ'. -/
@@ -1233,7 +1241,7 @@ theorem csSup_Ioo [DenselyOrdered α] (h : a < b) : sSup (Ioo a b) = b :=
 
 /- warning: csupr_le -> ciSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) c)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) c) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) c)
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι f) c)
 Case conversion may be inaccurate. Consider using '#align csupr_le ciSup_leₓ'. -/
@@ -1244,7 +1252,7 @@ theorem ciSup_le [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, f x ≤ c) :
 
 /- warning: le_csupr -> le_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f c) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f))
 Case conversion may be inaccurate. Consider using '#align le_csupr le_ciSupₓ'. -/
@@ -1255,7 +1263,7 @@ theorem le_ciSup {f : ι → α} (H : BddAbove (range f)) (c : ι) : f c ≤ iSu
 
 /- warning: le_csupr_of_le -> le_ciSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f c)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {a : α} {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (f c)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f)))
 Case conversion may be inaccurate. Consider using '#align le_csupr_of_le le_ciSup_of_leₓ'. -/
@@ -1265,7 +1273,7 @@ theorem le_ciSup_of_le {f : ι → α} (H : BddAbove (range f)) (c : ι) (h : a
 
 /- warning: csupr_mono -> ciSup_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι g)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι g)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι g))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι g)) -> (forall (x : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f x) (g x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι g))
 Case conversion may be inaccurate. Consider using '#align csupr_mono ciSup_monoₓ'. -/
@@ -1279,7 +1287,7 @@ theorem ciSup_mono {f g : ι → α} (B : BddAbove (range g)) (H : ∀ x, f x 
 
 /- warning: le_csupr_set -> le_ciSup_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i)))))
 Case conversion may be inaccurate. Consider using '#align le_csupr_set le_ciSup_setₓ'. -/
@@ -1290,7 +1298,7 @@ theorem le_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) {c : 
 
 /- warning: cinfi_mono -> ciInf_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι g))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (x : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f x) (g x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι g))
 Case conversion may be inaccurate. Consider using '#align cinfi_mono ciInf_monoₓ'. -/
@@ -1301,7 +1309,7 @@ theorem ciInf_mono {f g : ι → α} (B : BddBelow (range f)) (H : ∀ x, f x 
 
 /- warning: le_cinfi -> le_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (f x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (f x)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (f x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι f))
 Case conversion may be inaccurate. Consider using '#align le_cinfi le_ciInfₓ'. -/
@@ -1312,7 +1320,7 @@ theorem le_ciInf [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, c ≤ f x) :
 
 /- warning: cinfi_le -> ciInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (f c))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (f c))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) (f c))
 Case conversion may be inaccurate. Consider using '#align cinfi_le ciInf_leₓ'. -/
@@ -1323,7 +1331,7 @@ theorem ciInf_le {f : ι → α} (H : BddBelow (range f)) (c : ι) : iInf f ≤
 
 /- warning: cinfi_le_of_le -> ciInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) a))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {a : α} {f : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f c) a) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) a))
 Case conversion may be inaccurate. Consider using '#align cinfi_le_of_le ciInf_le_of_leₓ'. -/
@@ -1333,7 +1341,7 @@ theorem ciInf_le_of_le {f : ι → α} (H : BddBelow (range f)) (c : ι) (h : f
 
 /- warning: cinfi_set_le -> ciInf_set_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) (f c)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) (f c)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))) (f c)))
 Case conversion may be inaccurate. Consider using '#align cinfi_set_le ciInf_set_leₓ'. -/
@@ -1413,7 +1421,7 @@ theorem ciInf_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :
 
 /- warning: csupr_eq_of_forall_le_of_forall_lt_exists_gt -> ciSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
 Case conversion may be inaccurate. Consider using '#align csupr_eq_of_forall_le_of_forall_lt_exists_gt ciSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
@@ -1428,7 +1436,7 @@ theorem ciSup_eq_of_forall_le_of_forall_lt_exists_gt [Nonempty ι] {f : ι → 
 
 /- warning: cinfi_eq_of_forall_ge_of_forall_gt_exists_lt -> ciInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
 Case conversion may be inaccurate. Consider using '#align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt ciInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
@@ -1442,7 +1450,7 @@ theorem ciInf_eq_of_forall_ge_of_forall_gt_exists_lt [Nonempty ι] {f : ι → 
 
 /- warning: monotone.csupr_mem_Inter_Icc_of_antitone -> Monotone.ciSup_mem_Inter_Icc_of_antitone is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) f) -> (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) g) -> (LE.le.{max u2 u1} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f g) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) f) -> (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) g) -> (LE.le.{max u2 u1} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f g) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) f) -> (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) g) -> (LE.le.{max u1 u2} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f g) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
 Case conversion may be inaccurate. Consider using '#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_Inter_Icc_of_antitoneₓ'. -/
@@ -1459,7 +1467,7 @@ theorem Monotone.ciSup_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β 
 
 /- warning: csupr_mem_Inter_Icc_of_antitone_Icc -> ciSup_mem_Inter_Icc_of_antitone_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β (Set.{u1} α) (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))) -> (forall (n : β), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f n) (g n)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β (Set.{u1} α) (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))) -> (forall (n : β), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f n) (g n)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β (Set.{u1} α) (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))) -> (forall (n : β), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f n) (g n)) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
 Case conversion may be inaccurate. Consider using '#align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_Inter_Icc_of_antitone_Iccₓ'. -/
@@ -1475,7 +1483,7 @@ theorem ciSup_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α
 
 /- warning: cSup_eq_of_is_forall_le_of_forall_le_imp_ge -> csSup_eq_of_is_forall_le_of_forall_le_imp_ge is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (ub : α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a ub)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b ub)) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (ub : α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a ub)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b ub)) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (ub : α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a ub)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b ub)) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) b)
 Case conversion may be inaccurate. Consider using '#align cSup_eq_of_is_forall_le_of_forall_le_imp_ge csSup_eq_of_is_forall_le_of_forall_le_imp_geₓ'. -/
@@ -1513,7 +1521,7 @@ variable [ConditionallyCompleteLinearOrder α] {s t : Set α} {a b : α}
 
 /- warning: exists_lt_of_lt_cSup -> exists_lt_of_lt_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b a)))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup exists_lt_of_lt_csSupₓ'. -/
@@ -1527,7 +1535,7 @@ theorem exists_lt_of_lt_csSup (hs : s.Nonempty) (hb : b < sSup s) : ∃ a ∈ s,
 
 /- warning: exists_lt_of_lt_csupr -> exists_lt_of_lt_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f)) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f)) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (f i)))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f)) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (f i)))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr exists_lt_of_lt_ciSupₓ'. -/
@@ -1541,7 +1549,7 @@ theorem exists_lt_of_lt_ciSup [Nonempty ι] {f : ι → α} (h : b < iSup f) : 
 
 /- warning: exists_lt_of_cInf_lt -> exists_lt_of_csInf_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b)))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_cInf_lt exists_lt_of_csInf_ltₓ'. -/
@@ -1553,7 +1561,7 @@ theorem exists_lt_of_csInf_lt (hs : s.Nonempty) (hb : sInf s < b) : ∃ a ∈ s,
 
 /- warning: exists_lt_of_cinfi_lt -> exists_lt_of_ciInf_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) a) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) a) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (f i) a))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) a) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (f i) a))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_cinfi_lt exists_lt_of_ciInf_ltₓ'. -/
@@ -1570,7 +1578,7 @@ variable [IsWellOrder α (· < ·)]
 
 /- warning: Inf_eq_argmin_on -> sInf_eq_argmin_on is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (IsWellOrder.to_isWellFounded.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) _inst_2)) s hs)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (IsWellOrder.to_isWellFounded.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) _inst_2)) s hs)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) _inst_2)) s hs)
 Case conversion may be inaccurate. Consider using '#align Inf_eq_argmin_on sInf_eq_argmin_onₓ'. -/
@@ -1581,7 +1589,7 @@ theorem sInf_eq_argmin_on (hs : s.Nonempty) :
 
 /- warning: is_least_Inf -> isLeast_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_csInfₓ'. -/
@@ -1593,7 +1601,7 @@ theorem isLeast_csInf (hs : s.Nonempty) : IsLeast s (sInf s) :=
 
 /- warning: le_cInf_iff' -> le_csInf_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_iff' le_csInf_iff'ₓ'. -/
@@ -1603,7 +1611,7 @@ theorem le_csInf_iff' (hs : s.Nonempty) : b ≤ sInf s ↔ b ∈ lowerBounds s :
 
 /- warning: Inf_mem -> csInf_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 Case conversion may be inaccurate. Consider using '#align Inf_mem csInf_memₓ'. -/
@@ -1613,7 +1621,7 @@ theorem csInf_mem (hs : s.Nonempty) : sInf s ∈ s :=
 
 /- warning: infi_mem -> ciInf_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 Case conversion may be inaccurate. Consider using '#align infi_mem ciInf_memₓ'. -/
@@ -1623,7 +1631,7 @@ theorem ciInf_mem [Nonempty ι] (f : ι → α) : iInf f ∈ range f :=
 
 /- warning: monotone_on.map_Inf -> MonotoneOn.map_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone_on.map_Inf MonotoneOn.map_csInfₓ'. -/
@@ -1634,7 +1642,7 @@ theorem MonotoneOn.map_csInf {β : Type _} [ConditionallyCompleteLattice β] {f
 
 /- warning: monotone.map_Inf -> Monotone.map_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone.map_Inf Monotone.map_csInfₓ'. -/
@@ -1715,7 +1723,7 @@ theorem isLUB_csSup' {s : Set α} (hs : BddAbove s) : IsLUB s (sSup s) :=
 
 /- warning: cSup_le_iff' -> csSup_le_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) x a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) x a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) x a)))
 Case conversion may be inaccurate. Consider using '#align cSup_le_iff' csSup_le_iff'ₓ'. -/
@@ -1725,7 +1733,7 @@ theorem csSup_le_iff' {s : Set α} (hs : BddAbove s) {a : α} : sSup s ≤ a ↔
 
 /- warning: cSup_le' -> csSup_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
 Case conversion may be inaccurate. Consider using '#align cSup_le' csSup_le'ₓ'. -/
@@ -1735,7 +1743,7 @@ theorem csSup_le' {s : Set α} {a : α} (h : a ∈ upperBounds s) : sSup s ≤ a
 
 /- warning: le_cSup_iff' -> le_csSup_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 Case conversion may be inaccurate. Consider using '#align le_cSup_iff' le_csSup_iff'ₓ'. -/
@@ -1746,7 +1754,7 @@ theorem le_csSup_iff' {s : Set α} {a : α} (h : BddAbove s) :
 
 /- warning: le_csupr_iff' -> le_ciSup_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (s i) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι s)) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (s i) b) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {s : ι -> α} {a : α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι s)) -> (Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (s i) b) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a b)))
 Case conversion may be inaccurate. Consider using '#align le_csupr_iff' le_ciSup_iff'ₓ'. -/
@@ -1756,7 +1764,7 @@ theorem le_ciSup_iff' {s : ι → α} {a : α} (h : BddAbove (range s)) :
 
 /- warning: le_cInf_iff'' -> le_csInf_iff'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_iff'' le_csInf_iff''ₓ'. -/
@@ -1767,7 +1775,7 @@ theorem le_csInf_iff'' {s : Set α} {a : α} (ne : s.Nonempty) :
 
 /- warning: le_cinfi_iff' -> le_ciInf_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i))
 but is expected to have type
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i))
 Case conversion may be inaccurate. Consider using '#align le_cinfi_iff' le_ciInf_iff'ₓ'. -/
@@ -1777,7 +1785,7 @@ theorem le_ciInf_iff' [Nonempty ι] {f : ι → α} {a : α} : a ≤ iInf f ↔
 
 /- warning: cInf_le' -> csInf_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
 Case conversion may be inaccurate. Consider using '#align cInf_le' csInf_le'ₓ'. -/
@@ -1787,7 +1795,7 @@ theorem csInf_le' {s : Set α} {a : α} (h : a ∈ s) : sInf s ≤ a :=
 
 /- warning: cinfi_le' -> ciInf_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (f i)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (f i)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι f) (f i)
 Case conversion may be inaccurate. Consider using '#align cinfi_le' ciInf_le'ₓ'. -/
@@ -1797,7 +1805,7 @@ theorem ciInf_le' (f : ι → α) (i : ι) : iInf f ≤ f i :=
 
 /- warning: exists_lt_of_lt_cSup' -> exists_lt_of_lt_csSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'ₓ'. -/
@@ -1809,7 +1817,7 @@ theorem exists_lt_of_lt_csSup' {s : Set α} {a : α} (h : a < sSup s) : ∃ b 
 
 /- warning: csupr_le_iff' -> ciSup_le_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f)) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f)) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a) (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f)) -> (forall {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i)) a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) a))
 Case conversion may be inaccurate. Consider using '#align csupr_le_iff' ciSup_le_iff'ₓ'. -/
@@ -1820,7 +1828,7 @@ theorem ciSup_le_iff' {f : ι → α} (h : BddAbove (range f)) {a : α} :
 
 /- warning: csupr_le' -> ciSup_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a)
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i)) a)
 Case conversion may be inaccurate. Consider using '#align csupr_le' ciSup_le'ₓ'. -/
@@ -1830,7 +1838,7 @@ theorem ciSup_le' {f : ι → α} {a : α} (h : ∀ i, f i ≤ a) : (⨆ i, f i)
 
 /- warning: exists_lt_of_lt_csupr' -> exists_lt_of_lt_ciSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i)))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α} {a : α}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (f i)))
 Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'ₓ'. -/
@@ -1842,7 +1850,7 @@ theorem exists_lt_of_lt_ciSup' {f : ι → α} {a : α} (h : a < ⨆ i, f i) : 
 
 /- warning: csupr_mono' -> ciSup_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι' g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι' g))
 but is expected to have type
   forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι f) (iSup.{u2, u3} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι' g))
 Case conversion may be inaccurate. Consider using '#align csupr_mono' ciSup_mono'ₓ'. -/
@@ -1853,7 +1861,7 @@ theorem ciSup_mono' {ι'} {f : ι → α} {g : ι' → α} (hg : BddAbove (range
 
 /- warning: cInf_le_cInf' -> csInf_le_csInf' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
 Case conversion may be inaccurate. Consider using '#align cInf_le_cInf' csInf_le_csInf'ₓ'. -/
@@ -2045,7 +2053,7 @@ variable [Preorder α] [ConditionallyCompleteLattice β] {f : α → β} (h_mono
 
 /- warning: monotone.le_cSup_image -> Monotone.le_csSup_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddAbove.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f c) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddAbove.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f c) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α} {c : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c s) -> (BddAbove.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (f c) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s))))
 Case conversion may be inaccurate. Consider using '#align monotone.le_cSup_image Monotone.le_csSup_imageₓ'. -/
@@ -2056,7 +2064,7 @@ theorem le_csSup_image {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddAbove s
 
 /- warning: monotone.cSup_image_le -> Monotone.csSup_image_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (upperBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f B))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (upperBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f B))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (forall {B : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) B (upperBounds.{u2} α _inst_1 s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)) (f B))))
 Case conversion may be inaccurate. Consider using '#align monotone.cSup_image_le Monotone.csSup_image_leₓ'. -/
@@ -2067,7 +2075,7 @@ theorem csSup_image_le {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ upper
 
 /- warning: monotone.cInf_image_le -> Monotone.csInf_image_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddBelow.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f c)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddBelow.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f c)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α} {c : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c s) -> (BddBelow.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)) (f c)))
 Case conversion may be inaccurate. Consider using '#align monotone.cInf_image_le Monotone.csInf_image_leₓ'. -/
@@ -2078,7 +2086,7 @@ theorem csInf_image_le {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddBelow s
 
 /- warning: monotone.le_cInf_image -> Monotone.le_csInf_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (lowerBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f B) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (lowerBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f B) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (forall {B : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) B (lowerBounds.{u2} α _inst_1 s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (f B) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)))))
 Case conversion may be inaccurate. Consider using '#align monotone.le_cInf_image Monotone.le_csInf_imageₓ'. -/
@@ -2191,7 +2199,7 @@ variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [No
 
 /- warning: order_iso.map_cSup -> OrderIso.map_csSup is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (iSup.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup OrderIso.map_csSupₓ'. -/
@@ -2202,7 +2210,7 @@ theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAb
 
 /- warning: order_iso.map_cSup' -> OrderIso.map_csSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup' OrderIso.map_csSup'ₓ'. -/
@@ -2213,7 +2221,7 @@ theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddA
 
 /- warning: order_iso.map_csupr -> OrderIso.map_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => 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(ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iSup.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr OrderIso.map_ciSupₓ'. -/
@@ -2224,7 +2232,7 @@ theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
 
 /- warning: order_iso.map_csupr_set -> OrderIso.map_ciSup_set is a dubious translation:
 lean 3 declaration is
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(LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) 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+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u3} γ} {f : γ -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α 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_inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} 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 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β 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u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr_set OrderIso.map_ciSup_setₓ'. -/
@@ -2235,7 +2243,7 @@ theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbo
 
 /- warning: order_iso.map_cInf -> OrderIso.map_csInf is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (iInf.{u1, succ u2} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf OrderIso.map_csInfₓ'. -/
@@ -2246,7 +2254,7 @@ theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBe
 
 /- warning: order_iso.map_cInf' -> OrderIso.map_csInf' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf' OrderIso.map_csInf'ₓ'. -/
@@ -2257,7 +2265,7 @@ theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddB
 
 /- warning: order_iso.map_cinfi -> OrderIso.map_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toHasLe.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => 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(ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iInf.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi OrderIso.map_ciInfₓ'. -/
@@ -2268,7 +2276,7 @@ theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
 
 /- warning: order_iso.map_cinfi_set -> OrderIso.map_ciInf_set is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iInf.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi_set OrderIso.map_ciInf_setₓ'. -/
@@ -2529,7 +2537,7 @@ theorem WithTop.iSup_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyComple
 
 /- warning: with_top.supr_coe_lt_top -> WithTop.iSup_coe_lt_top is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (LT.lt.{u2} (WithTop.{u2} α) (Preorder.toLT.{u2} (WithTop.{u2} α) (WithTop.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))))) (iSup.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (LT.lt.{u2} (WithTop.{u2} α) (Preorder.toHasLt.{u2} (WithTop.{u2} α) (WithTop.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))))) (iSup.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f))
 but is expected to have type
   forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (LT.lt.{u1} (WithTop.{u1} α) (Preorder.toLT.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))))) (iSup.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f))
 Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_lt_top WithTop.iSup_coe_lt_topₓ'. -/

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

@@ -52,70 +52,70 @@ open Classical
 
 noncomputable instance {α : Type _} [Preorder α] [SupSet α] : SupSet (WithTop α) :=
   ⟨fun S =>
-    if ⊤ ∈ S then ⊤ else if BddAbove (coe ⁻¹' S : Set α) then ↑(supₛ (coe ⁻¹' S : Set α)) else ⊤⟩
+    if ⊤ ∈ S then ⊤ else if BddAbove (coe ⁻¹' S : Set α) then ↑(sSup (coe ⁻¹' S : Set α)) else ⊤⟩
 
 noncomputable instance {α : Type _} [InfSet α] : InfSet (WithTop α) :=
-  ⟨fun S => if S ⊆ {⊤} then ⊤ else ↑(infₛ (coe ⁻¹' S : Set α))⟩
+  ⟨fun S => if S ⊆ {⊤} then ⊤ else ↑(sInf (coe ⁻¹' S : Set α))⟩
 
 noncomputable instance {α : Type _} [SupSet α] : SupSet (WithBot α) :=
-  ⟨(@WithTop.hasInf αᵒᵈ _).infₛ⟩
+  ⟨(@WithTop.hasInf αᵒᵈ _).sInf⟩
 
 noncomputable instance {α : Type _} [Preorder α] [InfSet α] : InfSet (WithBot α) :=
-  ⟨(@WithTop.hasSup αᵒᵈ _ _).supₛ⟩
+  ⟨(@WithTop.hasSup αᵒᵈ _ _).sSup⟩
 
-#print WithTop.supₛ_eq /-
-theorem WithTop.supₛ_eq [Preorder α] [SupSet α] {s : Set (WithTop α)} (hs : ⊤ ∉ s)
-    (hs' : BddAbove (coe ⁻¹' s : Set α)) : supₛ s = ↑(supₛ (coe ⁻¹' s) : α) :=
+#print WithTop.sSup_eq /-
+theorem WithTop.sSup_eq [Preorder α] [SupSet α] {s : Set (WithTop α)} (hs : ⊤ ∉ s)
+    (hs' : BddAbove (coe ⁻¹' s : Set α)) : sSup s = ↑(sSup (coe ⁻¹' s) : α) :=
   (if_neg hs).trans <| if_pos hs'
-#align with_top.Sup_eq WithTop.supₛ_eq
+#align with_top.Sup_eq WithTop.sSup_eq
 -/
 
-#print WithTop.infₛ_eq /-
-theorem WithTop.infₛ_eq [InfSet α] {s : Set (WithTop α)} (hs : ¬s ⊆ {⊤}) :
-    infₛ s = ↑(infₛ (coe ⁻¹' s) : α) :=
+#print WithTop.sInf_eq /-
+theorem WithTop.sInf_eq [InfSet α] {s : Set (WithTop α)} (hs : ¬s ⊆ {⊤}) :
+    sInf s = ↑(sInf (coe ⁻¹' s) : α) :=
   if_neg hs
-#align with_top.Inf_eq WithTop.infₛ_eq
+#align with_top.Inf_eq WithTop.sInf_eq
 -/
 
-/- warning: with_bot.Inf_eq -> WithBot.infₛ_eq is a dubious translation:
+/- warning: with_bot.Inf_eq -> WithBot.sInf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (Membership.Mem.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.hasMem.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α)) s)) -> (BddBelow.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)) -> (Eq.{succ u1} (WithBot.{u1} α) (InfSet.infₛ.{u1} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (InfSet.infₛ.{u1} α _inst_2 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s))))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (Membership.Mem.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.hasMem.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α)) s)) -> (BddBelow.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)) -> (Eq.{succ u1} (WithBot.{u1} α) (InfSet.sInf.{u1} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (InfSet.sInf.{u1} α _inst_2 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (Membership.mem.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.instMembershipSet.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α)) s)) -> (BddBelow.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s)) -> (Eq.{succ u1} (WithBot.{u1} α) (InfSet.infₛ.{u1} (WithBot.{u1} α) (instInfSetWithBot.{u1} α _inst_1 _inst_2) s) (WithBot.some.{u1} α (InfSet.infₛ.{u1} α _inst_2 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s))))
-Case conversion may be inaccurate. Consider using '#align with_bot.Inf_eq WithBot.infₛ_eqₓ'. -/
-theorem WithBot.infₛ_eq [Preorder α] [InfSet α] {s : Set (WithBot α)} (hs : ⊥ ∉ s)
-    (hs' : BddBelow (coe ⁻¹' s : Set α)) : infₛ s = ↑(infₛ (coe ⁻¹' s) : α) :=
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (Membership.mem.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.instMembershipSet.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α)) s)) -> (BddBelow.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s)) -> (Eq.{succ u1} (WithBot.{u1} α) (InfSet.sInf.{u1} (WithBot.{u1} α) (instInfSetWithBot.{u1} α _inst_1 _inst_2) s) (WithBot.some.{u1} α (InfSet.sInf.{u1} α _inst_2 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s))))
+Case conversion may be inaccurate. Consider using '#align with_bot.Inf_eq WithBot.sInf_eqₓ'. -/
+theorem WithBot.sInf_eq [Preorder α] [InfSet α] {s : Set (WithBot α)} (hs : ⊥ ∉ s)
+    (hs' : BddBelow (coe ⁻¹' s : Set α)) : sInf s = ↑(sInf (coe ⁻¹' s) : α) :=
   (if_neg hs).trans <| if_pos hs'
-#align with_bot.Inf_eq WithBot.infₛ_eq
+#align with_bot.Inf_eq WithBot.sInf_eq
 
-/- warning: with_bot.Sup_eq -> WithBot.supₛ_eq is a dubious translation:
+/- warning: with_bot.Sup_eq -> WithBot.sSup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (HasSubset.Subset.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.hasSubset.{u1} (WithBot.{u1} α)) s (Singleton.singleton.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.hasSingleton.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α))))) -> (Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (SupSet.supₛ.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s))))
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (HasSubset.Subset.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.hasSubset.{u1} (WithBot.{u1} α)) s (Singleton.singleton.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.hasSingleton.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α))))) -> (Eq.{succ u1} (WithBot.{u1} α) (SupSet.sSup.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (SupSet.sSup.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (HasSubset.Subset.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.instHasSubsetSet.{u1} (WithBot.{u1} α)) s (Singleton.singleton.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.instSingletonSet.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α))))) -> (Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) s) (WithBot.some.{u1} α (SupSet.supₛ.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s))))
-Case conversion may be inaccurate. Consider using '#align with_bot.Sup_eq WithBot.supₛ_eqₓ'. -/
-theorem WithBot.supₛ_eq [SupSet α] {s : Set (WithBot α)} (hs : ¬s ⊆ {⊥}) :
-    supₛ s = ↑(supₛ (coe ⁻¹' s) : α) :=
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (HasSubset.Subset.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.instHasSubsetSet.{u1} (WithBot.{u1} α)) s (Singleton.singleton.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.instSingletonSet.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α))))) -> (Eq.{succ u1} (WithBot.{u1} α) (SupSet.sSup.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) s) (WithBot.some.{u1} α (SupSet.sSup.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s))))
+Case conversion may be inaccurate. Consider using '#align with_bot.Sup_eq WithBot.sSup_eqₓ'. -/
+theorem WithBot.sSup_eq [SupSet α] {s : Set (WithBot α)} (hs : ¬s ⊆ {⊥}) :
+    sSup s = ↑(sSup (coe ⁻¹' s) : α) :=
   if_neg hs
-#align with_bot.Sup_eq WithBot.supₛ_eq
+#align with_bot.Sup_eq WithBot.sSup_eq
 
-#print WithTop.infₛ_empty /-
+#print WithTop.sInf_empty /-
 @[simp]
-theorem WithTop.infₛ_empty {α : Type _} [InfSet α] : infₛ (∅ : Set (WithTop α)) = ⊤ :=
+theorem WithTop.sInf_empty {α : Type _} [InfSet α] : sInf (∅ : Set (WithTop α)) = ⊤ :=
   if_pos <| Set.empty_subset _
-#align with_top.cInf_empty WithTop.infₛ_empty
+#align with_top.cInf_empty WithTop.sInf_empty
 -/
 
-#print WithTop.infᵢ_empty /-
+#print WithTop.iInf_empty /-
 @[simp]
-theorem WithTop.infᵢ_empty {α : Type _} [IsEmpty ι] [InfSet α] (f : ι → WithTop α) :
-    (⨅ i, f i) = ⊤ := by rw [infᵢ, range_eq_empty, WithTop.infₛ_empty]
-#align with_top.cinfi_empty WithTop.infᵢ_empty
+theorem WithTop.iInf_empty {α : Type _} [IsEmpty ι] [InfSet α] (f : ι → WithTop α) :
+    (⨅ i, f i) = ⊤ := by rw [iInf, range_eq_empty, WithTop.sInf_empty]
+#align with_top.cinfi_empty WithTop.iInf_empty
 -/
 
-#print WithTop.coe_infₛ' /-
-theorem WithTop.coe_infₛ' [InfSet α] {s : Set α} (hs : s.Nonempty) :
-    ↑(infₛ s) = (infₛ (coe '' s) : WithTop α) :=
+#print WithTop.coe_sInf' /-
+theorem WithTop.coe_sInf' [InfSet α] {s : Set α} (hs : s.Nonempty) :
+    ↑(sInf s) = (sInf (coe '' s) : WithTop α) :=
   by
   obtain ⟨x, hx⟩ := hs
   change _ = ite _ _ _
@@ -123,109 +123,109 @@ theorem WithTop.coe_infₛ' [InfSet α] {s : Set α} (hs : s.Nonempty) :
   · cases h (mem_image_of_mem _ hx)
   · rw [preimage_image_eq]
     exact Option.some_injective _
-#align with_top.coe_Inf' WithTop.coe_infₛ'
+#align with_top.coe_Inf' WithTop.coe_sInf'
 -/
 
-#print WithTop.coe_infᵢ /-
+#print WithTop.coe_iInf /-
 @[norm_cast]
-theorem WithTop.coe_infᵢ [Nonempty ι] [InfSet α] (f : ι → α) :
+theorem WithTop.coe_iInf [Nonempty ι] [InfSet α] (f : ι → α) :
     ↑(⨅ i, f i) = (⨅ i, f i : WithTop α) := by
-  rw [infᵢ, infᵢ, WithTop.coe_infₛ' (range_nonempty f), range_comp]
-#align with_top.coe_infi WithTop.coe_infᵢ
+  rw [iInf, iInf, WithTop.coe_sInf' (range_nonempty f), range_comp]
+#align with_top.coe_infi WithTop.coe_iInf
 -/
 
-#print WithTop.coe_supₛ' /-
-theorem WithTop.coe_supₛ' [Preorder α] [SupSet α] {s : Set α} (hs : BddAbove s) :
-    ↑(supₛ s) = (supₛ (coe '' s) : WithTop α) :=
+#print WithTop.coe_sSup' /-
+theorem WithTop.coe_sSup' [Preorder α] [SupSet α] {s : Set α} (hs : BddAbove s) :
+    ↑(sSup s) = (sSup (coe '' s) : WithTop α) :=
   by
   change _ = ite _ _ _
   rw [if_neg, preimage_image_eq, if_pos hs]
   · exact Option.some_injective _
   · rintro ⟨x, h, ⟨⟩⟩
-#align with_top.coe_Sup' WithTop.coe_supₛ'
+#align with_top.coe_Sup' WithTop.coe_sSup'
 -/
 
-/- warning: with_top.coe_supr -> WithTop.coe_supᵢ is a dubious translation:
+/- warning: with_top.coe_supr -> WithTop.coe_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : SupSet.{u1} α] (f : ι -> α), (BddAbove.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) -> (Eq.{succ u1} (WithTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (supᵢ.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (WithTop.{u1} α) (WithTop.hasSup.{u1} α _inst_1 _inst_2) ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : SupSet.{u1} α] (f : ι -> α), (BddAbove.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) -> (Eq.{succ u1} (WithTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (iSup.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (iSup.{u1, u2} (WithTop.{u1} α) (WithTop.hasSup.{u1} α _inst_1 _inst_2) ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : SupSet.{u2} α] (f : ι -> α), (BddAbove.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) -> (Eq.{succ u2} (WithTop.{u2} α) (WithTop.some.{u2} α (supᵢ.{u2, u1} α _inst_2 ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} (WithTop.{u2} α) (instSupSetWithTop.{u2} α _inst_1 _inst_2) ι (fun (i : ι) => WithTop.some.{u2} α (f i))))
-Case conversion may be inaccurate. Consider using '#align with_top.coe_supr WithTop.coe_supᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : SupSet.{u2} α] (f : ι -> α), (BddAbove.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) -> (Eq.{succ u2} (WithTop.{u2} α) (WithTop.some.{u2} α (iSup.{u2, u1} α _inst_2 ι (fun (i : ι) => f i))) (iSup.{u2, u1} (WithTop.{u2} α) (instSupSetWithTop.{u2} α _inst_1 _inst_2) ι (fun (i : ι) => WithTop.some.{u2} α (f i))))
+Case conversion may be inaccurate. Consider using '#align with_top.coe_supr WithTop.coe_iSupₓ'. -/
 @[norm_cast]
-theorem WithTop.coe_supᵢ [Preorder α] [SupSet α] (f : ι → α) (h : BddAbove (Set.range f)) :
-    ↑(⨆ i, f i) = (⨆ i, f i : WithTop α) := by rw [supᵢ, supᵢ, WithTop.coe_supₛ' h, range_comp]
-#align with_top.coe_supr WithTop.coe_supᵢ
+theorem WithTop.coe_iSup [Preorder α] [SupSet α] (f : ι → α) (h : BddAbove (Set.range f)) :
+    ↑(⨆ i, f i) = (⨆ i, f i : WithTop α) := by rw [iSup, iSup, WithTop.coe_sSup' h, range_comp]
+#align with_top.coe_supr WithTop.coe_iSup
 
-/- warning: with_bot.cSup_empty -> WithBot.csupₛ_empty is a dubious translation:
+/- warning: with_bot.cSup_empty -> WithBot.csSup_empty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α], Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.hasEmptyc.{u1} (WithBot.{u1} α)))) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α))
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α], Eq.{succ u1} (WithBot.{u1} α) (SupSet.sSup.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.hasEmptyc.{u1} (WithBot.{u1} α)))) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α], Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.instEmptyCollectionSet.{u1} (WithBot.{u1} α)))) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α))
-Case conversion may be inaccurate. Consider using '#align with_bot.cSup_empty WithBot.csupₛ_emptyₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α], Eq.{succ u1} (WithBot.{u1} α) (SupSet.sSup.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.instEmptyCollectionSet.{u1} (WithBot.{u1} α)))) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α))
+Case conversion may be inaccurate. Consider using '#align with_bot.cSup_empty WithBot.csSup_emptyₓ'. -/
 @[simp]
-theorem WithBot.csupₛ_empty {α : Type _} [SupSet α] : supₛ (∅ : Set (WithBot α)) = ⊥ :=
+theorem WithBot.csSup_empty {α : Type _} [SupSet α] : sSup (∅ : Set (WithBot α)) = ⊥ :=
   if_pos <| Set.empty_subset _
-#align with_bot.cSup_empty WithBot.csupₛ_empty
+#align with_bot.cSup_empty WithBot.csSup_empty
 
-/- warning: with_bot.csupr_empty -> WithBot.csupᵢ_empty is a dubious translation:
+/- warning: with_bot.csupr_empty -> WithBot.ciSup_empty is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : IsEmpty.{u1} ι] [_inst_2 : SupSet.{u2} α] (f : ι -> (WithBot.{u2} α)), Eq.{succ u2} (WithBot.{u2} α) (supᵢ.{u2, u1} (WithBot.{u2} α) (WithBot.hasSup.{u2} α _inst_2) ι (fun (i : ι) => f i)) (Bot.bot.{u2} (WithBot.{u2} α) (WithBot.hasBot.{u2} α))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : IsEmpty.{u1} ι] [_inst_2 : SupSet.{u2} α] (f : ι -> (WithBot.{u2} α)), Eq.{succ u2} (WithBot.{u2} α) (iSup.{u2, u1} (WithBot.{u2} α) (WithBot.hasSup.{u2} α _inst_2) ι (fun (i : ι) => f i)) (Bot.bot.{u2} (WithBot.{u2} α) (WithBot.hasBot.{u2} α))
 but is expected to have type
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : IsEmpty.{u1} ι] [_inst_2 : SupSet.{u2} α] (f : ι -> (WithBot.{u2} α)), Eq.{succ u2} (WithBot.{u2} α) (supᵢ.{u2, u1} (WithBot.{u2} α) (instSupSetWithBot.{u2} α _inst_2) ι (fun (i : ι) => f i)) (Bot.bot.{u2} (WithBot.{u2} α) (WithBot.bot.{u2} α))
-Case conversion may be inaccurate. Consider using '#align with_bot.csupr_empty WithBot.csupᵢ_emptyₓ'. -/
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : IsEmpty.{u1} ι] [_inst_2 : SupSet.{u2} α] (f : ι -> (WithBot.{u2} α)), Eq.{succ u2} (WithBot.{u2} α) (iSup.{u2, u1} (WithBot.{u2} α) (instSupSetWithBot.{u2} α _inst_2) ι (fun (i : ι) => f i)) (Bot.bot.{u2} (WithBot.{u2} α) (WithBot.bot.{u2} α))
+Case conversion may be inaccurate. Consider using '#align with_bot.csupr_empty WithBot.ciSup_emptyₓ'. -/
 @[simp]
-theorem WithBot.csupᵢ_empty {α : Type _} [IsEmpty ι] [SupSet α] (f : ι → WithBot α) :
+theorem WithBot.ciSup_empty {α : Type _} [IsEmpty ι] [SupSet α] (f : ι → WithBot α) :
     (⨆ i, f i) = ⊥ :=
-  @WithTop.infᵢ_empty _ αᵒᵈ _ _ _
-#align with_bot.csupr_empty WithBot.csupᵢ_empty
+  @WithTop.iInf_empty _ αᵒᵈ _ _ _
+#align with_bot.csupr_empty WithBot.ciSup_empty
 
-/- warning: with_bot.coe_Sup' -> WithBot.coe_supₛ' is a dubious translation:
+/- warning: with_bot.coe_Sup' -> WithBot.coe_sSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (SupSet.supₛ.{u1} α _inst_1 s)) (SupSet.supₛ.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) (Set.image.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)))
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (SupSet.sSup.{u1} α _inst_1 s)) (SupSet.sSup.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) (Set.image.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithBot.{u1} α) (WithBot.some.{u1} α (SupSet.supₛ.{u1} α _inst_1 s)) (SupSet.supₛ.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) (Set.image.{u1, u1} α (WithBot.{u1} α) (fun (a : α) => WithBot.some.{u1} α a) s)))
-Case conversion may be inaccurate. Consider using '#align with_bot.coe_Sup' WithBot.coe_supₛ'ₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithBot.{u1} α) (WithBot.some.{u1} α (SupSet.sSup.{u1} α _inst_1 s)) (SupSet.sSup.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) (Set.image.{u1, u1} α (WithBot.{u1} α) (fun (a : α) => WithBot.some.{u1} α a) s)))
+Case conversion may be inaccurate. Consider using '#align with_bot.coe_Sup' WithBot.coe_sSup'ₓ'. -/
 @[norm_cast]
-theorem WithBot.coe_supₛ' [SupSet α] {s : Set α} (hs : s.Nonempty) :
-    ↑(supₛ s) = (supₛ (coe '' s) : WithBot α) :=
-  @WithTop.coe_infₛ' αᵒᵈ _ _ hs
-#align with_bot.coe_Sup' WithBot.coe_supₛ'
+theorem WithBot.coe_sSup' [SupSet α] {s : Set α} (hs : s.Nonempty) :
+    ↑(sSup s) = (sSup (coe '' s) : WithBot α) :=
+  @WithTop.coe_sInf' αᵒᵈ _ _ hs
+#align with_bot.coe_Sup' WithBot.coe_sSup'
 
-/- warning: with_bot.coe_supr -> WithBot.coe_supᵢ is a dubious translation:
+/- warning: with_bot.coe_supr -> WithBot.coe_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : SupSet.{u1} α] (f : ι -> α), Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (supᵢ.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_2) ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : SupSet.{u1} α] (f : ι -> α), Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (iSup.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (iSup.{u1, u2} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_2) ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (f i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : SupSet.{u1} α] (f : ι -> α), Eq.{succ u1} (WithBot.{u1} α) (WithBot.some.{u1} α (supᵢ.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (supᵢ.{u1, u2} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_2) ι (fun (i : ι) => WithBot.some.{u1} α (f i)))
-Case conversion may be inaccurate. Consider using '#align with_bot.coe_supr WithBot.coe_supᵢₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] [_inst_2 : SupSet.{u1} α] (f : ι -> α), Eq.{succ u1} (WithBot.{u1} α) (WithBot.some.{u1} α (iSup.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (iSup.{u1, u2} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_2) ι (fun (i : ι) => WithBot.some.{u1} α (f i)))
+Case conversion may be inaccurate. Consider using '#align with_bot.coe_supr WithBot.coe_iSupₓ'. -/
 @[norm_cast]
-theorem WithBot.coe_supᵢ [Nonempty ι] [SupSet α] (f : ι → α) :
+theorem WithBot.coe_iSup [Nonempty ι] [SupSet α] (f : ι → α) :
     ↑(⨆ i, f i) = (⨆ i, f i : WithBot α) :=
-  @WithTop.coe_infᵢ αᵒᵈ _ _ _ _
-#align with_bot.coe_supr WithBot.coe_supᵢ
+  @WithTop.coe_iInf αᵒᵈ _ _ _ _
+#align with_bot.coe_supr WithBot.coe_iSup
 
-/- warning: with_bot.coe_Inf' -> WithBot.coe_infₛ' is a dubious translation:
+/- warning: with_bot.coe_Inf' -> WithBot.coe_sInf' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α _inst_1 s) -> (Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (InfSet.infₛ.{u1} α _inst_2 s)) (InfSet.infₛ.{u1} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) (Set.image.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)))
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α _inst_1 s) -> (Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (InfSet.sInf.{u1} α _inst_2 s)) (InfSet.sInf.{u1} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) (Set.image.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α _inst_1 s) -> (Eq.{succ u1} (WithBot.{u1} α) (WithBot.some.{u1} α (InfSet.infₛ.{u1} α _inst_2 s)) (InfSet.infₛ.{u1} (WithBot.{u1} α) (instInfSetWithBot.{u1} α _inst_1 _inst_2) (Set.image.{u1, u1} α (WithBot.{u1} α) (fun (a : α) => WithBot.some.{u1} α a) s)))
-Case conversion may be inaccurate. Consider using '#align with_bot.coe_Inf' WithBot.coe_infₛ'ₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α _inst_1 s) -> (Eq.{succ u1} (WithBot.{u1} α) (WithBot.some.{u1} α (InfSet.sInf.{u1} α _inst_2 s)) (InfSet.sInf.{u1} (WithBot.{u1} α) (instInfSetWithBot.{u1} α _inst_1 _inst_2) (Set.image.{u1, u1} α (WithBot.{u1} α) (fun (a : α) => WithBot.some.{u1} α a) s)))
+Case conversion may be inaccurate. Consider using '#align with_bot.coe_Inf' WithBot.coe_sInf'ₓ'. -/
 @[norm_cast]
-theorem WithBot.coe_infₛ' [Preorder α] [InfSet α] {s : Set α} (hs : BddBelow s) :
-    ↑(infₛ s) = (infₛ (coe '' s) : WithBot α) :=
-  @WithTop.coe_supₛ' αᵒᵈ _ _ _ hs
-#align with_bot.coe_Inf' WithBot.coe_infₛ'
+theorem WithBot.coe_sInf' [Preorder α] [InfSet α] {s : Set α} (hs : BddBelow s) :
+    ↑(sInf s) = (sInf (coe '' s) : WithBot α) :=
+  @WithTop.coe_sSup' αᵒᵈ _ _ _ hs
+#align with_bot.coe_Inf' WithBot.coe_sInf'
 
-/- warning: with_bot.coe_infi -> WithBot.coe_infᵢ is a dubious translation:
+/- warning: with_bot.coe_infi -> WithBot.coe_iInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] (f : ι -> α), (BddBelow.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) -> (Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (infᵢ.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (infᵢ.{u1, u2} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (f i))))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] (f : ι -> α), (BddBelow.{u1} α _inst_1 (Set.range.{u1, u2} α ι f)) -> (Eq.{succ u1} (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (iInf.{u1, u2} α _inst_2 ι (fun (i : ι) => f i))) (iInf.{u1, u2} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) ι (fun (i : ι) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (f i))))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : InfSet.{u2} α] (f : ι -> α), (BddBelow.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) -> (Eq.{succ u2} (WithBot.{u2} α) (WithBot.some.{u2} α (infᵢ.{u2, u1} α _inst_2 ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} (WithBot.{u2} α) (instInfSetWithBot.{u2} α _inst_1 _inst_2) ι (fun (i : ι) => WithBot.some.{u2} α (f i))))
-Case conversion may be inaccurate. Consider using '#align with_bot.coe_infi WithBot.coe_infᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : InfSet.{u2} α] (f : ι -> α), (BddBelow.{u2} α _inst_1 (Set.range.{u2, u1} α ι f)) -> (Eq.{succ u2} (WithBot.{u2} α) (WithBot.some.{u2} α (iInf.{u2, u1} α _inst_2 ι (fun (i : ι) => f i))) (iInf.{u2, u1} (WithBot.{u2} α) (instInfSetWithBot.{u2} α _inst_1 _inst_2) ι (fun (i : ι) => WithBot.some.{u2} α (f i))))
+Case conversion may be inaccurate. Consider using '#align with_bot.coe_infi WithBot.coe_iInfₓ'. -/
 @[norm_cast]
-theorem WithBot.coe_infᵢ [Preorder α] [InfSet α] (f : ι → α) (h : BddBelow (Set.range f)) :
+theorem WithBot.coe_iInf [Preorder α] [InfSet α] (f : ι → α) (h : BddBelow (Set.range f)) :
     ↑(⨅ i, f i) = (⨅ i, f i : WithBot α) :=
-  @WithTop.coe_supᵢ αᵒᵈ _ _ _ _ h
-#align with_bot.coe_infi WithBot.coe_infᵢ
+  @WithTop.coe_iSup αᵒᵈ _ _ _ _ h
+#align with_bot.coe_infi WithBot.coe_iInf
 
 end
 
@@ -276,7 +276,7 @@ boundedness.-/
 class ConditionallyCompleteLinearOrderBot (α : Type _) extends ConditionallyCompleteLinearOrder α,
   Bot α where
   bot_le : ∀ x : α, ⊥ ≤ x
-  csupₛ_empty : Sup ∅ = ⊥
+  csSup_empty : Sup ∅ = ⊥
 #align conditionally_complete_linear_order_bot ConditionallyCompleteLinearOrderBot
 -/
 
@@ -297,10 +297,10 @@ instance (priority := 100) CompleteLattice.toConditionallyCompleteLattice [Compl
   {
     ‹CompleteLattice
         α› with
-    le_cSup := by intros <;> apply le_supₛ <;> assumption
-    cSup_le := by intros <;> apply supₛ_le <;> assumption
-    cInf_le := by intros <;> apply infₛ_le <;> assumption
-    le_cInf := by intros <;> apply le_infₛ <;> assumption }
+    le_cSup := by intros <;> apply le_sSup <;> assumption
+    cSup_le := by intros <;> apply sSup_le <;> assumption
+    cInf_le := by intros <;> apply sInf_le <;> assumption
+    le_cInf := by intros <;> apply le_sInf <;> assumption }
 #align complete_lattice.to_conditionally_complete_lattice CompleteLattice.toConditionallyCompleteLattice
 -/
 
@@ -309,7 +309,7 @@ instance (priority := 100) CompleteLattice.toConditionallyCompleteLattice [Compl
 instance (priority := 100) CompleteLinearOrder.toConditionallyCompleteLinearOrderBot {α : Type _}
     [CompleteLinearOrder α] : ConditionallyCompleteLinearOrderBot α :=
   { CompleteLattice.toConditionallyCompleteLattice, ‹CompleteLinearOrder α› with
-    csupₛ_empty := supₛ_empty }
+    csSup_empty := sSup_empty }
 #align complete_linear_order.to_conditionally_complete_linear_order_bot CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
 -/
 
@@ -324,14 +324,14 @@ noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _)
     [i₂ : OrderBot α] [h : IsWellOrder α (· < ·)] : ConditionallyCompleteLinearOrderBot α :=
   { i₁, i₂,
     LinearOrder.toLattice with
-    infₛ := fun s => if hs : s.Nonempty then h.wf.min s hs else ⊥
+    sInf := fun s => if hs : s.Nonempty then h.wf.min s hs else ⊥
     cInf_le := fun s a hs has => by
       have s_ne : s.nonempty := ⟨a, has⟩
       simpa [s_ne] using not_lt.1 (h.wf.not_lt_min s s_ne has)
     le_cInf := fun s a hs has => by
       simp only [hs, dif_pos]
       exact has (h.wf.min_mem s hs)
-    supₛ := fun s => if hs : (upperBounds s).Nonempty then h.wf.min _ hs else ⊥
+    sSup := fun s => if hs : (upperBounds s).Nonempty then h.wf.min _ hs else ⊥
     le_cSup := fun s a hs has =>
       by
       have h's : (upperBounds s).Nonempty := hs
@@ -342,7 +342,7 @@ noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _)
       have h's : (upperBounds s).Nonempty := ⟨a, has⟩
       simp only [h's, dif_pos]
       simpa using h.wf.not_lt_min _ h's has
-    csupₛ_empty := by simpa using eq_bot_iff.2 (not_lt.1 <| h.wf.not_lt_min _ _ <| mem_univ ⊥) }
+    csSup_empty := by simpa using eq_bot_iff.2 (not_lt.1 <| h.wf.not_lt_min _ _ <| mem_univ ⊥) }
 #align is_well_order.conditionally_complete_linear_order_bot IsWellOrder.conditionallyCompleteLinearOrderBot
 -/
 
@@ -364,7 +364,7 @@ instance (α : Type _) [ConditionallyCompleteLinearOrder α] : ConditionallyComp
 
 end OrderDual
 
-#print conditionallyCompleteLatticeOfSupₛ /-
+#print conditionallyCompleteLatticeOfsSup /-
 /-- Create a `conditionally_complete_lattice` from a `partial_order` and `Sup` function
 that returns the least upper bound of a nonempty set which is bounded above. Usually this
 constructor provides poor definitional equalities.  If other fields are known explicitly, they
@@ -380,44 +380,44 @@ instance : conditionally_complete_lattice my_T :=
   ..conditionally_complete_lattice_of_Sup my_T _ }
 ```
 -/
-def conditionallyCompleteLatticeOfSupₛ (α : Type _) [H1 : PartialOrder α] [H2 : SupSet α]
+def conditionallyCompleteLatticeOfsSup (α : Type _) [H1 : PartialOrder α] [H2 : SupSet α]
     (bdd_above_pair : ∀ a b : α, BddAbove ({a, b} : Set α))
     (bdd_below_pair : ∀ a b : α, BddBelow ({a, b} : Set α))
-    (is_lub_Sup : ∀ s : Set α, BddAbove s → s.Nonempty → IsLUB s (supₛ s)) :
+    (is_lub_Sup : ∀ s : Set α, BddAbove s → s.Nonempty → IsLUB s (sSup s)) :
     ConditionallyCompleteLattice α :=
   { H1, H2 with
-    sup := fun a b => supₛ {a, b}
+    sup := fun a b => sSup {a, b}
     le_sup_left := fun a b =>
-      (isLUB_supₛ {a, b} (bdd_above_pair a b) (insert_nonempty _ _)).1 (mem_insert _ _)
+      (isLUB_sSup {a, b} (bdd_above_pair a b) (insert_nonempty _ _)).1 (mem_insert _ _)
     le_sup_right := fun a b =>
-      (isLUB_supₛ {a, b} (bdd_above_pair a b) (insert_nonempty _ _)).1
+      (isLUB_sSup {a, b} (bdd_above_pair a b) (insert_nonempty _ _)).1
         (mem_insert_of_mem _ (mem_singleton _))
     sup_le := fun a b c hac hbc =>
-      (isLUB_supₛ {a, b} (bdd_above_pair a b) (insert_nonempty _ _)).2
+      (isLUB_sSup {a, b} (bdd_above_pair a b) (insert_nonempty _ _)).2
         (forall_insert_of_forall (forall_eq.mpr hbc) hac)
-    inf := fun a b => supₛ (lowerBounds {a, b})
+    inf := fun a b => sSup (lowerBounds {a, b})
     inf_le_left := fun a b =>
-      (isLUB_supₛ (lowerBounds {a, b}) (Nonempty.bddAbove_lowerBounds ⟨a, mem_insert _ _⟩)
+      (isLUB_sSup (lowerBounds {a, b}) (Nonempty.bddAbove_lowerBounds ⟨a, mem_insert _ _⟩)
             (bdd_below_pair a b)).2
         fun c hc => hc <| mem_insert _ _
     inf_le_right := fun a b =>
-      (isLUB_supₛ (lowerBounds {a, b}) (Nonempty.bddAbove_lowerBounds ⟨a, mem_insert _ _⟩)
+      (isLUB_sSup (lowerBounds {a, b}) (Nonempty.bddAbove_lowerBounds ⟨a, mem_insert _ _⟩)
             (bdd_below_pair a b)).2
         fun c hc => hc <| mem_insert_of_mem _ (mem_singleton _)
     le_inf := fun c a b hca hcb =>
-      (isLUB_supₛ (lowerBounds {a, b}) (Nonempty.bddAbove_lowerBounds ⟨a, mem_insert _ _⟩)
+      (isLUB_sSup (lowerBounds {a, b}) (Nonempty.bddAbove_lowerBounds ⟨a, mem_insert _ _⟩)
             ⟨c, forall_insert_of_forall (forall_eq.mpr hcb) hca⟩).1
         (forall_insert_of_forall (forall_eq.mpr hcb) hca)
-    infₛ := fun s => supₛ (lowerBounds s)
-    cSup_le := fun s a hs ha => (isLUB_supₛ s ⟨a, ha⟩ hs).2 ha
-    le_cSup := fun s a hs ha => (isLUB_supₛ s hs ⟨a, ha⟩).1 ha
+    sInf := fun s => sSup (lowerBounds s)
+    cSup_le := fun s a hs ha => (isLUB_sSup s ⟨a, ha⟩ hs).2 ha
+    le_cSup := fun s a hs ha => (isLUB_sSup s hs ⟨a, ha⟩).1 ha
     cInf_le := fun s a hs ha =>
-      (isLUB_supₛ (lowerBounds s) (Nonempty.bddAbove_lowerBounds ⟨a, ha⟩) hs).2 fun b hb => hb ha
-    le_cInf := fun s a hs ha => (isLUB_supₛ (lowerBounds s) hs.bddAbove_lowerBounds ⟨a, ha⟩).1 ha }
-#align conditionally_complete_lattice_of_Sup conditionallyCompleteLatticeOfSupₛ
+      (isLUB_sSup (lowerBounds s) (Nonempty.bddAbove_lowerBounds ⟨a, ha⟩) hs).2 fun b hb => hb ha
+    le_cInf := fun s a hs ha => (isLUB_sSup (lowerBounds s) hs.bddAbove_lowerBounds ⟨a, ha⟩).1 ha }
+#align conditionally_complete_lattice_of_Sup conditionallyCompleteLatticeOfsSup
 -/
 
-#print conditionallyCompleteLatticeOfInfₛ /-
+#print conditionallyCompleteLatticeOfsInf /-
 /-- Create a `conditionally_complete_lattice_of_Inf` from a `partial_order` and `Inf` function
 that returns the greatest lower bound of a nonempty set which is bounded below. Usually this
 constructor provides poor definitional equalities.  If other fields are known explicitly, they
@@ -433,522 +433,522 @@ instance : conditionally_complete_lattice my_T :=
   ..conditionally_complete_lattice_of_Inf my_T _ }
 ```
 -/
-def conditionallyCompleteLatticeOfInfₛ (α : Type _) [H1 : PartialOrder α] [H2 : InfSet α]
+def conditionallyCompleteLatticeOfsInf (α : Type _) [H1 : PartialOrder α] [H2 : InfSet α]
     (bdd_above_pair : ∀ a b : α, BddAbove ({a, b} : Set α))
     (bdd_below_pair : ∀ a b : α, BddBelow ({a, b} : Set α))
-    (is_glb_Inf : ∀ s : Set α, BddBelow s → s.Nonempty → IsGLB s (infₛ s)) :
+    (is_glb_Inf : ∀ s : Set α, BddBelow s → s.Nonempty → IsGLB s (sInf s)) :
     ConditionallyCompleteLattice α :=
   { H1, H2 with
-    inf := fun a b => infₛ {a, b}
+    inf := fun a b => sInf {a, b}
     inf_le_left := fun a b =>
-      (isGLB_infₛ {a, b} (bdd_below_pair a b) (insert_nonempty _ _)).1 (mem_insert _ _)
+      (isGLB_sInf {a, b} (bdd_below_pair a b) (insert_nonempty _ _)).1 (mem_insert _ _)
     inf_le_right := fun a b =>
-      (isGLB_infₛ {a, b} (bdd_below_pair a b) (insert_nonempty _ _)).1
+      (isGLB_sInf {a, b} (bdd_below_pair a b) (insert_nonempty _ _)).1
         (mem_insert_of_mem _ (mem_singleton _))
     le_inf := fun c a b hca hcb =>
-      (isGLB_infₛ {a, b} (bdd_below_pair a b) (insert_nonempty _ _)).2
+      (isGLB_sInf {a, b} (bdd_below_pair a b) (insert_nonempty _ _)).2
         (forall_insert_of_forall (forall_eq.mpr hcb) hca)
-    sup := fun a b => infₛ (upperBounds {a, b})
+    sup := fun a b => sInf (upperBounds {a, b})
     le_sup_left := fun a b =>
-      (isGLB_infₛ (upperBounds {a, b}) (Nonempty.bddBelow_upperBounds ⟨a, mem_insert _ _⟩)
+      (isGLB_sInf (upperBounds {a, b}) (Nonempty.bddBelow_upperBounds ⟨a, mem_insert _ _⟩)
             (bdd_above_pair a b)).2
         fun c hc => hc <| mem_insert _ _
     le_sup_right := fun a b =>
-      (isGLB_infₛ (upperBounds {a, b}) (Nonempty.bddBelow_upperBounds ⟨a, mem_insert _ _⟩)
+      (isGLB_sInf (upperBounds {a, b}) (Nonempty.bddBelow_upperBounds ⟨a, mem_insert _ _⟩)
             (bdd_above_pair a b)).2
         fun c hc => hc <| mem_insert_of_mem _ (mem_singleton _)
     sup_le := fun a b c hac hbc =>
-      (isGLB_infₛ (upperBounds {a, b}) (Nonempty.bddBelow_upperBounds ⟨a, mem_insert _ _⟩)
+      (isGLB_sInf (upperBounds {a, b}) (Nonempty.bddBelow_upperBounds ⟨a, mem_insert _ _⟩)
             ⟨c, forall_insert_of_forall (forall_eq.mpr hbc) hac⟩).1
         (forall_insert_of_forall (forall_eq.mpr hbc) hac)
-    supₛ := fun s => infₛ (upperBounds s)
-    le_cInf := fun s a hs ha => (isGLB_infₛ s ⟨a, ha⟩ hs).2 ha
-    cInf_le := fun s a hs ha => (isGLB_infₛ s hs ⟨a, ha⟩).1 ha
+    sSup := fun s => sInf (upperBounds s)
+    le_cInf := fun s a hs ha => (isGLB_sInf s ⟨a, ha⟩ hs).2 ha
+    cInf_le := fun s a hs ha => (isGLB_sInf s hs ⟨a, ha⟩).1 ha
     le_cSup := fun s a hs ha =>
-      (isGLB_infₛ (upperBounds s) (Nonempty.bddBelow_upperBounds ⟨a, ha⟩) hs).2 fun b hb => hb ha
-    cSup_le := fun s a hs ha => (isGLB_infₛ (upperBounds s) hs.bddBelow_upperBounds ⟨a, ha⟩).1 ha }
-#align conditionally_complete_lattice_of_Inf conditionallyCompleteLatticeOfInfₛ
+      (isGLB_sInf (upperBounds s) (Nonempty.bddBelow_upperBounds ⟨a, ha⟩) hs).2 fun b hb => hb ha
+    cSup_le := fun s a hs ha => (isGLB_sInf (upperBounds s) hs.bddBelow_upperBounds ⟨a, ha⟩).1 ha }
+#align conditionally_complete_lattice_of_Inf conditionallyCompleteLatticeOfsInf
 -/
 
-#print conditionallyCompleteLatticeOfLatticeOfSupₛ /-
+#print conditionallyCompleteLatticeOfLatticeOfsSup /-
 /-- A version of `conditionally_complete_lattice_of_Sup` when we already know that `α` is a lattice.
 
 This should only be used when it is both hard and unnecessary to provide `Inf` explicitly. -/
-def conditionallyCompleteLatticeOfLatticeOfSupₛ (α : Type _) [H1 : Lattice α] [H2 : SupSet α]
-    (is_lub_Sup : ∀ s : Set α, BddAbove s → s.Nonempty → IsLUB s (supₛ s)) :
+def conditionallyCompleteLatticeOfLatticeOfsSup (α : Type _) [H1 : Lattice α] [H2 : SupSet α]
+    (is_lub_Sup : ∀ s : Set α, BddAbove s → s.Nonempty → IsLUB s (sSup s)) :
     ConditionallyCompleteLattice α :=
   { H1,
-    conditionallyCompleteLatticeOfSupₛ α
+    conditionallyCompleteLatticeOfsSup α
       (fun a b => ⟨a ⊔ b, forall_insert_of_forall (forall_eq.mpr le_sup_right) le_sup_left⟩)
       (fun a b => ⟨a ⊓ b, forall_insert_of_forall (forall_eq.mpr inf_le_right) inf_le_left⟩)
-      isLUB_supₛ with }
-#align conditionally_complete_lattice_of_lattice_of_Sup conditionallyCompleteLatticeOfLatticeOfSupₛ
+      isLUB_sSup with }
+#align conditionally_complete_lattice_of_lattice_of_Sup conditionallyCompleteLatticeOfLatticeOfsSup
 -/
 
-#print conditionallyCompleteLatticeOfLatticeOfInfₛ /-
+#print conditionallyCompleteLatticeOfLatticeOfsInf /-
 /-- A version of `conditionally_complete_lattice_of_Inf` when we already know that `α` is a lattice.
 
 This should only be used when it is both hard and unnecessary to provide `Sup` explicitly. -/
-def conditionallyCompleteLatticeOfLatticeOfInfₛ (α : Type _) [H1 : Lattice α] [H2 : InfSet α]
-    (is_glb_Inf : ∀ s : Set α, BddBelow s → s.Nonempty → IsGLB s (infₛ s)) :
+def conditionallyCompleteLatticeOfLatticeOfsInf (α : Type _) [H1 : Lattice α] [H2 : InfSet α]
+    (is_glb_Inf : ∀ s : Set α, BddBelow s → s.Nonempty → IsGLB s (sInf s)) :
     ConditionallyCompleteLattice α :=
   { H1,
-    conditionallyCompleteLatticeOfInfₛ α
+    conditionallyCompleteLatticeOfsInf α
       (fun a b => ⟨a ⊔ b, forall_insert_of_forall (forall_eq.mpr le_sup_right) le_sup_left⟩)
       (fun a b => ⟨a ⊓ b, forall_insert_of_forall (forall_eq.mpr inf_le_right) inf_le_left⟩)
-      isGLB_infₛ with }
-#align conditionally_complete_lattice_of_lattice_of_Inf conditionallyCompleteLatticeOfLatticeOfInfₛ
+      isGLB_sInf with }
+#align conditionally_complete_lattice_of_lattice_of_Inf conditionallyCompleteLatticeOfLatticeOfsInf
 -/
 
 section ConditionallyCompleteLattice
 
 variable [ConditionallyCompleteLattice α] {s t : Set α} {a b : α}
 
-/- warning: le_cSup -> le_csupₛ is a dubious translation:
+/- warning: le_cSup -> le_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align le_cSup le_csupₛₓ'. -/
-theorem le_csupₛ (h₁ : BddAbove s) (h₂ : a ∈ s) : a ≤ supₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align le_cSup le_csSupₓ'. -/
+theorem le_csSup (h₁ : BddAbove s) (h₂ : a ∈ s) : a ≤ sSup s :=
   ConditionallyCompleteLattice.le_cSup s a h₁ h₂
-#align le_cSup le_csupₛ
+#align le_cSup le_csSup
 
-/- warning: cSup_le -> csupₛ_le is a dubious translation:
+/- warning: cSup_le -> csSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align cSup_le csupₛ_leₓ'. -/
-theorem csupₛ_le (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, b ≤ a) : supₛ s ≤ a :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align cSup_le csSup_leₓ'. -/
+theorem csSup_le (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, b ≤ a) : sSup s ≤ a :=
   ConditionallyCompleteLattice.cSup_le s a h₁ h₂
-#align cSup_le csupₛ_le
+#align cSup_le csSup_le
 
-/- warning: cInf_le -> cinfₛ_le is a dubious translation:
+/- warning: cInf_le -> csInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align cInf_le cinfₛ_leₓ'. -/
-theorem cinfₛ_le (h₁ : BddBelow s) (h₂ : a ∈ s) : infₛ s ≤ a :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align cInf_le csInf_leₓ'. -/
+theorem csInf_le (h₁ : BddBelow s) (h₂ : a ∈ s) : sInf s ≤ a :=
   ConditionallyCompleteLattice.cInf_le s a h₁ h₂
-#align cInf_le cinfₛ_le
+#align cInf_le csInf_le
 
-/- warning: le_cInf -> le_cinfₛ is a dubious translation:
+/- warning: le_cInf -> le_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align le_cInf le_cinfₛₓ'. -/
-theorem le_cinfₛ (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, a ≤ b) : a ≤ infₛ s :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align le_cInf le_csInfₓ'. -/
+theorem le_csInf (h₁ : s.Nonempty) (h₂ : ∀ b ∈ s, a ≤ b) : a ≤ sInf s :=
   ConditionallyCompleteLattice.le_cInf s a h₁ h₂
-#align le_cInf le_cinfₛ
+#align le_cInf le_csInf
 
-/- warning: le_cSup_of_le -> le_csupₛ_of_le is a dubious translation:
+/- warning: le_cSup_of_le -> le_csSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align le_cSup_of_le le_csupₛ_of_leₓ'. -/
-theorem le_csupₛ_of_le (hs : BddAbove s) (hb : b ∈ s) (h : a ≤ b) : a ≤ supₛ s :=
-  le_trans h (le_csupₛ hs hb)
-#align le_cSup_of_le le_csupₛ_of_le
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align le_cSup_of_le le_csSup_of_leₓ'. -/
+theorem le_csSup_of_le (hs : BddAbove s) (hb : b ∈ s) (h : a ≤ b) : a ≤ sSup s :=
+  le_trans h (le_csSup hs hb)
+#align le_cSup_of_le le_csSup_of_le
 
-/- warning: cInf_le_of_le -> cinfₛ_le_of_le is a dubious translation:
+/- warning: cInf_le_of_le -> csInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align cInf_le_of_le cinfₛ_le_of_leₓ'. -/
-theorem cinfₛ_le_of_le (hs : BddBelow s) (hb : b ∈ s) (h : b ≤ a) : infₛ s ≤ a :=
-  le_trans (cinfₛ_le hs hb) h
-#align cInf_le_of_le cinfₛ_le_of_le
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align cInf_le_of_le csInf_le_of_leₓ'. -/
+theorem csInf_le_of_le (hs : BddBelow s) (hb : b ∈ s) (h : b ≤ a) : sInf s ≤ a :=
+  le_trans (csInf_le hs hb) h
+#align cInf_le_of_le csInf_le_of_le
 
-/- warning: cSup_le_cSup -> csupₛ_le_csupₛ is a dubious translation:
+/- warning: cSup_le_cSup -> csSup_le_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t))
-Case conversion may be inaccurate. Consider using '#align cSup_le_cSup csupₛ_le_csupₛₓ'. -/
-theorem csupₛ_le_csupₛ (ht : BddAbove t) (hs : s.Nonempty) (h : s ⊆ t) : supₛ s ≤ supₛ t :=
-  csupₛ_le hs fun a ha => le_csupₛ ht (h ha)
-#align cSup_le_cSup csupₛ_le_csupₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t))
+Case conversion may be inaccurate. Consider using '#align cSup_le_cSup csSup_le_csSupₓ'. -/
+theorem csSup_le_csSup (ht : BddAbove t) (hs : s.Nonempty) (h : s ⊆ t) : sSup s ≤ sSup t :=
+  csSup_le hs fun a ha => le_csSup ht (h ha)
+#align cSup_le_cSup csSup_le_csSup
 
-/- warning: cInf_le_cInf -> cinfₛ_le_cinfₛ is a dubious translation:
+/- warning: cInf_le_cInf -> csInf_le_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align cInf_le_cInf cinfₛ_le_cinfₛₓ'. -/
-theorem cinfₛ_le_cinfₛ (ht : BddBelow t) (hs : s.Nonempty) (h : s ⊆ t) : infₛ t ≤ infₛ s :=
-  le_cinfₛ hs fun a ha => cinfₛ_le ht (h ha)
-#align cInf_le_cInf cinfₛ_le_cinfₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align cInf_le_cInf csInf_le_csInfₓ'. -/
+theorem csInf_le_csInf (ht : BddBelow t) (hs : s.Nonempty) (h : s ⊆ t) : sInf t ≤ sInf s :=
+  le_csInf hs fun a ha => csInf_le ht (h ha)
+#align cInf_le_cInf csInf_le_csInf
 
-/- warning: le_cSup_iff -> le_csupₛ_iff is a dubious translation:
+/- warning: le_cSup_iff -> le_csSup_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
-Case conversion may be inaccurate. Consider using '#align le_cSup_iff le_csupₛ_iffₓ'. -/
-theorem le_csupₛ_iff (h : BddAbove s) (hs : s.Nonempty) :
-    a ≤ supₛ s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
-  ⟨fun h b hb => le_trans h (csupₛ_le hs hb), fun hb => hb _ fun x => le_csupₛ h⟩
-#align le_cSup_iff le_csupₛ_iff
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
+Case conversion may be inaccurate. Consider using '#align le_cSup_iff le_csSup_iffₓ'. -/
+theorem le_csSup_iff (h : BddAbove s) (hs : s.Nonempty) :
+    a ≤ sSup s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
+  ⟨fun h b hb => le_trans h (csSup_le hs hb), fun hb => hb _ fun x => le_csSup h⟩
+#align le_cSup_iff le_csSup_iff
 
-/- warning: cInf_le_iff -> cinfₛ_le_iff is a dubious translation:
+/- warning: cInf_le_iff -> csInf_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
-Case conversion may be inaccurate. Consider using '#align cInf_le_iff cinfₛ_le_iffₓ'. -/
-theorem cinfₛ_le_iff (h : BddBelow s) (hs : s.Nonempty) : infₛ s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
-  ⟨fun h b hb => le_trans (le_cinfₛ hs hb) h, fun hb => hb _ fun x => cinfₛ_le h⟩
-#align cInf_le_iff cinfₛ_le_iff
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
+Case conversion may be inaccurate. Consider using '#align cInf_le_iff csInf_le_iffₓ'. -/
+theorem csInf_le_iff (h : BddBelow s) (hs : s.Nonempty) : sInf s ≤ a ↔ ∀ b ∈ lowerBounds s, b ≤ a :=
+  ⟨fun h b hb => le_trans (le_csInf hs hb) h, fun hb => hb _ fun x => csInf_le h⟩
+#align cInf_le_iff csInf_le_iff
 
-/- warning: is_lub_cSup -> isLUB_csupₛ is a dubious translation:
+/- warning: is_lub_cSup -> isLUB_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align is_lub_cSup isLUB_csupₛₓ'. -/
-theorem isLUB_csupₛ (ne : s.Nonempty) (H : BddAbove s) : IsLUB s (supₛ s) :=
-  ⟨fun x => le_csupₛ H, fun x => csupₛ_le Ne⟩
-#align is_lub_cSup isLUB_csupₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align is_lub_cSup isLUB_csSupₓ'. -/
+theorem isLUB_csSup (ne : s.Nonempty) (H : BddAbove s) : IsLUB s (sSup s) :=
+  ⟨fun x => le_csSup H, fun x => csSup_le Ne⟩
+#align is_lub_cSup isLUB_csSup
 
-/- warning: is_lub_csupr -> isLUB_csupᵢ is a dubious translation:
+/- warning: is_lub_csupr -> isLUB_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_lub_csupr isLUB_csupᵢₓ'. -/
-theorem isLUB_csupᵢ [Nonempty ι] {f : ι → α} (H : BddAbove (range f)) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align is_lub_csupr isLUB_ciSupₓ'. -/
+theorem isLUB_ciSup [Nonempty ι] {f : ι → α} (H : BddAbove (range f)) :
     IsLUB (range f) (⨆ i, f i) :=
-  isLUB_csupₛ (range_nonempty f) H
-#align is_lub_csupr isLUB_csupᵢ
+  isLUB_csSup (range_nonempty f) H
+#align is_lub_csupr isLUB_ciSup
 
-/- warning: is_lub_csupr_set -> isLUB_csupᵢ_set is a dubious translation:
+/- warning: is_lub_csupr_set -> isLUB_ciSup_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))))
-Case conversion may be inaccurate. Consider using '#align is_lub_csupr_set isLUB_csupᵢ_setₓ'. -/
-theorem isLUB_csupᵢ_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) (Hne : s.Nonempty) :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))))
+Case conversion may be inaccurate. Consider using '#align is_lub_csupr_set isLUB_ciSup_setₓ'. -/
+theorem isLUB_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) (Hne : s.Nonempty) :
     IsLUB (f '' s) (⨆ i : s, f i) := by
-  rw [← supₛ_image']
-  exact isLUB_csupₛ (Hne.image _) H
-#align is_lub_csupr_set isLUB_csupᵢ_set
+  rw [← sSup_image']
+  exact isLUB_csSup (Hne.image _) H
+#align is_lub_csupr_set isLUB_ciSup_set
 
-/- warning: is_glb_cInf -> isGLB_cinfₛ is a dubious translation:
+/- warning: is_glb_cInf -> isGLB_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align is_glb_cInf isGLB_cinfₛₓ'. -/
-theorem isGLB_cinfₛ (ne : s.Nonempty) (H : BddBelow s) : IsGLB s (infₛ s) :=
-  ⟨fun x => cinfₛ_le H, fun x => le_cinfₛ Ne⟩
-#align is_glb_cInf isGLB_cinfₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align is_glb_cInf isGLB_csInfₓ'. -/
+theorem isGLB_csInf (ne : s.Nonempty) (H : BddBelow s) : IsGLB s (sInf s) :=
+  ⟨fun x => csInf_le H, fun x => le_csInf Ne⟩
+#align is_glb_cInf isGLB_csInf
 
-/- warning: is_glb_cinfi -> isGLB_cinfᵢ is a dubious translation:
+/- warning: is_glb_cinfi -> isGLB_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => f i)))
-Case conversion may be inaccurate. Consider using '#align is_glb_cinfi isGLB_cinfᵢₓ'. -/
-theorem isGLB_cinfᵢ [Nonempty ι] {f : ι → α} (H : BddBelow (range f)) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => f i)))
+Case conversion may be inaccurate. Consider using '#align is_glb_cinfi isGLB_ciInfₓ'. -/
+theorem isGLB_ciInf [Nonempty ι] {f : ι → α} (H : BddBelow (range f)) :
     IsGLB (range f) (⨅ i, f i) :=
-  isGLB_cinfₛ (range_nonempty f) H
-#align is_glb_cinfi isGLB_cinfᵢ
+  isGLB_csInf (range_nonempty f) H
+#align is_glb_cinfi isGLB_ciInf
 
-/- warning: is_glb_cinfi_set -> isGLB_cinfᵢ_set is a dubious translation:
+/- warning: is_glb_cinfi_set -> isGLB_ciInf_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))))
-Case conversion may be inaccurate. Consider using '#align is_glb_cinfi_set isGLB_cinfᵢ_setₓ'. -/
-theorem isGLB_cinfᵢ_set {f : β → α} {s : Set β} (H : BddBelow (f '' s)) (Hne : s.Nonempty) :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (Set.Nonempty.{u2} β s) -> (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))))
+Case conversion may be inaccurate. Consider using '#align is_glb_cinfi_set isGLB_ciInf_setₓ'. -/
+theorem isGLB_ciInf_set {f : β → α} {s : Set β} (H : BddBelow (f '' s)) (Hne : s.Nonempty) :
     IsGLB (f '' s) (⨅ i : s, f i) :=
-  @isLUB_csupᵢ_set αᵒᵈ _ _ _ _ H Hne
-#align is_glb_cinfi_set isGLB_cinfᵢ_set
+  @isLUB_ciSup_set αᵒᵈ _ _ _ _ H Hne
+#align is_glb_cinfi_set isGLB_ciInf_set
 
-/- warning: csupr_le_iff -> csupᵢ_le_iff is a dubious translation:
+/- warning: csupr_le_iff -> ciSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a))
-Case conversion may be inaccurate. Consider using '#align csupr_le_iff csupᵢ_le_iffₓ'. -/
-theorem csupᵢ_le_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddAbove (range f)) :
-    supᵢ f ≤ a ↔ ∀ i, f i ≤ a :=
-  (isLUB_le_iff <| isLUB_csupᵢ hf).trans forall_range_iff
-#align csupr_le_iff csupᵢ_le_iff
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι f) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a))
+Case conversion may be inaccurate. Consider using '#align csupr_le_iff ciSup_le_iffₓ'. -/
+theorem ciSup_le_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddAbove (range f)) :
+    iSup f ≤ a ↔ ∀ i, f i ≤ a :=
+  (isLUB_le_iff <| isLUB_ciSup hf).trans forall_range_iff
+#align csupr_le_iff ciSup_le_iff
 
-/- warning: le_cinfi_iff -> le_cinfᵢ_iff is a dubious translation:
+/- warning: le_cinfi_iff -> le_ciInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i)))
-Case conversion may be inaccurate. Consider using '#align le_cinfi_iff le_cinfᵢ_iffₓ'. -/
-theorem le_cinfᵢ_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddBelow (range f)) :
-    a ≤ infᵢ f ↔ ∀ i, a ≤ f i :=
-  (le_isGLB_iff <| isGLB_cinfᵢ hf).trans forall_range_iff
-#align le_cinfi_iff le_cinfᵢ_iff
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i)))
+Case conversion may be inaccurate. Consider using '#align le_cinfi_iff le_ciInf_iffₓ'. -/
+theorem le_ciInf_iff [Nonempty ι] {f : ι → α} {a : α} (hf : BddBelow (range f)) :
+    a ≤ iInf f ↔ ∀ i, a ≤ f i :=
+  (le_isGLB_iff <| isGLB_ciInf hf).trans forall_range_iff
+#align le_cinfi_iff le_ciInf_iff
 
-/- warning: csupr_set_le_iff -> csupᵢ_set_le_iff is a dubious translation:
+/- warning: csupr_set_le_iff -> ciSup_set_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) a) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i))) a) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i))) a) (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a)))
-Case conversion may be inaccurate. Consider using '#align csupr_set_le_iff csupᵢ_set_le_iffₓ'. -/
-theorem csupᵢ_set_le_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i))) a) (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) a)))
+Case conversion may be inaccurate. Consider using '#align csupr_set_le_iff ciSup_set_le_iffₓ'. -/
+theorem ciSup_set_le_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddAbove (f '' s)) : (⨆ i : s, f i) ≤ a ↔ ∀ i ∈ s, f i ≤ a :=
-  (isLUB_le_iff <| isLUB_csupᵢ_set hf hs).trans ball_image_iff
-#align csupr_set_le_iff csupᵢ_set_le_iff
+  (isLUB_le_iff <| isLUB_ciSup_set hf hs).trans ball_image_iff
+#align csupr_set_le_iff ciSup_set_le_iff
 
-/- warning: le_cinfi_set_iff -> le_cinfᵢ_set_iff is a dubious translation:
+/- warning: le_cinfi_set_iff -> le_ciInf_set_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i)))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} ι) Type.{u2} (Set.hasCoeToSort.{u2} ι) s) ι (coeSubtype.{succ u2} ι (fun (x : ι) => Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) x s))))) i)))) (forall (i : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i)))) (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i))))
-Case conversion may be inaccurate. Consider using '#align le_cinfi_set_iff le_cinfᵢ_set_iffₓ'. -/
-theorem le_cinfᵢ_set_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {ι : Type.{u2}} {s : Set.{u2} ι} {f : ι -> α} {a : α}, (Set.Nonempty.{u2} ι s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} ι α f s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} ι s) (fun (i : Set.Elem.{u2} ι s) => f (Subtype.val.{succ u2} ι (fun (x : ι) => Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) x s) i)))) (forall (i : ι), (Membership.mem.{u2, u2} ι (Set.{u2} ι) (Set.instMembershipSet.{u2} ι) i s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f i))))
+Case conversion may be inaccurate. Consider using '#align le_cinfi_set_iff le_ciInf_set_iffₓ'. -/
+theorem le_ciInf_set_iff {ι : Type _} {s : Set ι} {f : ι → α} {a : α} (hs : s.Nonempty)
     (hf : BddBelow (f '' s)) : (a ≤ ⨅ i : s, f i) ↔ ∀ i ∈ s, a ≤ f i :=
-  (le_isGLB_iff <| isGLB_cinfᵢ_set hf hs).trans ball_image_iff
-#align le_cinfi_set_iff le_cinfᵢ_set_iff
+  (le_isGLB_iff <| isGLB_ciInf_set hf hs).trans ball_image_iff
+#align le_cinfi_set_iff le_ciInf_set_iff
 
-/- warning: is_lub.cSup_eq -> IsLUB.csupₛ_eq is a dubious translation:
+/- warning: is_lub.cSup_eq -> IsLUB.csSup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align is_lub.cSup_eq IsLUB.csupₛ_eqₓ'. -/
-theorem IsLUB.csupₛ_eq (H : IsLUB s a) (ne : s.Nonempty) : supₛ s = a :=
-  (isLUB_csupₛ Ne ⟨a, H.1⟩).unique H
-#align is_lub.cSup_eq IsLUB.csupₛ_eq
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align is_lub.cSup_eq IsLUB.csSup_eqₓ'. -/
+theorem IsLUB.csSup_eq (H : IsLUB s a) (ne : s.Nonempty) : sSup s = a :=
+  (isLUB_csSup Ne ⟨a, H.1⟩).unique H
+#align is_lub.cSup_eq IsLUB.csSup_eq
 
-/- warning: is_lub.csupr_eq -> IsLUB.csupᵢ_eq is a dubious translation:
+/- warning: is_lub.csupr_eq -> IsLUB.ciSup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
-Case conversion may be inaccurate. Consider using '#align is_lub.csupr_eq IsLUB.csupᵢ_eqₓ'. -/
-theorem IsLUB.csupᵢ_eq [Nonempty ι] {f : ι → α} (H : IsLUB (range f) a) : (⨆ i, f i) = a :=
-  H.csupₛ_eq (range_nonempty f)
-#align is_lub.csupr_eq IsLUB.csupᵢ_eq
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
+Case conversion may be inaccurate. Consider using '#align is_lub.csupr_eq IsLUB.ciSup_eqₓ'. -/
+theorem IsLUB.ciSup_eq [Nonempty ι] {f : ι → α} (H : IsLUB (range f) a) : (⨆ i, f i) = a :=
+  H.csSup_eq (range_nonempty f)
+#align is_lub.csupr_eq IsLUB.ciSup_eq
 
-/- warning: is_lub.csupr_set_eq -> IsLUB.csupᵢ_set_eq is a dubious translation:
+/- warning: is_lub.csupr_set_eq -> IsLUB.ciSup_set_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) a)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) a)
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))) a)
-Case conversion may be inaccurate. Consider using '#align is_lub.csupr_set_eq IsLUB.csupᵢ_set_eqₓ'. -/
-theorem IsLUB.csupᵢ_set_eq {s : Set β} {f : β → α} (H : IsLUB (f '' s) a) (Hne : s.Nonempty) :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))) a)
+Case conversion may be inaccurate. Consider using '#align is_lub.csupr_set_eq IsLUB.ciSup_set_eqₓ'. -/
+theorem IsLUB.ciSup_set_eq {s : Set β} {f : β → α} (H : IsLUB (f '' s) a) (Hne : s.Nonempty) :
     (⨆ i : s, f i) = a :=
-  IsLUB.csupₛ_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
-#align is_lub.csupr_set_eq IsLUB.csupᵢ_set_eq
+  IsLUB.csSup_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
+#align is_lub.csupr_set_eq IsLUB.ciSup_set_eq
 
-/- warning: is_greatest.cSup_eq -> IsGreatest.csupₛ_eq is a dubious translation:
+/- warning: is_greatest.cSup_eq -> IsGreatest.csSup_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align is_greatest.cSup_eq IsGreatest.csupₛ_eqₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align is_greatest.cSup_eq IsGreatest.csSup_eqₓ'. -/
 /-- A greatest element of a set is the supremum of this set. -/
-theorem IsGreatest.csupₛ_eq (H : IsGreatest s a) : supₛ s = a :=
-  H.IsLUB.csupₛ_eq H.Nonempty
-#align is_greatest.cSup_eq IsGreatest.csupₛ_eq
+theorem IsGreatest.csSup_eq (H : IsGreatest s a) : sSup s = a :=
+  H.IsLUB.csSup_eq H.Nonempty
+#align is_greatest.cSup_eq IsGreatest.csSup_eq
 
-/- warning: is_greatest.Sup_mem -> IsGreatest.csupₛ_mem is a dubious translation:
+/- warning: is_greatest.Sup_mem -> IsGreatest.csSup_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) s)
-Case conversion may be inaccurate. Consider using '#align is_greatest.Sup_mem IsGreatest.csupₛ_memₓ'. -/
-theorem IsGreatest.csupₛ_mem (H : IsGreatest s a) : supₛ s ∈ s :=
-  H.csupₛ_eq.symm ▸ H.1
-#align is_greatest.Sup_mem IsGreatest.csupₛ_mem
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) s)
+Case conversion may be inaccurate. Consider using '#align is_greatest.Sup_mem IsGreatest.csSup_memₓ'. -/
+theorem IsGreatest.csSup_mem (H : IsGreatest s a) : sSup s ∈ s :=
+  H.csSup_eq.symm ▸ H.1
+#align is_greatest.Sup_mem IsGreatest.csSup_mem
 
-/- warning: is_glb.cInf_eq -> IsGLB.cinfₛ_eq is a dubious translation:
+/- warning: is_glb.cInf_eq -> IsGLB.csInf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align is_glb.cInf_eq IsGLB.cinfₛ_eqₓ'. -/
-theorem IsGLB.cinfₛ_eq (H : IsGLB s a) (ne : s.Nonempty) : infₛ s = a :=
-  (isGLB_cinfₛ Ne ⟨a, H.1⟩).unique H
-#align is_glb.cInf_eq IsGLB.cinfₛ_eq
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align is_glb.cInf_eq IsGLB.csInf_eqₓ'. -/
+theorem IsGLB.csInf_eq (H : IsGLB s a) (ne : s.Nonempty) : sInf s = a :=
+  (isGLB_csInf Ne ⟨a, H.1⟩).unique H
+#align is_glb.cInf_eq IsGLB.csInf_eq
 
-/- warning: is_glb.cinfi_eq -> IsGLB.cinfᵢ_eq is a dubious translation:
+/- warning: is_glb.cinfi_eq -> IsGLB.ciInf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
-Case conversion may be inaccurate. Consider using '#align is_glb.cinfi_eq IsGLB.cinfᵢ_eqₓ'. -/
-theorem IsGLB.cinfᵢ_eq [Nonempty ι] {f : ι → α} (H : IsGLB (range f) a) : (⨅ i, f i) = a :=
-  H.cinfₛ_eq (range_nonempty f)
-#align is_glb.cinfi_eq IsGLB.cinfᵢ_eq
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f) a) -> (Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) a)
+Case conversion may be inaccurate. Consider using '#align is_glb.cinfi_eq IsGLB.ciInf_eqₓ'. -/
+theorem IsGLB.ciInf_eq [Nonempty ι] {f : ι → α} (H : IsGLB (range f) a) : (⨅ i, f i) = a :=
+  H.csInf_eq (range_nonempty f)
+#align is_glb.cinfi_eq IsGLB.ciInf_eq
 
-/- warning: is_glb.cinfi_set_eq -> IsGLB.cinfᵢ_set_eq is a dubious translation:
+/- warning: is_glb.cinfi_set_eq -> IsGLB.ciInf_set_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) a)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) a)
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))) a)
-Case conversion may be inaccurate. Consider using '#align is_glb.cinfi_set_eq IsGLB.cinfᵢ_set_eqₓ'. -/
-theorem IsGLB.cinfᵢ_set_eq {s : Set β} {f : β → α} (H : IsGLB (f '' s) a) (Hne : s.Nonempty) :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {s : Set.{u2} β} {f : β -> α}, (IsGLB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s) a) -> (Set.Nonempty.{u2} β s) -> (Eq.{succ u1} α (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))) a)
+Case conversion may be inaccurate. Consider using '#align is_glb.cinfi_set_eq IsGLB.ciInf_set_eqₓ'. -/
+theorem IsGLB.ciInf_set_eq {s : Set β} {f : β → α} (H : IsGLB (f '' s) a) (Hne : s.Nonempty) :
     (⨅ i : s, f i) = a :=
-  IsGLB.cinfₛ_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
-#align is_glb.cinfi_set_eq IsGLB.cinfᵢ_set_eq
+  IsGLB.csInf_eq (image_eq_range f s ▸ H) (image_eq_range f s ▸ Hne.image f)
+#align is_glb.cinfi_set_eq IsGLB.ciInf_set_eq
 
-/- warning: is_least.cInf_eq -> IsLeast.cinfₛ_eq is a dubious translation:
+/- warning: is_least.cInf_eq -> IsLeast.csInf_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
-Case conversion may be inaccurate. Consider using '#align is_least.cInf_eq IsLeast.cinfₛ_eqₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) a)
+Case conversion may be inaccurate. Consider using '#align is_least.cInf_eq IsLeast.csInf_eqₓ'. -/
 /-- A least element of a set is the infimum of this set. -/
-theorem IsLeast.cinfₛ_eq (H : IsLeast s a) : infₛ s = a :=
-  H.IsGLB.cinfₛ_eq H.Nonempty
-#align is_least.cInf_eq IsLeast.cinfₛ_eq
+theorem IsLeast.csInf_eq (H : IsLeast s a) : sInf s = a :=
+  H.IsGLB.csInf_eq H.Nonempty
+#align is_least.cInf_eq IsLeast.csInf_eq
 
-/- warning: is_least.Inf_mem -> IsLeast.cinfₛ_mem is a dubious translation:
+/- warning: is_least.Inf_mem -> IsLeast.csInf_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) s)
-Case conversion may be inaccurate. Consider using '#align is_least.Inf_mem IsLeast.cinfₛ_memₓ'. -/
-theorem IsLeast.cinfₛ_mem (H : IsLeast s a) : infₛ s ∈ s :=
-  H.cinfₛ_eq.symm ▸ H.1
-#align is_least.Inf_mem IsLeast.cinfₛ_mem
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s a) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) s)
+Case conversion may be inaccurate. Consider using '#align is_least.Inf_mem IsLeast.csInf_memₓ'. -/
+theorem IsLeast.csInf_mem (H : IsLeast s a) : sInf s ∈ s :=
+  H.csInf_eq.symm ▸ H.1
+#align is_least.Inf_mem IsLeast.csInf_mem
 
-/- warning: subset_Icc_cInf_cSup -> subset_Icc_cinfₛ_csupₛ is a dubious translation:
+/- warning: subset_Icc_cInf_cSup -> subset_Icc_csInf_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align subset_Icc_cInf_cSup subset_Icc_cinfₛ_csupₛₓ'. -/
-theorem subset_Icc_cinfₛ_csupₛ (hb : BddBelow s) (ha : BddAbove s) : s ⊆ Icc (infₛ s) (supₛ s) :=
-  fun x hx => ⟨cinfₛ_le hb hx, le_csupₛ ha hx⟩
-#align subset_Icc_cInf_cSup subset_Icc_cinfₛ_csupₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align subset_Icc_cInf_cSup subset_Icc_csInf_csSupₓ'. -/
+theorem subset_Icc_csInf_csSup (hb : BddBelow s) (ha : BddAbove s) : s ⊆ Icc (sInf s) (sSup s) :=
+  fun x hx => ⟨csInf_le hb hx, le_csSup ha hx⟩
+#align subset_Icc_cInf_cSup subset_Icc_csInf_csSup
 
-/- warning: cSup_le_iff -> csupₛ_le_iff is a dubious translation:
+/- warning: cSup_le_iff -> csSup_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) a) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
-Case conversion may be inaccurate. Consider using '#align cSup_le_iff csupₛ_le_iffₓ'. -/
-theorem csupₛ_le_iff (hb : BddAbove s) (hs : s.Nonempty) : supₛ s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
-  isLUB_le_iff (isLUB_csupₛ hs hb)
-#align cSup_le_iff csupₛ_le_iff
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) a) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)))
+Case conversion may be inaccurate. Consider using '#align cSup_le_iff csSup_le_iffₓ'. -/
+theorem csSup_le_iff (hb : BddAbove s) (hs : s.Nonempty) : sSup s ≤ a ↔ ∀ b ∈ s, b ≤ a :=
+  isLUB_le_iff (isLUB_csSup hs hb)
+#align cSup_le_iff csSup_le_iff
 
-/- warning: le_cInf_iff -> le_cinfₛ_iff is a dubious translation:
+/- warning: le_cInf_iff -> le_csInf_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
-Case conversion may be inaccurate. Consider using '#align le_cInf_iff le_cinfₛ_iffₓ'. -/
-theorem le_cinfₛ_iff (hb : BddBelow s) (hs : s.Nonempty) : a ≤ infₛ s ↔ ∀ b ∈ s, a ≤ b :=
-  le_isGLB_iff (isGLB_cinfₛ hs hb)
-#align le_cInf_iff le_cinfₛ_iff
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)))
+Case conversion may be inaccurate. Consider using '#align le_cInf_iff le_csInf_iffₓ'. -/
+theorem le_csInf_iff (hb : BddBelow s) (hs : s.Nonempty) : a ≤ sInf s ↔ ∀ b ∈ s, a ≤ b :=
+  le_isGLB_iff (isGLB_csInf hs hb)
+#align le_cInf_iff le_csInf_iff
 
-/- warning: cSup_lower_bounds_eq_cInf -> csupₛ_lower_bounds_eq_cinfₛ is a dubious translation:
+/- warning: cSup_lower_bounds_eq_cInf -> csSup_lower_bounds_eq_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align cSup_lower_bounds_eq_cInf csupₛ_lower_bounds_eq_cinfₛₓ'. -/
-theorem csupₛ_lower_bounds_eq_cinfₛ {s : Set α} (h : BddBelow s) (hs : s.Nonempty) :
-    supₛ (lowerBounds s) = infₛ s :=
-  (isLUB_csupₛ h <| hs.mono fun x hx y hy => hy hx).unique (isGLB_cinfₛ hs h).IsLUB
-#align cSup_lower_bounds_eq_cInf csupₛ_lower_bounds_eq_cinfₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align cSup_lower_bounds_eq_cInf csSup_lower_bounds_eq_csInfₓ'. -/
+theorem csSup_lower_bounds_eq_csInf {s : Set α} (h : BddBelow s) (hs : s.Nonempty) :
+    sSup (lowerBounds s) = sInf s :=
+  (isLUB_csSup h <| hs.mono fun x hx y hy => hy hx).unique (isGLB_csInf hs h).IsLUB
+#align cSup_lower_bounds_eq_cInf csSup_lower_bounds_eq_csInf
 
-/- warning: cInf_upper_bounds_eq_cSup -> cinfₛ_upper_bounds_eq_csupₛ is a dubious translation:
+/- warning: cInf_upper_bounds_eq_cSup -> csInf_upper_bounds_eq_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align cInf_upper_bounds_eq_cSup cinfₛ_upper_bounds_eq_csupₛₓ'. -/
-theorem cinfₛ_upper_bounds_eq_csupₛ {s : Set α} (h : BddAbove s) (hs : s.Nonempty) :
-    infₛ (upperBounds s) = supₛ s :=
-  (isGLB_cinfₛ h <| hs.mono fun x hx y hy => hy hx).unique (isLUB_csupₛ hs h).IsGLB
-#align cInf_upper_bounds_eq_cSup cinfₛ_upper_bounds_eq_csupₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align cInf_upper_bounds_eq_cSup csInf_upper_bounds_eq_csSupₓ'. -/
+theorem csInf_upper_bounds_eq_csSup {s : Set α} (h : BddAbove s) (hs : s.Nonempty) :
+    sInf (upperBounds s) = sSup s :=
+  (isGLB_csInf h <| hs.mono fun x hx y hy => hy hx).unique (isLUB_csSup hs h).IsGLB
+#align cInf_upper_bounds_eq_cSup csInf_upper_bounds_eq_csSup
 
-/- warning: not_mem_of_lt_cInf -> not_mem_of_lt_cinfₛ is a dubious translation:
+/- warning: not_mem_of_lt_cInf -> not_mem_of_lt_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))
-Case conversion may be inaccurate. Consider using '#align not_mem_of_lt_cInf not_mem_of_lt_cinfₛₓ'. -/
-theorem not_mem_of_lt_cinfₛ {x : α} {s : Set α} (h : x < infₛ s) (hs : BddBelow s) : x ∉ s :=
-  fun hx => lt_irrefl _ (h.trans_le (cinfₛ_le hs hx))
-#align not_mem_of_lt_cInf not_mem_of_lt_cinfₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) x (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))
+Case conversion may be inaccurate. Consider using '#align not_mem_of_lt_cInf not_mem_of_lt_csInfₓ'. -/
+theorem not_mem_of_lt_csInf {x : α} {s : Set α} (h : x < sInf s) (hs : BddBelow s) : x ∉ s :=
+  fun hx => lt_irrefl _ (h.trans_le (csInf_le hs hx))
+#align not_mem_of_lt_cInf not_mem_of_lt_csInf
 
-/- warning: not_mem_of_cSup_lt -> not_mem_of_csupₛ_lt is a dubious translation:
+/- warning: not_mem_of_cSup_lt -> not_mem_of_csSup_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) x) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) x) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) x) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))
-Case conversion may be inaccurate. Consider using '#align not_mem_of_cSup_lt not_mem_of_csupₛ_ltₓ'. -/
-theorem not_mem_of_csupₛ_lt {x : α} {s : Set α} (h : supₛ s < x) (hs : BddAbove s) : x ∉ s :=
-  @not_mem_of_lt_cinfₛ αᵒᵈ _ x s h hs
-#align not_mem_of_cSup_lt not_mem_of_csupₛ_lt
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {x : α} {s : Set.{u1} α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) x) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s))
+Case conversion may be inaccurate. Consider using '#align not_mem_of_cSup_lt not_mem_of_csSup_ltₓ'. -/
+theorem not_mem_of_csSup_lt {x : α} {s : Set α} (h : sSup s < x) (hs : BddAbove s) : x ∉ s :=
+  @not_mem_of_lt_csInf αᵒᵈ _ x s h hs
+#align not_mem_of_cSup_lt not_mem_of_csSup_lt
 
-/- warning: cSup_eq_of_forall_le_of_forall_lt_exists_gt -> csupₛ_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
+/- warning: cSup_eq_of_forall_le_of_forall_lt_exists_gt -> csSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w a)))) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w a)))) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) b)
-Case conversion may be inaccurate. Consider using '#align cSup_eq_of_forall_le_of_forall_lt_exists_gt csupₛ_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w a)))) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) b)
+Case conversion may be inaccurate. Consider using '#align cSup_eq_of_forall_le_of_forall_lt_exists_gt csSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
 /-- Introduction rule to prove that `b` is the supremum of `s`: it suffices to check that `b`
 is larger than all elements of `s`, and that this is not the case of any `w<b`.
 See `Sup_eq_of_forall_le_of_forall_lt_exists_gt` for a version in complete lattices. -/
-theorem csupₛ_eq_of_forall_le_of_forall_lt_exists_gt (hs : s.Nonempty) (H : ∀ a ∈ s, a ≤ b)
-    (H' : ∀ w, w < b → ∃ a ∈ s, w < a) : supₛ s = b :=
-  eq_of_le_of_not_lt (csupₛ_le hs H) fun hb =>
+theorem csSup_eq_of_forall_le_of_forall_lt_exists_gt (hs : s.Nonempty) (H : ∀ a ∈ s, a ≤ b)
+    (H' : ∀ w, w < b → ∃ a ∈ s, w < a) : sSup s = b :=
+  eq_of_le_of_not_lt (csSup_le hs H) fun hb =>
     let ⟨a, ha, ha'⟩ := H' _ hb
-    lt_irrefl _ <| ha'.trans_le <| le_csupₛ ⟨b, H⟩ ha
-#align cSup_eq_of_forall_le_of_forall_lt_exists_gt csupₛ_eq_of_forall_le_of_forall_lt_exists_gt
+    lt_irrefl _ <| ha'.trans_le <| le_csSup ⟨b, H⟩ ha
+#align cSup_eq_of_forall_le_of_forall_lt_exists_gt csSup_eq_of_forall_le_of_forall_lt_exists_gt
 
-/- warning: cInf_eq_of_forall_ge_of_forall_gt_exists_lt -> cinfₛ_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
+/- warning: cInf_eq_of_forall_ge_of_forall_gt_exists_lt -> csInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a w)))) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a w)))) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) b)
-Case conversion may be inaccurate. Consider using '#align cInf_eq_of_forall_ge_of_forall_gt_exists_lt cinfₛ_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a w)))) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) b)
+Case conversion may be inaccurate. Consider using '#align cInf_eq_of_forall_ge_of_forall_gt_exists_lt csInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
 /-- Introduction rule to prove that `b` is the infimum of `s`: it suffices to check that `b`
 is smaller than all elements of `s`, and that this is not the case of any `w>b`.
 See `Inf_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in complete lattices. -/
-theorem cinfₛ_eq_of_forall_ge_of_forall_gt_exists_lt :
-    s.Nonempty → (∀ a ∈ s, b ≤ a) → (∀ w, b < w → ∃ a ∈ s, a < w) → infₛ s = b :=
-  @csupₛ_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _
-#align cInf_eq_of_forall_ge_of_forall_gt_exists_lt cinfₛ_eq_of_forall_ge_of_forall_gt_exists_lt
+theorem csInf_eq_of_forall_ge_of_forall_gt_exists_lt :
+    s.Nonempty → (∀ a ∈ s, b ≤ a) → (∀ w, b < w → ∃ a ∈ s, a < w) → sInf s = b :=
+  @csSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _
+#align cInf_eq_of_forall_ge_of_forall_gt_exists_lt csInf_eq_of_forall_ge_of_forall_gt_exists_lt
 
-/- warning: lt_cSup_of_lt -> lt_csupₛ_of_lt is a dubious translation:
+/- warning: lt_cSup_of_lt -> lt_csSup_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align lt_cSup_of_lt lt_csupₛ_of_ltₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b a) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align lt_cSup_of_lt lt_csSup_of_ltₓ'. -/
 /-- b < Sup s when there is an element a in s with b < a, when s is bounded above.
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness above for one direction, nonemptiness and linear
 order for the other one), so we formulate separately the two implications, contrary to
 the complete_lattice case.-/
-theorem lt_csupₛ_of_lt (hs : BddAbove s) (ha : a ∈ s) (h : b < a) : b < supₛ s :=
-  lt_of_lt_of_le h (le_csupₛ hs ha)
-#align lt_cSup_of_lt lt_csupₛ_of_lt
+theorem lt_csSup_of_lt (hs : BddAbove s) (ha : a ∈ s) (h : b < a) : b < sSup s :=
+  lt_of_lt_of_le h (le_csSup hs ha)
+#align lt_cSup_of_lt lt_csSup_of_lt
 
-/- warning: cInf_lt_of_lt -> cinfₛ_lt_of_lt is a dubious translation:
+/- warning: cInf_lt_of_lt -> csInf_lt_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) b)
-Case conversion may be inaccurate. Consider using '#align cInf_lt_of_lt cinfₛ_lt_of_ltₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α} {b : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) b)
+Case conversion may be inaccurate. Consider using '#align cInf_lt_of_lt csInf_lt_of_ltₓ'. -/
 /-- Inf s < b when there is an element a in s with a < b, when s is bounded below.
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness below for one direction, nonemptiness and linear
 order for the other one), so we formulate separately the two implications, contrary to
 the complete_lattice case.-/
-theorem cinfₛ_lt_of_lt : BddBelow s → a ∈ s → a < b → infₛ s < b :=
-  @lt_csupₛ_of_lt αᵒᵈ _ _ _ _
-#align cInf_lt_of_lt cinfₛ_lt_of_lt
+theorem csInf_lt_of_lt : BddBelow s → a ∈ s → a < b → sInf s < b :=
+  @lt_csSup_of_lt αᵒᵈ _ _ _ _
+#align cInf_lt_of_lt csInf_lt_of_lt
 
 /- warning: exists_between_of_forall_le -> exists_between_of_forall_le is a dubious translation:
 lean 3 declaration is
@@ -960,532 +960,532 @@ Case conversion may be inaccurate. Consider using '#align exists_between_of_fora
 of a nonempty set `t`, then there exists an element between these sets. -/
 theorem exists_between_of_forall_le (sne : s.Nonempty) (tne : t.Nonempty)
     (hst : ∀ x ∈ s, ∀ y ∈ t, x ≤ y) : (upperBounds s ∩ lowerBounds t).Nonempty :=
-  ⟨infₛ t, fun x hx => le_cinfₛ tne <| hst x hx, fun y hy => cinfₛ_le (sne.mono hst) hy⟩
+  ⟨sInf t, fun x hx => le_csInf tne <| hst x hx, fun y hy => csInf_le (sne.mono hst) hy⟩
 #align exists_between_of_forall_le exists_between_of_forall_le
 
-/- warning: cSup_singleton -> csupₛ_singleton is a dubious translation:
+/- warning: cSup_singleton -> csSup_singleton is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
-Case conversion may be inaccurate. Consider using '#align cSup_singleton csupₛ_singletonₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
+Case conversion may be inaccurate. Consider using '#align cSup_singleton csSup_singletonₓ'. -/
 /-- The supremum of a singleton is the element of the singleton-/
 @[simp]
-theorem csupₛ_singleton (a : α) : supₛ {a} = a :=
-  isGreatest_singleton.csupₛ_eq
-#align cSup_singleton csupₛ_singleton
+theorem csSup_singleton (a : α) : sSup {a} = a :=
+  isGreatest_singleton.csSup_eq
+#align cSup_singleton csSup_singleton
 
-/- warning: cInf_singleton -> cinfₛ_singleton is a dubious translation:
+/- warning: cInf_singleton -> csInf_singleton is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
-Case conversion may be inaccurate. Consider using '#align cInf_singleton cinfₛ_singletonₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)) a
+Case conversion may be inaccurate. Consider using '#align cInf_singleton csInf_singletonₓ'. -/
 /-- The infimum of a singleton is the element of the singleton-/
 @[simp]
-theorem cinfₛ_singleton (a : α) : infₛ {a} = a :=
-  isLeast_singleton.cinfₛ_eq
-#align cInf_singleton cinfₛ_singleton
+theorem csInf_singleton (a : α) : sInf {a} = a :=
+  isLeast_singleton.csInf_eq
+#align cInf_singleton csInf_singleton
 
-/- warning: cSup_pair -> csupₛ_pair is a dubious translation:
+/- warning: cSup_pair -> csSup_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
-Case conversion may be inaccurate. Consider using '#align cSup_pair csupₛ_pairₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
+Case conversion may be inaccurate. Consider using '#align cSup_pair csSup_pairₓ'. -/
 @[simp]
-theorem csupₛ_pair (a b : α) : supₛ {a, b} = a ⊔ b :=
-  (@isLUB_pair _ _ a b).csupₛ_eq (insert_nonempty _ _)
-#align cSup_pair csupₛ_pair
+theorem csSup_pair (a b : α) : sSup {a, b} = a ⊔ b :=
+  (@isLUB_pair _ _ a b).csSup_eq (insert_nonempty _ _)
+#align cSup_pair csSup_pair
 
-/- warning: cInf_pair -> cinfₛ_pair is a dubious translation:
+/- warning: cInf_pair -> csInf_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a b)
-Case conversion may be inaccurate. Consider using '#align cInf_pair cinfₛ_pairₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a b)
+Case conversion may be inaccurate. Consider using '#align cInf_pair csInf_pairₓ'. -/
 @[simp]
-theorem cinfₛ_pair (a b : α) : infₛ {a, b} = a ⊓ b :=
-  (@isGLB_pair _ _ a b).cinfₛ_eq (insert_nonempty _ _)
-#align cInf_pair cinfₛ_pair
+theorem csInf_pair (a b : α) : sInf {a, b} = a ⊓ b :=
+  (@isGLB_pair _ _ a b).csInf_eq (insert_nonempty _ _)
+#align cInf_pair csInf_pair
 
-/- warning: cInf_le_cSup -> cinfₛ_le_csupₛ is a dubious translation:
+/- warning: cInf_le_cSup -> csInf_le_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
-Case conversion may be inaccurate. Consider using '#align cInf_le_cSup cinfₛ_le_csupₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s))
+Case conversion may be inaccurate. Consider using '#align cInf_le_cSup csInf_le_csSupₓ'. -/
 /-- If a set is bounded below and above, and nonempty, its infimum is less than or equal to
 its supremum.-/
-theorem cinfₛ_le_csupₛ (hb : BddBelow s) (ha : BddAbove s) (ne : s.Nonempty) : infₛ s ≤ supₛ s :=
-  isGLB_le_isLUB (isGLB_cinfₛ Ne hb) (isLUB_csupₛ Ne ha) Ne
-#align cInf_le_cSup cinfₛ_le_csupₛ
+theorem csInf_le_csSup (hb : BddBelow s) (ha : BddAbove s) (ne : s.Nonempty) : sInf s ≤ sSup s :=
+  isGLB_le_isLUB (isGLB_csInf Ne hb) (isLUB_csSup Ne ha) Ne
+#align cInf_le_cSup csInf_le_csSup
 
-/- warning: cSup_union -> csupₛ_union is a dubious translation:
+/- warning: cSup_union -> csSup_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
-Case conversion may be inaccurate. Consider using '#align cSup_union csupₛ_unionₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
+Case conversion may be inaccurate. Consider using '#align cSup_union csSup_unionₓ'. -/
 /-- The sup of a union of two sets is the max of the suprema of each subset, under the assumptions
 that all sets are bounded above and nonempty.-/
-theorem csupₛ_union (hs : BddAbove s) (sne : s.Nonempty) (ht : BddAbove t) (tne : t.Nonempty) :
-    supₛ (s ∪ t) = supₛ s ⊔ supₛ t :=
-  ((isLUB_csupₛ sne hs).union (isLUB_csupₛ tne ht)).csupₛ_eq sne.inl
-#align cSup_union csupₛ_union
+theorem csSup_union (hs : BddAbove s) (sne : s.Nonempty) (ht : BddAbove t) (tne : t.Nonempty) :
+    sSup (s ∪ t) = sSup s ⊔ sSup t :=
+  ((isLUB_csSup sne hs).union (isLUB_csSup tne ht)).csSup_eq sne.inl
+#align cSup_union csSup_union
 
-/- warning: cInf_union -> cinfₛ_union is a dubious translation:
+/- warning: cInf_union -> csInf_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)))
-Case conversion may be inaccurate. Consider using '#align cInf_union cinfₛ_unionₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)))
+Case conversion may be inaccurate. Consider using '#align cInf_union csInf_unionₓ'. -/
 /-- The inf of a union of two sets is the min of the infima of each subset, under the assumptions
 that all sets are bounded below and nonempty.-/
-theorem cinfₛ_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tne : t.Nonempty) :
-    infₛ (s ∪ t) = infₛ s ⊓ infₛ t :=
-  @csupₛ_union αᵒᵈ _ _ _ hs sne ht tne
-#align cInf_union cinfₛ_union
+theorem csInf_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tne : t.Nonempty) :
+    sInf (s ∪ t) = sInf s ⊓ sInf t :=
+  @csSup_union αᵒᵈ _ _ _ hs sne ht tne
+#align cInf_union csInf_union
 
-/- warning: cSup_inter_le -> csupₛ_inter_le is a dubious translation:
+/- warning: cSup_inter_le -> csSup_inter_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
-Case conversion may be inaccurate. Consider using '#align cSup_inter_le csupₛ_inter_leₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
+Case conversion may be inaccurate. Consider using '#align cSup_inter_le csSup_inter_leₓ'. -/
 /-- The supremum of an intersection of two sets is bounded by the minimum of the suprema of each
 set, if all sets are bounded above and nonempty.-/
-theorem csupₛ_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).Nonempty) :
-    supₛ (s ∩ t) ≤ supₛ s ⊓ supₛ t :=
-  csupₛ_le hst fun x hx => le_inf (le_csupₛ hs hx.1) (le_csupₛ ht hx.2)
-#align cSup_inter_le csupₛ_inter_le
+theorem csSup_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).Nonempty) :
+    sSup (s ∩ t) ≤ sSup s ⊓ sSup t :=
+  csSup_le hst fun x hx => le_inf (le_csSup hs hx.1) (le_csSup ht hx.2)
+#align cSup_inter_le csSup_inter_le
 
-/- warning: le_cInf_inter -> le_cinfₛ_inter is a dubious translation:
+/- warning: le_cInf_inter -> le_csInf_inter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)))
-Case conversion may be inaccurate. Consider using '#align le_cInf_inter le_cinfₛ_interₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)))
+Case conversion may be inaccurate. Consider using '#align le_cInf_inter le_csInf_interₓ'. -/
 /-- The infimum of an intersection of two sets is bounded below by the maximum of the
 infima of each set, if all sets are bounded below and nonempty.-/
-theorem le_cinfₛ_inter :
-    BddBelow s → BddBelow t → (s ∩ t).Nonempty → infₛ s ⊔ infₛ t ≤ infₛ (s ∩ t) :=
-  @csupₛ_inter_le αᵒᵈ _ _ _
-#align le_cInf_inter le_cinfₛ_inter
+theorem le_csInf_inter :
+    BddBelow s → BddBelow t → (s ∩ t).Nonempty → sInf s ⊔ sInf t ≤ sInf (s ∩ t) :=
+  @csSup_inter_le αᵒᵈ _ _ _
+#align le_cInf_inter le_csInf_inter
 
-/- warning: cSup_insert -> csupₛ_insert is a dubious translation:
+/- warning: cSup_insert -> csSup_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align cSup_insert csupₛ_insertₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align cSup_insert csSup_insertₓ'. -/
 /-- The supremum of insert a s is the maximum of a and the supremum of s, if s is
 nonempty and bounded above.-/
-theorem csupₛ_insert (hs : BddAbove s) (sne : s.Nonempty) : supₛ (insert a s) = a ⊔ supₛ s :=
-  ((isLUB_csupₛ sne hs).insert a).csupₛ_eq (insert_nonempty a s)
-#align cSup_insert csupₛ_insert
+theorem csSup_insert (hs : BddAbove s) (sne : s.Nonempty) : sSup (insert a s) = a ⊔ sSup s :=
+  ((isLUB_csSup sne hs).insert a).csSup_eq (insert_nonempty a s)
+#align cSup_insert csSup_insert
 
-/- warning: cInf_insert -> cinfₛ_insert is a dubious translation:
+/- warning: cInf_insert -> csInf_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)))
-Case conversion may be inaccurate. Consider using '#align cInf_insert cinfₛ_insertₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)))
+Case conversion may be inaccurate. Consider using '#align cInf_insert csInf_insertₓ'. -/
 /-- The infimum of insert a s is the minimum of a and the infimum of s, if s is
 nonempty and bounded below.-/
-theorem cinfₛ_insert (hs : BddBelow s) (sne : s.Nonempty) : infₛ (insert a s) = a ⊓ infₛ s :=
-  @csupₛ_insert αᵒᵈ _ _ _ hs sne
-#align cInf_insert cinfₛ_insert
+theorem csInf_insert (hs : BddBelow s) (sne : s.Nonempty) : sInf (insert a s) = a ⊓ sInf s :=
+  @csSup_insert αᵒᵈ _ _ _ hs sne
+#align cInf_insert csInf_insert
 
-/- warning: cInf_Icc -> cinfₛ_Icc is a dubious translation:
+/- warning: cInf_Icc -> csInf_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
-Case conversion may be inaccurate. Consider using '#align cInf_Icc cinfₛ_Iccₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+Case conversion may be inaccurate. Consider using '#align cInf_Icc csInf_Iccₓ'. -/
 @[simp]
-theorem cinfₛ_Icc (h : a ≤ b) : infₛ (Icc a b) = a :=
-  (isGLB_Icc h).cinfₛ_eq (nonempty_Icc.2 h)
-#align cInf_Icc cinfₛ_Icc
+theorem csInf_Icc (h : a ≤ b) : sInf (Icc a b) = a :=
+  (isGLB_Icc h).csInf_eq (nonempty_Icc.2 h)
+#align cInf_Icc csInf_Icc
 
-/- warning: cInf_Ici -> cinfₛ_Ici is a dubious translation:
+/- warning: cInf_Ici -> csInf_Ici is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
-Case conversion may be inaccurate. Consider using '#align cInf_Ici cinfₛ_Iciₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+Case conversion may be inaccurate. Consider using '#align cInf_Ici csInf_Iciₓ'. -/
 @[simp]
-theorem cinfₛ_Ici : infₛ (Ici a) = a :=
-  isLeast_Ici.cinfₛ_eq
-#align cInf_Ici cinfₛ_Ici
+theorem csInf_Ici : sInf (Ici a) = a :=
+  isLeast_Ici.csInf_eq
+#align cInf_Ici csInf_Ici
 
-/- warning: cInf_Ico -> cinfₛ_Ico is a dubious translation:
+/- warning: cInf_Ico -> csInf_Ico is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
-Case conversion may be inaccurate. Consider using '#align cInf_Ico cinfₛ_Icoₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+Case conversion may be inaccurate. Consider using '#align cInf_Ico csInf_Icoₓ'. -/
 @[simp]
-theorem cinfₛ_Ico (h : a < b) : infₛ (Ico a b) = a :=
-  (isGLB_Ico h).cinfₛ_eq (nonempty_Ico.2 h)
-#align cInf_Ico cinfₛ_Ico
+theorem csInf_Ico (h : a < b) : sInf (Ico a b) = a :=
+  (isGLB_Ico h).csInf_eq (nonempty_Ico.2 h)
+#align cInf_Ico csInf_Ico
 
-/- warning: cInf_Ioc -> cinfₛ_Ioc is a dubious translation:
+/- warning: cInf_Ioc -> csInf_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
-Case conversion may be inaccurate. Consider using '#align cInf_Ioc cinfₛ_Iocₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+Case conversion may be inaccurate. Consider using '#align cInf_Ioc csInf_Iocₓ'. -/
 @[simp]
-theorem cinfₛ_Ioc [DenselyOrdered α] (h : a < b) : infₛ (Ioc a b) = a :=
-  (isGLB_Ioc h).cinfₛ_eq (nonempty_Ioc.2 h)
-#align cInf_Ioc cinfₛ_Ioc
+theorem csInf_Ioc [DenselyOrdered α] (h : a < b) : sInf (Ioc a b) = a :=
+  (isGLB_Ioc h).csInf_eq (nonempty_Ioc.2 h)
+#align cInf_Ioc csInf_Ioc
 
-/- warning: cInf_Ioi -> cinfₛ_Ioi is a dubious translation:
+/- warning: cInf_Ioi -> csInf_Ioi is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
-Case conversion may be inaccurate. Consider using '#align cInf_Ioi cinfₛ_Ioiₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMaxOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioi.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+Case conversion may be inaccurate. Consider using '#align cInf_Ioi csInf_Ioiₓ'. -/
 @[simp]
-theorem cinfₛ_Ioi [NoMaxOrder α] [DenselyOrdered α] : infₛ (Ioi a) = a :=
-  cinfₛ_eq_of_forall_ge_of_forall_gt_exists_lt nonempty_Ioi (fun _ => le_of_lt) fun w hw => by
+theorem csInf_Ioi [NoMaxOrder α] [DenselyOrdered α] : sInf (Ioi a) = a :=
+  csInf_eq_of_forall_ge_of_forall_gt_exists_lt nonempty_Ioi (fun _ => le_of_lt) fun w hw => by
     simpa using exists_between hw
-#align cInf_Ioi cinfₛ_Ioi
+#align cInf_Ioi csInf_Ioi
 
-/- warning: cInf_Ioo -> cinfₛ_Ioo is a dubious translation:
+/- warning: cInf_Ioo -> csInf_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
-Case conversion may be inaccurate. Consider using '#align cInf_Ioo cinfₛ_Iooₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) a)
+Case conversion may be inaccurate. Consider using '#align cInf_Ioo csInf_Iooₓ'. -/
 @[simp]
-theorem cinfₛ_Ioo [DenselyOrdered α] (h : a < b) : infₛ (Ioo a b) = a :=
-  (isGLB_Ioo h).cinfₛ_eq (nonempty_Ioo.2 h)
-#align cInf_Ioo cinfₛ_Ioo
+theorem csInf_Ioo [DenselyOrdered α] (h : a < b) : sInf (Ioo a b) = a :=
+  (isGLB_Ioo h).csInf_eq (nonempty_Ioo.2 h)
+#align cInf_Ioo csInf_Ioo
 
-/- warning: cSup_Icc -> csupₛ_Icc is a dubious translation:
+/- warning: cSup_Icc -> csSup_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
-Case conversion may be inaccurate. Consider using '#align cSup_Icc csupₛ_Iccₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+Case conversion may be inaccurate. Consider using '#align cSup_Icc csSup_Iccₓ'. -/
 @[simp]
-theorem csupₛ_Icc (h : a ≤ b) : supₛ (Icc a b) = b :=
-  (isLUB_Icc h).csupₛ_eq (nonempty_Icc.2 h)
-#align cSup_Icc csupₛ_Icc
+theorem csSup_Icc (h : a ≤ b) : sSup (Icc a b) = b :=
+  (isLUB_Icc h).csSup_eq (nonempty_Icc.2 h)
+#align cSup_Icc csSup_Icc
 
-/- warning: cSup_Ico -> csupₛ_Ico is a dubious translation:
+/- warning: cSup_Ico -> csSup_Ico is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
-Case conversion may be inaccurate. Consider using '#align cSup_Ico csupₛ_Icoₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+Case conversion may be inaccurate. Consider using '#align cSup_Ico csSup_Icoₓ'. -/
 @[simp]
-theorem csupₛ_Ico [DenselyOrdered α] (h : a < b) : supₛ (Ico a b) = b :=
-  (isLUB_Ico h).csupₛ_eq (nonempty_Ico.2 h)
-#align cSup_Ico csupₛ_Ico
+theorem csSup_Ico [DenselyOrdered α] (h : a < b) : sSup (Ico a b) = b :=
+  (isLUB_Ico h).csSup_eq (nonempty_Ico.2 h)
+#align cSup_Ico csSup_Ico
 
-/- warning: cSup_Iic -> csupₛ_Iic is a dubious translation:
+/- warning: cSup_Iic -> csSup_Iic is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
-Case conversion may be inaccurate. Consider using '#align cSup_Iic csupₛ_Iicₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α}, Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+Case conversion may be inaccurate. Consider using '#align cSup_Iic csSup_Iicₓ'. -/
 @[simp]
-theorem csupₛ_Iic : supₛ (Iic a) = a :=
-  isGreatest_Iic.csupₛ_eq
-#align cSup_Iic csupₛ_Iic
+theorem csSup_Iic : sSup (Iic a) = a :=
+  isGreatest_Iic.csSup_eq
+#align cSup_Iic csSup_Iic
 
-/- warning: cSup_Iio -> csupₛ_Iio is a dubious translation:
+/- warning: cSup_Iio -> csSup_Iio is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
-Case conversion may be inaccurate. Consider using '#align cSup_Iio csupₛ_Iioₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} [_inst_2 : NoMinOrder.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))] [_inst_3 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Iio.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a)) a
+Case conversion may be inaccurate. Consider using '#align cSup_Iio csSup_Iioₓ'. -/
 @[simp]
-theorem csupₛ_Iio [NoMinOrder α] [DenselyOrdered α] : supₛ (Iio a) = a :=
-  csupₛ_eq_of_forall_le_of_forall_lt_exists_gt nonempty_Iio (fun _ => le_of_lt) fun w hw => by
+theorem csSup_Iio [NoMinOrder α] [DenselyOrdered α] : sSup (Iio a) = a :=
+  csSup_eq_of_forall_le_of_forall_lt_exists_gt nonempty_Iio (fun _ => le_of_lt) fun w hw => by
     simpa [and_comm'] using exists_between hw
-#align cSup_Iio csupₛ_Iio
+#align cSup_Iio csSup_Iio
 
-/- warning: cSup_Ioc -> csupₛ_Ioc is a dubious translation:
+/- warning: cSup_Ioc -> csSup_Ioc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
-Case conversion may be inaccurate. Consider using '#align cSup_Ioc csupₛ_Iocₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+Case conversion may be inaccurate. Consider using '#align cSup_Ioc csSup_Iocₓ'. -/
 @[simp]
-theorem csupₛ_Ioc (h : a < b) : supₛ (Ioc a b) = b :=
-  (isLUB_Ioc h).csupₛ_eq (nonempty_Ioc.2 h)
-#align cSup_Ioc csupₛ_Ioc
+theorem csSup_Ioc (h : a < b) : sSup (Ioc a b) = b :=
+  (isLUB_Ioc h).csSup_eq (nonempty_Ioc.2 h)
+#align cSup_Ioc csSup_Ioc
 
-/- warning: cSup_Ioo -> csupₛ_Ioo is a dubious translation:
+/- warning: cSup_Ioo -> csSup_Ioo is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
-Case conversion may be inaccurate. Consider using '#align cSup_Ioo csupₛ_Iooₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {b : α} [_inst_2 : DenselyOrdered.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))], (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) a b)) b)
+Case conversion may be inaccurate. Consider using '#align cSup_Ioo csSup_Iooₓ'. -/
 @[simp]
-theorem csupₛ_Ioo [DenselyOrdered α] (h : a < b) : supₛ (Ioo a b) = b :=
-  (isLUB_Ioo h).csupₛ_eq (nonempty_Ioo.2 h)
-#align cSup_Ioo csupₛ_Ioo
+theorem csSup_Ioo [DenselyOrdered α] (h : a < b) : sSup (Ioo a b) = b :=
+  (isLUB_Ioo h).csSup_eq (nonempty_Ioo.2 h)
+#align cSup_Ioo csSup_Ioo
 
-/- warning: csupr_le -> csupᵢ_le is a dubious translation:
+/- warning: csupr_le -> ciSup_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) c)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) c)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι f) c)
-Case conversion may be inaccurate. Consider using '#align csupr_le csupᵢ_leₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) c) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι f) c)
+Case conversion may be inaccurate. Consider using '#align csupr_le ciSup_leₓ'. -/
 /-- The indexed supremum of a function is bounded above by a uniform bound-/
-theorem csupᵢ_le [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, f x ≤ c) : supᵢ f ≤ c :=
-  csupₛ_le (range_nonempty f) (by rwa [forall_range_iff])
-#align csupr_le csupᵢ_le
+theorem ciSup_le [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, f x ≤ c) : iSup f ≤ c :=
+  csSup_le (range_nonempty f) (by rwa [forall_range_iff])
+#align csupr_le ciSup_le
 
-/- warning: le_csupr -> le_csupᵢ is a dubious translation:
+/- warning: le_csupr -> le_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f c) (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f))
-Case conversion may be inaccurate. Consider using '#align le_csupr le_csupᵢₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f c) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f))
+Case conversion may be inaccurate. Consider using '#align le_csupr le_ciSupₓ'. -/
 /-- The indexed supremum of a function is bounded below by the value taken at one point-/
-theorem le_csupᵢ {f : ι → α} (H : BddAbove (range f)) (c : ι) : f c ≤ supᵢ f :=
-  le_csupₛ H (mem_range_self _)
-#align le_csupr le_csupᵢ
+theorem le_ciSup {f : ι → α} (H : BddAbove (range f)) (c : ι) : f c ≤ iSup f :=
+  le_csSup H (mem_range_self _)
+#align le_csupr le_ciSup
 
-/- warning: le_csupr_of_le -> le_csupᵢ_of_le is a dubious translation:
+/- warning: le_csupr_of_le -> le_ciSup_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (f c)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {a : α} {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (f c)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f)))
-Case conversion may be inaccurate. Consider using '#align le_csupr_of_le le_csupᵢ_of_leₓ'. -/
-theorem le_csupᵢ_of_le {f : ι → α} (H : BddAbove (range f)) (c : ι) (h : a ≤ f c) : a ≤ supᵢ f :=
-  le_trans h (le_csupᵢ H c)
-#align le_csupr_of_le le_csupᵢ_of_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {a : α} {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (f c)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) a (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f)))
+Case conversion may be inaccurate. Consider using '#align le_csupr_of_le le_ciSup_of_leₓ'. -/
+theorem le_ciSup_of_le {f : ι → α} (H : BddAbove (range f)) (c : ι) (h : a ≤ f c) : a ≤ iSup f :=
+  le_trans h (le_ciSup H c)
+#align le_csupr_of_le le_ciSup_of_le
 
-/- warning: csupr_mono -> csupᵢ_mono is a dubious translation:
+/- warning: csupr_mono -> ciSup_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι g)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι g)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι f) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι g))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι g)) -> (forall (x : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f x) (g x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f) (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι g))
-Case conversion may be inaccurate. Consider using '#align csupr_mono csupᵢ_monoₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι g)) -> (forall (x : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f x) (g x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι f) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) ι g))
+Case conversion may be inaccurate. Consider using '#align csupr_mono ciSup_monoₓ'. -/
 /-- The indexed supremum of two functions are comparable if the functions are pointwise comparable-/
-theorem csupᵢ_mono {f g : ι → α} (B : BddAbove (range g)) (H : ∀ x, f x ≤ g x) : supᵢ f ≤ supᵢ g :=
+theorem ciSup_mono {f g : ι → α} (B : BddAbove (range g)) (H : ∀ x, f x ≤ g x) : iSup f ≤ iSup g :=
   by
   cases isEmpty_or_nonempty ι
-  · rw [supᵢ_of_empty', supᵢ_of_empty']
-  · exact csupᵢ_le fun x => le_csupᵢ_of_le B x (H x)
-#align csupr_mono csupᵢ_mono
+  · rw [iSup_of_empty', iSup_of_empty']
+  · exact ciSup_le fun x => le_ciSup_of_le B x (H x)
+#align csupr_mono ciSup_mono
 
-/- warning: le_csupr_set -> le_csupᵢ_set is a dubious translation:
+/- warning: le_csupr_set -> le_ciSup_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i)))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i)))))
-Case conversion may be inaccurate. Consider using '#align le_csupr_set le_csupᵢ_setₓ'. -/
-theorem le_csupᵢ_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) {c : β} (hc : c ∈ s) :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i)))))
+Case conversion may be inaccurate. Consider using '#align le_csupr_set le_ciSup_setₓ'. -/
+theorem le_ciSup_set {f : β → α} {s : Set β} (H : BddAbove (f '' s)) {c : β} (hc : c ∈ s) :
     f c ≤ ⨆ i : s, f i :=
-  (le_csupₛ H <| mem_image_of_mem f hc).trans_eq supₛ_image'
-#align le_csupr_set le_csupᵢ_set
+  (le_csSup H <| mem_image_of_mem f hc).trans_eq sSup_image'
+#align le_csupr_set le_ciSup_set
 
-/- warning: cinfi_mono -> cinfᵢ_mono is a dubious translation:
+/- warning: cinfi_mono -> ciInf_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α} {g : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f x) (g x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι g))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (x : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f x) (g x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι g))
-Case conversion may be inaccurate. Consider using '#align cinfi_mono cinfᵢ_monoₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α} {g : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (x : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f x) (g x)) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι g))
+Case conversion may be inaccurate. Consider using '#align cinfi_mono ciInf_monoₓ'. -/
 /-- The indexed infimum of two functions are comparable if the functions are pointwise comparable-/
-theorem cinfᵢ_mono {f g : ι → α} (B : BddBelow (range f)) (H : ∀ x, f x ≤ g x) : infᵢ f ≤ infᵢ g :=
-  @csupᵢ_mono αᵒᵈ _ _ _ _ B H
-#align cinfi_mono cinfᵢ_mono
+theorem ciInf_mono {f g : ι → α} (B : BddBelow (range f)) (H : ∀ x, f x ≤ g x) : iInf f ≤ iInf g :=
+  @ciSup_mono αᵒᵈ _ _ _ _ B H
+#align cinfi_mono ciInf_mono
 
-/- warning: le_cinfi -> le_cinfᵢ is a dubious translation:
+/- warning: le_cinfi -> le_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (f x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (f x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (f x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι f))
-Case conversion may be inaccurate. Consider using '#align le_cinfi le_cinfᵢₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {c : α}, (forall (x : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (f x)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) c (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι f))
+Case conversion may be inaccurate. Consider using '#align le_cinfi le_ciInfₓ'. -/
 /-- The indexed minimum of a function is bounded below by a uniform lower bound-/
-theorem le_cinfᵢ [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, c ≤ f x) : c ≤ infᵢ f :=
-  @csupᵢ_le αᵒᵈ _ _ _ _ _ H
-#align le_cinfi le_cinfᵢ
+theorem le_ciInf [Nonempty ι] {f : ι → α} {c : α} (H : ∀ x, c ≤ f x) : c ≤ iInf f :=
+  @ciSup_le αᵒᵈ _ _ _ _ _ H
+#align le_cinfi le_ciInf
 
-/- warning: cinfi_le -> cinfᵢ_le is a dubious translation:
+/- warning: cinfi_le -> ciInf_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (f c))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) (f c))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) (f c))
-Case conversion may be inaccurate. Consider using '#align cinfi_le cinfᵢ_leₓ'. -/
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {f : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) (f c))
+Case conversion may be inaccurate. Consider using '#align cinfi_le ciInf_leₓ'. -/
 /-- The indexed infimum of a function is bounded above by the value taken at one point-/
-theorem cinfᵢ_le {f : ι → α} (H : BddBelow (range f)) (c : ι) : infᵢ f ≤ f c :=
-  @le_csupᵢ αᵒᵈ _ _ _ H c
-#align cinfi_le cinfᵢ_le
+theorem ciInf_le {f : ι → α} (H : BddBelow (range f)) (c : ι) : iInf f ≤ f c :=
+  @le_ciSup αᵒᵈ _ _ _ H c
+#align cinfi_le ciInf_le
 
-/- warning: cinfi_le_of_le -> cinfᵢ_le_of_le is a dubious translation:
+/- warning: cinfi_le_of_le -> ciInf_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {a : α} {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u2} α ι f)) -> (forall (c : ι), (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f c) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι f) a))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {a : α} {f : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f c) a) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) a))
-Case conversion may be inaccurate. Consider using '#align cinfi_le_of_le cinfᵢ_le_of_leₓ'. -/
-theorem cinfᵢ_le_of_le {f : ι → α} (H : BddBelow (range f)) (c : ι) (h : f c ≤ a) : infᵢ f ≤ a :=
-  @le_csupᵢ_of_le αᵒᵈ _ _ _ _ H c h
-#align cinfi_le_of_le cinfᵢ_le_of_le
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] {a : α} {f : ι -> α}, (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (Set.range.{u2, u1} α ι f)) -> (forall (c : ι), (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (f c) a) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) ι f) a))
+Case conversion may be inaccurate. Consider using '#align cinfi_le_of_le ciInf_le_of_leₓ'. -/
+theorem ciInf_le_of_le {f : ι → α} (H : BddBelow (range f)) (c : ι) (h : f c ≤ a) : iInf f ≤ a :=
+  @le_ciSup_of_le αᵒᵈ _ _ _ _ H c h
+#align cinfi_le_of_le ciInf_le_of_le
 
-/- warning: cinfi_set_le -> cinfᵢ_set_le is a dubious translation:
+/- warning: cinfi_set_le -> ciInf_set_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) (f c)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (i : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => f ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) i))) (f c)))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))) (f c)))
-Case conversion may be inaccurate. Consider using '#align cinfi_set_le cinfᵢ_set_leₓ'. -/
-theorem cinfᵢ_set_le {f : β → α} {s : Set β} (H : BddBelow (f '' s)) {c : β} (hc : c ∈ s) :
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {f : β -> α} {s : Set.{u2} β}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u2, u1} β α f s)) -> (forall {c : β}, (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) c s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Set.Elem.{u2} β s) (fun (i : Set.Elem.{u2} β s) => f (Subtype.val.{succ u2} β (fun (x : β) => Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) i))) (f c)))
+Case conversion may be inaccurate. Consider using '#align cinfi_set_le ciInf_set_leₓ'. -/
+theorem ciInf_set_le {f : β → α} {s : Set β} (H : BddBelow (f '' s)) {c : β} (hc : c ∈ s) :
     (⨅ i : s, f i) ≤ f c :=
-  @le_csupᵢ_set αᵒᵈ _ _ _ _ H _ hc
-#align cinfi_set_le cinfᵢ_set_le
+  @le_ciSup_set αᵒᵈ _ _ _ _ H _ hc
+#align cinfi_set_le ciInf_set_le
 
-/- warning: csupr_const -> csupᵢ_const is a dubious translation:
+/- warning: csupr_const -> ciSup_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (b : ι) => a)) a
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (b : ι) => a)) a
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
-Case conversion may be inaccurate. Consider using '#align csupr_const csupᵢ_constₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
+Case conversion may be inaccurate. Consider using '#align csupr_const ciSup_constₓ'. -/
 @[simp]
-theorem csupᵢ_const [hι : Nonempty ι] {a : α} : (⨆ b : ι, a) = a := by
-  rw [supᵢ, range_const, csupₛ_singleton]
-#align csupr_const csupᵢ_const
+theorem ciSup_const [hι : Nonempty ι] {a : α} : (⨆ b : ι, a) = a := by
+  rw [iSup, range_const, csSup_singleton]
+#align csupr_const ciSup_const
 
-/- warning: cinfi_const -> cinfᵢ_const is a dubious translation:
+/- warning: cinfi_const -> ciInf_const is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (b : ι) => a)) a
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (b : ι) => a)) a
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
-Case conversion may be inaccurate. Consider using '#align cinfi_const cinfᵢ_constₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [hι : Nonempty.{u2} ι] {a : α}, Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (b : ι) => a)) a
+Case conversion may be inaccurate. Consider using '#align cinfi_const ciInf_constₓ'. -/
 @[simp]
-theorem cinfᵢ_const [hι : Nonempty ι] {a : α} : (⨅ b : ι, a) = a :=
-  @csupᵢ_const αᵒᵈ _ _ _ _
-#align cinfi_const cinfᵢ_const
+theorem ciInf_const [hι : Nonempty ι] {a : α} : (⨅ b : ι, a) = a :=
+  @ciSup_const αᵒᵈ _ _ _ _
+#align cinfi_const ciInf_const
 
-/- warning: supr_unique -> csupᵢ_unique is a dubious translation:
+/- warning: supr_unique -> ciSup_unique is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.inhabited.{u2} ι _inst_2)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.inhabited.{u2} ι _inst_2)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.instInhabited.{u2} ι _inst_2)))
-Case conversion may be inaccurate. Consider using '#align supr_unique csupᵢ_uniqueₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.instInhabited.{u2} ι _inst_2)))
+Case conversion may be inaccurate. Consider using '#align supr_unique ciSup_uniqueₓ'. -/
 @[simp]
-theorem csupᵢ_unique [Unique ι] {s : ι → α} : (⨆ i, s i) = s default :=
+theorem ciSup_unique [Unique ι] {s : ι → α} : (⨆ i, s i) = s default :=
   by
   have : ∀ i, s i = s default := fun i => congr_arg s (Unique.eq_default i)
-  simp only [this, csupᵢ_const]
-#align supr_unique csupᵢ_unique
+  simp only [this, ciSup_const]
+#align supr_unique ciSup_unique
 
-/- warning: infi_unique -> cinfᵢ_unique is a dubious translation:
+/- warning: infi_unique -> ciInf_unique is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.inhabited.{u2} ι _inst_2)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.inhabited.{u2} ι _inst_2)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.instInhabited.{u2} ι _inst_2)))
-Case conversion may be inaccurate. Consider using '#align infi_unique cinfᵢ_uniqueₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : Unique.{u2} ι] {s : ι -> α}, Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => s i)) (s (Inhabited.default.{u2} ι (Unique.instInhabited.{u2} ι _inst_2)))
+Case conversion may be inaccurate. Consider using '#align infi_unique ciInf_uniqueₓ'. -/
 @[simp]
-theorem cinfᵢ_unique [Unique ι] {s : ι → α} : (⨅ i, s i) = s default :=
-  @csupᵢ_unique αᵒᵈ _ _ _ _
-#align infi_unique cinfᵢ_unique
+theorem ciInf_unique [Unique ι] {s : ι → α} : (⨅ i, s i) = s default :=
+  @ciSup_unique αᵒᵈ _ _ _ _
+#align infi_unique ciInf_unique
 
-/- warning: csupr_pos -> csupᵢ_pos is a dubious translation:
+/- warning: csupr_pos -> ciSup_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
-Case conversion may be inaccurate. Consider using '#align csupr_pos csupᵢ_posₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
+Case conversion may be inaccurate. Consider using '#align csupr_pos ciSup_posₓ'. -/
 @[simp]
-theorem csupᵢ_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
+theorem ciSup_pos {p : Prop} {f : p → α} (hp : p) : (⨆ h : p, f h) = f hp :=
   haveI := uniqueProp hp
-  csupᵢ_unique
-#align csupr_pos csupᵢ_pos
+  ciSup_unique
+#align csupr_pos ciSup_pos
 
-/- warning: cinfi_pos -> cinfᵢ_pos is a dubious translation:
+/- warning: cinfi_pos -> ciInf_pos is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iInf.{u1, 0} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (infᵢ.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
-Case conversion may be inaccurate. Consider using '#align cinfi_pos cinfᵢ_posₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {p : Prop} {f : p -> α} (hp : p), Eq.{succ u1} α (iInf.{u1, 0} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) p (fun (h : p) => f h)) (f hp)
+Case conversion may be inaccurate. Consider using '#align cinfi_pos ciInf_posₓ'. -/
 @[simp]
-theorem cinfᵢ_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
-  @csupᵢ_pos αᵒᵈ _ _ _ hp
-#align cinfi_pos cinfᵢ_pos
+theorem ciInf_pos {p : Prop} {f : p → α} (hp : p) : (⨅ h : p, f h) = f hp :=
+  @ciSup_pos αᵒᵈ _ _ _ hp
+#align cinfi_pos ciInf_pos
 
-/- warning: csupr_eq_of_forall_le_of_forall_lt_exists_gt -> csupᵢ_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
+/- warning: csupr_eq_of_forall_le_of_forall_lt_exists_gt -> ciSup_eq_of_forall_le_of_forall_lt_exists_gt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w (f i)))) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w (f i)))) -> (Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
-Case conversion may be inaccurate. Consider using '#align csupr_eq_of_forall_le_of_forall_lt_exists_gt csupᵢ_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) b) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w b) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) w (f i)))) -> (Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
+Case conversion may be inaccurate. Consider using '#align csupr_eq_of_forall_le_of_forall_lt_exists_gt ciSup_eq_of_forall_le_of_forall_lt_exists_gtₓ'. -/
 /-- Introduction rule to prove that `b` is the supremum of `f`: it suffices to check that `b`
 is larger than `f i` for all `i`, and that this is not the case of any `w<b`.
 See `supr_eq_of_forall_le_of_forall_lt_exists_gt` for a version in complete lattices. -/
-theorem csupᵢ_eq_of_forall_le_of_forall_lt_exists_gt [Nonempty ι] {f : ι → α} (h₁ : ∀ i, f i ≤ b)
+theorem ciSup_eq_of_forall_le_of_forall_lt_exists_gt [Nonempty ι] {f : ι → α} (h₁ : ∀ i, f i ≤ b)
     (h₂ : ∀ w, w < b → ∃ i, w < f i) : (⨆ i : ι, f i) = b :=
-  csupₛ_eq_of_forall_le_of_forall_lt_exists_gt (range_nonempty f) (forall_range_iff.mpr h₁)
+  csSup_eq_of_forall_le_of_forall_lt_exists_gt (range_nonempty f) (forall_range_iff.mpr h₁)
     fun w hw => exists_range_iff.mpr <| h₂ w hw
-#align csupr_eq_of_forall_le_of_forall_lt_exists_gt csupᵢ_eq_of_forall_le_of_forall_lt_exists_gt
+#align csupr_eq_of_forall_le_of_forall_lt_exists_gt ciSup_eq_of_forall_le_of_forall_lt_exists_gt
 
-/- warning: cinfi_eq_of_forall_ge_of_forall_gt_exists_lt -> cinfᵢ_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
+/- warning: cinfi_eq_of_forall_ge_of_forall_gt_exists_lt -> ciInf_eq_of_forall_ge_of_forall_gt_exists_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) w))) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) w))) -> (Eq.{succ u1} α (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
-Case conversion may be inaccurate. Consider using '#align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt cinfᵢ_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b (f i)) -> (forall (w : α), (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b w) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f i) w))) -> (Eq.{succ u1} α (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) ι (fun (i : ι) => f i)) b)
+Case conversion may be inaccurate. Consider using '#align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt ciInf_eq_of_forall_ge_of_forall_gt_exists_ltₓ'. -/
 /-- Introduction rule to prove that `b` is the infimum of `f`: it suffices to check that `b`
 is smaller than `f i` for all `i`, and that this is not the case of any `w>b`.
 See `infi_eq_of_forall_ge_of_forall_gt_exists_lt` for a version in complete lattices. -/
-theorem cinfᵢ_eq_of_forall_ge_of_forall_gt_exists_lt [Nonempty ι] {f : ι → α} (h₁ : ∀ i, b ≤ f i)
+theorem ciInf_eq_of_forall_ge_of_forall_gt_exists_lt [Nonempty ι] {f : ι → α} (h₁ : ∀ i, b ≤ f i)
     (h₂ : ∀ w, b < w → ∃ i, f i < w) : (⨅ i : ι, f i) = b :=
-  @csupᵢ_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _ ‹_› ‹_› ‹_›
-#align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt cinfᵢ_eq_of_forall_ge_of_forall_gt_exists_lt
+  @ciSup_eq_of_forall_le_of_forall_lt_exists_gt αᵒᵈ _ _ _ _ ‹_› ‹_› ‹_›
+#align cinfi_eq_of_forall_ge_of_forall_gt_exists_lt ciInf_eq_of_forall_ge_of_forall_gt_exists_lt
 
-/- warning: monotone.csupr_mem_Inter_Icc_of_antitone -> Monotone.csupᵢ_mem_Inter_Icc_of_antitone is a dubious translation:
+/- warning: monotone.csupr_mem_Inter_Icc_of_antitone -> Monotone.ciSup_mem_Inter_Icc_of_antitone is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) f) -> (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) g) -> (LE.le.{max u2 u1} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f g) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.interᵢ.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) f) -> (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) g) -> (LE.le.{max u2 u1} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f g) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) f) -> (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) g) -> (LE.le.{max u1 u2} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f g) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.interᵢ.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
-Case conversion may be inaccurate. Consider using '#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.csupᵢ_mem_Inter_Icc_of_antitoneₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Monotone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) f) -> (Antitone.{u2, u1} β α (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) g) -> (LE.le.{max u1 u2} (β -> α) (Pi.hasLe.{u2, u1} β (fun (ᾰ : β) => α) (fun (i : β) => Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) f g) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
+Case conversion may be inaccurate. Consider using '#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_Inter_Icc_of_antitoneₓ'. -/
 /-- Nested intervals lemma: if `f` is a monotone sequence, `g` is an antitone sequence, and
 `f n ≤ g n` for all `n`, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
-theorem Monotone.csupᵢ_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β → α} (hf : Monotone f)
+theorem Monotone.ciSup_mem_Inter_Icc_of_antitone [SemilatticeSup β] {f g : β → α} (hf : Monotone f)
     (hg : Antitone g) (h : f ≤ g) : (⨆ n, f n) ∈ ⋂ n, Icc (f n) (g n) :=
   by
   refine' mem_Inter.2 fun n => _
   haveI : Nonempty β := ⟨n⟩
   have : ∀ m, f m ≤ g n := fun m => hf.forall_le_of_antitone hg h m n
-  exact ⟨le_csupᵢ ⟨g <| n, forall_range_iff.2 this⟩ _, csupᵢ_le this⟩
-#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.csupᵢ_mem_Inter_Icc_of_antitone
+  exact ⟨le_ciSup ⟨g <| n, forall_range_iff.2 this⟩ _, ciSup_le this⟩
+#align monotone.csupr_mem_Inter_Icc_of_antitone Monotone.ciSup_mem_Inter_Icc_of_antitone
 
-/- warning: csupr_mem_Inter_Icc_of_antitone_Icc -> csupᵢ_mem_Inter_Icc_of_antitone_Icc is a dubious translation:
+/- warning: csupr_mem_Inter_Icc_of_antitone_Icc -> ciSup_mem_Inter_Icc_of_antitone_Icc is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β (Set.{u1} α) (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))) -> (forall (n : β), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f n) (g n)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.interᵢ.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β (Set.{u1} α) (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α))))))) (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))) -> (forall (n : β), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f n) (g n)) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β (Set.{u1} α) (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))) -> (forall (n : β), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f n) (g n)) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (supᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.interᵢ.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
-Case conversion may be inaccurate. Consider using '#align csupr_mem_Inter_Icc_of_antitone_Icc csupᵢ_mem_Inter_Icc_of_antitone_Iccₓ'. -/
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] {f : β -> α} {g : β -> α}, (Antitone.{u2, u1} β (Set.{u1} α) (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))) -> (forall (n : β), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (f n) (g n)) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (iSup.{u1, succ u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) β (fun (n : β) => f n)) (Set.iInter.{u1, succ u2} α β (fun (n : β) => Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (f n) (g n))))
+Case conversion may be inaccurate. Consider using '#align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_Inter_Icc_of_antitone_Iccₓ'. -/
 /-- Nested intervals lemma: if `[f n, g n]` is an antitone sequence of nonempty
 closed intervals, then `⨆ n, f n` belongs to all the intervals `[f n, g n]`. -/
-theorem csupᵢ_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α}
+theorem ciSup_mem_Inter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → α}
     (h : Antitone fun n => Icc (f n) (g n)) (h' : ∀ n, f n ≤ g n) :
     (⨆ n, f n) ∈ ⋂ n, Icc (f n) (g n) :=
-  Monotone.csupᵢ_mem_Inter_Icc_of_antitone
+  Monotone.ciSup_mem_Inter_Icc_of_antitone
     (fun m n hmn => ((Icc_subset_Icc_iff (h' n)).1 (h hmn)).1)
     (fun m n hmn => ((Icc_subset_Icc_iff (h' n)).1 (h hmn)).2) h'
-#align csupr_mem_Inter_Icc_of_antitone_Icc csupᵢ_mem_Inter_Icc_of_antitone_Icc
+#align csupr_mem_Inter_Icc_of_antitone_Icc ciSup_mem_Inter_Icc_of_antitone_Icc
 
-/- warning: cSup_eq_of_is_forall_le_of_forall_le_imp_ge -> csupₛ_eq_of_is_forall_le_of_forall_le_imp_ge is a dubious translation:
+/- warning: cSup_eq_of_is_forall_le_of_forall_le_imp_ge -> csSup_eq_of_is_forall_le_of_forall_le_imp_ge is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (ub : α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a ub)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b ub)) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (ub : α), (forall (a : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a ub)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b ub)) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (ub : α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a ub)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b ub)) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) b)
-Case conversion may be inaccurate. Consider using '#align cSup_eq_of_is_forall_le_of_forall_le_imp_ge csupₛ_eq_of_is_forall_le_of_forall_le_imp_geₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a b)) -> (forall (ub : α), (forall (a : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) a ub)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) b ub)) -> (Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) b)
+Case conversion may be inaccurate. Consider using '#align cSup_eq_of_is_forall_le_of_forall_le_imp_ge csSup_eq_of_is_forall_le_of_forall_le_imp_geₓ'. -/
 /-- Introduction rule to prove that b is the supremum of s: it suffices to check that
 1) b is an upper bound
 2) every other upper bound b' satisfies b ≤ b'.-/
-theorem csupₛ_eq_of_is_forall_le_of_forall_le_imp_ge (hs : s.Nonempty) (h_is_ub : ∀ a ∈ s, a ≤ b)
-    (h_b_le_ub : ∀ ub, (∀ a ∈ s, a ≤ ub) → b ≤ ub) : supₛ s = b :=
-  (csupₛ_le hs h_is_ub).antisymm (h_b_le_ub _ fun a => le_csupₛ ⟨b, h_is_ub⟩)
-#align cSup_eq_of_is_forall_le_of_forall_le_imp_ge csupₛ_eq_of_is_forall_le_of_forall_le_imp_ge
+theorem csSup_eq_of_is_forall_le_of_forall_le_imp_ge (hs : s.Nonempty) (h_is_ub : ∀ a ∈ s, a ≤ b)
+    (h_b_le_ub : ∀ ub, (∀ a ∈ s, a ≤ ub) → b ≤ ub) : sSup s = b :=
+  (csSup_le hs h_is_ub).antisymm (h_b_le_ub _ fun a => le_csSup ⟨b, h_is_ub⟩)
+#align cSup_eq_of_is_forall_le_of_forall_le_imp_ge csSup_eq_of_is_forall_le_of_forall_le_imp_ge
 
 end ConditionallyCompleteLattice
 
@@ -1495,14 +1495,14 @@ instance Pi.conditionallyCompleteLattice {ι : Type _} {α : ∀ i : ι, Type _}
   { Pi.lattice, Pi.supSet,
     Pi.infSet with
     le_cSup := fun s f ⟨g, hg⟩ hf i =>
-      le_csupₛ ⟨g i, Set.forall_range_iff.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
+      le_csSup ⟨g i, Set.forall_range_iff.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
     cSup_le := fun s f hs hf i =>
-      csupₛ_le (by haveI := hs.to_subtype <;> apply range_nonempty) fun b ⟨⟨g, hg⟩, hb⟩ =>
+      csSup_le (by haveI := hs.to_subtype <;> apply range_nonempty) fun b ⟨⟨g, hg⟩, hb⟩ =>
         hb ▸ hf hg i
     cInf_le := fun s f ⟨g, hg⟩ hf i =>
-      cinfₛ_le ⟨g i, Set.forall_range_iff.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
+      csInf_le ⟨g i, Set.forall_range_iff.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
     le_cInf := fun s f hs hf i =>
-      le_cinfₛ (by haveI := hs.to_subtype <;> apply range_nonempty) fun b ⟨⟨g, hg⟩, hb⟩ =>
+      le_csInf (by haveI := hs.to_subtype <;> apply range_nonempty) fun b ⟨⟨g, hg⟩, hb⟩ =>
         hb ▸ hf hg i }
 #align pi.conditionally_complete_lattice Pi.conditionallyCompleteLattice
 -/
@@ -1511,137 +1511,137 @@ section ConditionallyCompleteLinearOrder
 
 variable [ConditionallyCompleteLinearOrder α] {s t : Set α} {a b : α}
 
-/- warning: exists_lt_of_lt_cSup -> exists_lt_of_lt_csupₛ is a dubious translation:
+/- warning: exists_lt_of_lt_cSup -> exists_lt_of_lt_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b a)))
-Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup exists_lt_of_lt_csupₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b a)))
+Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup exists_lt_of_lt_csSupₓ'. -/
 /-- When b < Sup s, there is an element a in s with b < a, if s is nonempty and the order is
 a linear order. -/
-theorem exists_lt_of_lt_csupₛ (hs : s.Nonempty) (hb : b < supₛ s) : ∃ a ∈ s, b < a :=
+theorem exists_lt_of_lt_csSup (hs : s.Nonempty) (hb : b < sSup s) : ∃ a ∈ s, b < a :=
   by
   contrapose! hb
-  exact csupₛ_le hs hb
-#align exists_lt_of_lt_cSup exists_lt_of_lt_csupₛ
+  exact csSup_le hs hb
+#align exists_lt_of_lt_cSup exists_lt_of_lt_csSup
 
-/- warning: exists_lt_of_lt_csupr -> exists_lt_of_lt_csupᵢ is a dubious translation:
+/- warning: exists_lt_of_lt_csupr -> exists_lt_of_lt_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f)) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f)) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (f i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f)) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (f i)))
-Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr exists_lt_of_lt_csupᵢₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {b : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f)) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (f i)))
+Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr exists_lt_of_lt_ciSupₓ'. -/
 /-- Indexed version of the above lemma `exists_lt_of_lt_cSup`.
 When `b < supr f`, there is an element `i` such that `b < f i`.
 -/
-theorem exists_lt_of_lt_csupᵢ [Nonempty ι] {f : ι → α} (h : b < supᵢ f) : ∃ i, b < f i :=
-  let ⟨_, ⟨i, rfl⟩, h⟩ := exists_lt_of_lt_csupₛ (range_nonempty f) h
+theorem exists_lt_of_lt_ciSup [Nonempty ι] {f : ι → α} (h : b < iSup f) : ∃ i, b < f i :=
+  let ⟨_, ⟨i, rfl⟩, h⟩ := exists_lt_of_lt_csSup (range_nonempty f) h
   ⟨i, h⟩
-#align exists_lt_of_lt_csupr exists_lt_of_lt_csupᵢ
+#align exists_lt_of_lt_csupr exists_lt_of_lt_ciSup
 
-/- warning: exists_lt_of_cInf_lt -> exists_lt_of_cinfₛ_lt is a dubious translation:
+/- warning: exists_lt_of_cInf_lt -> exists_lt_of_csInf_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) b) -> (Exists.{succ u1} α (fun (a : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b)))
-Case conversion may be inaccurate. Consider using '#align exists_lt_of_cInf_lt exists_lt_of_cinfₛ_ltₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α}, (Set.Nonempty.{u1} α s) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) b) -> (Exists.{succ u1} α (fun (a : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) a b)))
+Case conversion may be inaccurate. Consider using '#align exists_lt_of_cInf_lt exists_lt_of_csInf_ltₓ'. -/
 /-- When Inf s < b, there is an element a in s with a < b, if s is nonempty and the order is
 a linear order.-/
-theorem exists_lt_of_cinfₛ_lt (hs : s.Nonempty) (hb : infₛ s < b) : ∃ a ∈ s, a < b :=
-  @exists_lt_of_lt_csupₛ αᵒᵈ _ _ _ hs hb
-#align exists_lt_of_cInf_lt exists_lt_of_cinfₛ_lt
+theorem exists_lt_of_csInf_lt (hs : s.Nonempty) (hb : sInf s < b) : ∃ a ∈ s, a < b :=
+  @exists_lt_of_lt_csSup αᵒᵈ _ _ _ hs hb
+#align exists_lt_of_cInf_lt exists_lt_of_csInf_lt
 
-/- warning: exists_lt_of_cinfi_lt -> exists_lt_of_cinfᵢ_lt is a dubious translation:
+/- warning: exists_lt_of_cinfi_lt -> exists_lt_of_ciInf_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) a) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) a) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (f i) a))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) a) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (f i) a))
-Case conversion may be inaccurate. Consider using '#align exists_lt_of_cinfi_lt exists_lt_of_cinfᵢ_ltₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {a : α} [_inst_2 : Nonempty.{u2} ι] {f : ι -> α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) a) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (f i) a))
+Case conversion may be inaccurate. Consider using '#align exists_lt_of_cinfi_lt exists_lt_of_ciInf_ltₓ'. -/
 /-- Indexed version of the above lemma `exists_lt_of_cInf_lt`
 When `infi f < a`, there is an element `i` such that `f i < a`.
 -/
-theorem exists_lt_of_cinfᵢ_lt [Nonempty ι] {f : ι → α} (h : infᵢ f < a) : ∃ i, f i < a :=
-  @exists_lt_of_lt_csupᵢ αᵒᵈ _ _ _ _ _ h
-#align exists_lt_of_cinfi_lt exists_lt_of_cinfᵢ_lt
+theorem exists_lt_of_ciInf_lt [Nonempty ι] {f : ι → α} (h : iInf f < a) : ∃ i, f i < a :=
+  @exists_lt_of_lt_ciSup αᵒᵈ _ _ _ _ _ h
+#align exists_lt_of_cinfi_lt exists_lt_of_ciInf_lt
 
 open Function
 
 variable [IsWellOrder α (· < ·)]
 
-/- warning: Inf_eq_argmin_on -> infₛ_eq_argmin_on is a dubious translation:
+/- warning: Inf_eq_argmin_on -> sInf_eq_argmin_on is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (IsWellOrder.to_isWellFounded.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) _inst_2)) s hs)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (IsWellOrder.to_isWellFounded.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) _inst_2)) s hs)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) _inst_2)) s hs)
-Case conversion may be inaccurate. Consider using '#align Inf_eq_argmin_on infₛ_eq_argmin_onₓ'. -/
-theorem infₛ_eq_argmin_on (hs : s.Nonempty) :
-    infₛ s = argminOn id (@IsWellFounded.wf α (· < ·) _) s hs :=
-  IsLeast.cinfₛ_eq ⟨argminOn_mem _ _ _ _, fun a ha => argminOn_le id _ _ ha⟩
-#align Inf_eq_argmin_on infₛ_eq_argmin_on
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) _inst_2)) s hs)
+Case conversion may be inaccurate. Consider using '#align Inf_eq_argmin_on sInf_eq_argmin_onₓ'. -/
+theorem sInf_eq_argmin_on (hs : s.Nonempty) :
+    sInf s = argminOn id (@IsWellFounded.wf α (· < ·) _) s hs :=
+  IsLeast.csInf_eq ⟨argminOn_mem _ _ _ _, fun a ha => argminOn_le id _ _ ha⟩
+#align Inf_eq_argmin_on sInf_eq_argmin_on
 
-/- warning: is_least_Inf -> isLeast_cinfₛ is a dubious translation:
+/- warning: is_least_Inf -> isLeast_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
-Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_cinfₛₓ'. -/
-theorem isLeast_cinfₛ (hs : s.Nonempty) : IsLeast s (infₛ s) :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
+Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_csInfₓ'. -/
+theorem isLeast_csInf (hs : s.Nonempty) : IsLeast s (sInf s) :=
   by
-  rw [infₛ_eq_argmin_on hs]
+  rw [sInf_eq_argmin_on hs]
   exact ⟨argmin_on_mem _ _ _ _, fun a ha => argmin_on_le id _ _ ha⟩
-#align is_least_Inf isLeast_cinfₛ
+#align is_least_Inf isLeast_csInf
 
-/- warning: le_cInf_iff' -> le_cinfₛ_iff' is a dubious translation:
+/- warning: le_cInf_iff' -> le_csInf_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
-Case conversion may be inaccurate. Consider using '#align le_cInf_iff' le_cinfₛ_iff'ₓ'. -/
-theorem le_cinfₛ_iff' (hs : s.Nonempty) : b ≤ infₛ s ↔ b ∈ lowerBounds s :=
-  le_isGLB_iff (isLeast_cinfₛ hs).IsGLB
-#align le_cInf_iff' le_cinfₛ_iff'
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
+Case conversion may be inaccurate. Consider using '#align le_cInf_iff' le_csInf_iff'ₓ'. -/
+theorem le_csInf_iff' (hs : s.Nonempty) : b ≤ sInf s ↔ b ∈ lowerBounds s :=
+  le_isGLB_iff (isLeast_csInf hs).IsGLB
+#align le_cInf_iff' le_csInf_iff'
 
-/- warning: Inf_mem -> cinfₛ_mem is a dubious translation:
+/- warning: Inf_mem -> csInf_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
-Case conversion may be inaccurate. Consider using '#align Inf_mem cinfₛ_memₓ'. -/
-theorem cinfₛ_mem (hs : s.Nonempty) : infₛ s ∈ s :=
-  (isLeast_cinfₛ hs).1
-#align Inf_mem cinfₛ_mem
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+Case conversion may be inaccurate. Consider using '#align Inf_mem csInf_memₓ'. -/
+theorem csInf_mem (hs : s.Nonempty) : sInf s ∈ s :=
+  (isLeast_csInf hs).1
+#align Inf_mem csInf_mem
 
-/- warning: infi_mem -> cinfᵢ_mem is a dubious translation:
+/- warning: infi_mem -> ciInf_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
-Case conversion may be inaccurate. Consider using '#align infi_mem cinfᵢ_memₓ'. -/
-theorem cinfᵢ_mem [Nonempty ι] (f : ι → α) : infᵢ f ∈ range f :=
-  cinfₛ_mem (range_nonempty f)
-#align infi_mem cinfᵢ_mem
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
+Case conversion may be inaccurate. Consider using '#align infi_mem ciInf_memₓ'. -/
+theorem ciInf_mem [Nonempty ι] (f : ι → α) : iInf f ∈ range f :=
+  csInf_mem (range_nonempty f)
+#align infi_mem ciInf_mem
 
-/- warning: monotone_on.map_Inf -> MonotoneOn.map_cinfₛ is a dubious translation:
+/- warning: monotone_on.map_Inf -> MonotoneOn.map_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone_on.map_Inf MonotoneOn.map_cinfₛₓ'. -/
-theorem MonotoneOn.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
-    (hf : MonotoneOn f s) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=
-  (hf.map_isLeast (isLeast_cinfₛ hs)).cinfₛ_eq.symm
-#align monotone_on.map_Inf MonotoneOn.map_cinfₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone_on.map_Inf MonotoneOn.map_csInfₓ'. -/
+theorem MonotoneOn.map_csInf {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
+    (hf : MonotoneOn f s) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
+  (hf.map_isLeast (isLeast_csInf hs)).csInf_eq.symm
+#align monotone_on.map_Inf MonotoneOn.map_csInf
 
-/- warning: monotone.map_Inf -> Monotone.map_cinfₛ is a dubious translation:
+/- warning: monotone.map_Inf -> Monotone.map_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
-Case conversion may be inaccurate. Consider using '#align monotone.map_Inf Monotone.map_cinfₛₓ'. -/
-theorem Monotone.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
-    (hf : Monotone f) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=
-  (hf.map_isLeast (isLeast_cinfₛ hs)).cinfₛ_eq.symm
-#align monotone.map_Inf Monotone.map_cinfₛ
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+Case conversion may be inaccurate. Consider using '#align monotone.map_Inf Monotone.map_csInfₓ'. -/
+theorem Monotone.map_csInf {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
+    (hf : Monotone f) (hs : s.Nonempty) : f (sInf s) = sInf (f '' s) :=
+  (hf.map_isLeast (isLeast_csInf hs)).csInf_eq.symm
+#align monotone.map_Inf Monotone.map_csInf
 
 end ConditionallyCompleteLinearOrder
 
@@ -1656,210 +1656,210 @@ section ConditionallyCompleteLinearOrderBot
 
 variable [ConditionallyCompleteLinearOrderBot α]
 
-/- warning: cSup_empty -> csupₛ_empty is a dubious translation:
+/- warning: cSup_empty -> csSup_empty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align cSup_empty csupₛ_emptyₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align cSup_empty csSup_emptyₓ'. -/
 @[simp]
-theorem csupₛ_empty : (supₛ ∅ : α) = ⊥ :=
+theorem csSup_empty : (sSup ∅ : α) = ⊥ :=
   ConditionallyCompleteLinearOrderBot.cSup_empty
-#align cSup_empty csupₛ_empty
+#align cSup_empty csSup_empty
 
-/- warning: csupr_of_empty -> csupᵢ_of_empty is a dubious translation:
+/- warning: csupr_of_empty -> ciSup_of_empty is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align csupr_of_empty csupᵢ_of_emptyₓ'. -/
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : IsEmpty.{u2} ι] (f : ι -> α), Eq.{succ u1} α (iSup.{u1, u2} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align csupr_of_empty ciSup_of_emptyₓ'. -/
 @[simp]
-theorem csupᵢ_of_empty [IsEmpty ι] (f : ι → α) : (⨆ i, f i) = ⊥ := by
-  rw [supᵢ_of_empty', csupₛ_empty]
-#align csupr_of_empty csupᵢ_of_empty
+theorem ciSup_of_empty [IsEmpty ι] (f : ι → α) : (⨆ i, f i) = ⊥ := by
+  rw [iSup_of_empty', csSup_empty]
+#align csupr_of_empty ciSup_of_empty
 
-/- warning: csupr_false -> csupᵢ_false is a dubious translation:
+/- warning: csupr_false -> ciSup_false is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : False -> α), Eq.{succ u1} α (supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) False (fun (i : False) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : False -> α), Eq.{succ u1} α (iSup.{u1, 0} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) False (fun (i : False) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : False -> α), Eq.{succ u1} α (supᵢ.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) False (fun (i : False) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align csupr_false csupᵢ_falseₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : False -> α), Eq.{succ u1} α (iSup.{u1, 0} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) False (fun (i : False) => f i)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align csupr_false ciSup_falseₓ'. -/
 @[simp]
-theorem csupᵢ_false (f : False → α) : (⨆ i, f i) = ⊥ :=
-  csupᵢ_of_empty f
-#align csupr_false csupᵢ_false
+theorem ciSup_false (f : False → α) : (⨆ i, f i) = ⊥ :=
+  ciSup_of_empty f
+#align csupr_false ciSup_false
 
-/- warning: cInf_univ -> cinfₛ_univ is a dubious translation:
+/- warning: cInf_univ -> csInf_univ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (Set.univ.{u1} α)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (Set.univ.{u1} α)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toHasBot.{u1} α _inst_1))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (Set.univ.{u1} α)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
-Case conversion may be inaccurate. Consider using '#align cInf_univ cinfₛ_univₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α], Eq.{succ u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) (Set.univ.{u1} α)) (Bot.bot.{u1} α (ConditionallyCompleteLinearOrderBot.toBot.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align cInf_univ csInf_univₓ'. -/
 @[simp]
-theorem cinfₛ_univ : infₛ (univ : Set α) = ⊥ :=
-  isLeast_univ.cinfₛ_eq
-#align cInf_univ cinfₛ_univ
+theorem csInf_univ : sInf (univ : Set α) = ⊥ :=
+  isLeast_univ.csInf_eq
+#align cInf_univ csInf_univ
 
-/- warning: is_lub_cSup' -> isLUB_csupₛ' is a dubious translation:
+/- warning: is_lub_cSup' -> isLUB_csSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s))
-Case conversion may be inaccurate. Consider using '#align is_lub_cSup' isLUB_csupₛ'ₓ'. -/
-theorem isLUB_csupₛ' {s : Set α} (hs : BddAbove s) : IsLUB s (supₛ s) :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (IsLUB.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s))
+Case conversion may be inaccurate. Consider using '#align is_lub_cSup' isLUB_csSup'ₓ'. -/
+theorem isLUB_csSup' {s : Set α} (hs : BddAbove s) : IsLUB s (sSup s) :=
   by
   rcases eq_empty_or_nonempty s with (rfl | hne)
-  · simp only [csupₛ_empty, isLUB_empty]
-  · exact isLUB_csupₛ hne hs
-#align is_lub_cSup' isLUB_csupₛ'
+  · simp only [csSup_empty, isLUB_empty]
+  · exact isLUB_csSup hne hs
+#align is_lub_cSup' isLUB_csSup'
 
-/- warning: cSup_le_iff' -> csupₛ_le_iff' is a dubious translation:
+/- warning: cSup_le_iff' -> csSup_le_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) x a)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) x a)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) x a)))
-Case conversion may be inaccurate. Consider using '#align cSup_le_iff' csupₛ_le_iff'ₓ'. -/
-theorem csupₛ_le_iff' {s : Set α} (hs : BddAbove s) {a : α} : supₛ s ≤ a ↔ ∀ x ∈ s, x ≤ a :=
-  isLUB_le_iff (isLUB_csupₛ' hs)
-#align cSup_le_iff' csupₛ_le_iff'
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) x a)))
+Case conversion may be inaccurate. Consider using '#align cSup_le_iff' csSup_le_iff'ₓ'. -/
+theorem csSup_le_iff' {s : Set α} (hs : BddAbove s) {a : α} : sSup s ≤ a ↔ ∀ x ∈ s, x ≤ a :=
+  isLUB_le_iff (isLUB_csSup' hs)
+#align cSup_le_iff' csSup_le_iff'
 
-/- warning: cSup_le' -> csupₛ_le' is a dubious translation:
+/- warning: cSup_le' -> csSup_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
-Case conversion may be inaccurate. Consider using '#align cSup_le' csupₛ_le'ₓ'. -/
-theorem csupₛ_le' {s : Set α} {a : α} (h : a ∈ upperBounds s) : supₛ s ≤ a :=
-  (csupₛ_le_iff' ⟨a, h⟩).2 h
-#align cSup_le' csupₛ_le'
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
+Case conversion may be inaccurate. Consider using '#align cSup_le' csSup_le'ₓ'. -/
+theorem csSup_le' {s : Set α} {a : α} (h : a ∈ upperBounds s) : sSup s ≤ a :=
+  (csSup_le_iff' ⟨a, h⟩).2 h
+#align cSup_le' csSup_le'
 
-/- warning: le_cSup_iff' -> le_csupₛ_iff' is a dubious translation:
+/- warning: le_cSup_iff' -> le_csSup_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
-Case conversion may be inaccurate. Consider using '#align le_cSup_iff' le_csupₛ_iff'ₓ'. -/
-theorem le_csupₛ_iff' {s : Set α} {a : α} (h : BddAbove s) :
-    a ≤ supₛ s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
-  ⟨fun h b hb => le_trans h (csupₛ_le' hb), fun hb => hb _ fun x => le_csupₛ h⟩
-#align le_cSup_iff' le_csupₛ_iff'
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (upperBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+Case conversion may be inaccurate. Consider using '#align le_cSup_iff' le_csSup_iff'ₓ'. -/
+theorem le_csSup_iff' {s : Set α} {a : α} (h : BddAbove s) :
+    a ≤ sSup s ↔ ∀ b, b ∈ upperBounds s → a ≤ b :=
+  ⟨fun h b hb => le_trans h (csSup_le' hb), fun hb => hb _ fun x => le_csSup h⟩
+#align le_cSup_iff' le_csSup_iff'
 
-/- warning: le_csupr_iff' -> le_csupᵢ_iff' is a dubious translation:
+/- warning: le_csupr_iff' -> le_ciSup_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (s i) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : ι -> α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι s)) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (s i) b) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {s : ι -> α} {a : α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι s)) -> (Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (s i) b) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a b)))
-Case conversion may be inaccurate. Consider using '#align le_csupr_iff' le_csupᵢ_iff'ₓ'. -/
-theorem le_csupᵢ_iff' {s : ι → α} {a : α} (h : BddAbove (range s)) :
-    a ≤ supᵢ s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by simp [supᵢ, h, le_csupₛ_iff', upperBounds]
-#align le_csupr_iff' le_csupᵢ_iff'
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {s : ι -> α} {a : α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι s)) -> (Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι s)) (forall (b : α), (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (s i) b) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a b)))
+Case conversion may be inaccurate. Consider using '#align le_csupr_iff' le_ciSup_iff'ₓ'. -/
+theorem le_ciSup_iff' {s : ι → α} {a : α} (h : BddAbove (range s)) :
+    a ≤ iSup s ↔ ∀ b, (∀ i, s i ≤ b) → a ≤ b := by simp [iSup, h, le_csSup_iff', upperBounds]
+#align le_csupr_iff' le_ciSup_iff'
 
-/- warning: le_cInf_iff'' -> le_cinfₛ_iff'' is a dubious translation:
+/- warning: le_cInf_iff'' -> le_csInf_iff'' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
-Case conversion may be inaccurate. Consider using '#align le_cInf_iff'' le_cinfₛ_iff''ₓ'. -/
-theorem le_cinfₛ_iff'' {s : Set α} {a : α} (ne : s.Nonempty) :
-    a ≤ infₛ s ↔ ∀ b : α, b ∈ s → a ≤ b :=
-  le_cinfₛ_iff ⟨⊥, fun a _ => bot_le⟩ Ne
-#align le_cInf_iff'' le_cinfₛ_iff''
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (forall (b : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+Case conversion may be inaccurate. Consider using '#align le_cInf_iff'' le_csInf_iff''ₓ'. -/
+theorem le_csInf_iff'' {s : Set α} {a : α} (ne : s.Nonempty) :
+    a ≤ sInf s ↔ ∀ b : α, b ∈ s → a ≤ b :=
+  le_csInf_iff ⟨⊥, fun a _ => bot_le⟩ Ne
+#align le_cInf_iff'' le_csInf_iff''
 
-/- warning: le_cinfi_iff' -> le_cinfᵢ_iff' is a dubious translation:
+/- warning: le_cinfi_iff' -> le_ciInf_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i))
-Case conversion may be inaccurate. Consider using '#align le_cinfi_iff' le_cinfᵢ_iff'ₓ'. -/
-theorem le_cinfᵢ_iff' [Nonempty ι] {f : ι → α} {a : α} : a ≤ infᵢ f ↔ ∀ i, a ≤ f i :=
-  le_cinfᵢ_iff ⟨⊥, fun a _ => bot_le⟩
-#align le_cinfi_iff' le_cinfᵢ_iff'
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] [_inst_2 : Nonempty.{u2} ι] {f : ι -> α} {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iInf.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f)) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i))
+Case conversion may be inaccurate. Consider using '#align le_cinfi_iff' le_ciInf_iff'ₓ'. -/
+theorem le_ciInf_iff' [Nonempty ι] {f : ι → α} {a : α} : a ≤ iInf f ↔ ∀ i, a ≤ f i :=
+  le_ciInf_iff ⟨⊥, fun a _ => bot_le⟩
+#align le_cinfi_iff' le_ciInf_iff'
 
-/- warning: cInf_le' -> cinfₛ_le' is a dubious translation:
+/- warning: cInf_le' -> csInf_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
-Case conversion may be inaccurate. Consider using '#align cInf_le' cinfₛ_le'ₓ'. -/
-theorem cinfₛ_le' {s : Set α} {a : α} (h : a ∈ s) : infₛ s ≤ a :=
-  cinfₛ_le ⟨⊥, fun a _ => bot_le⟩ h
-#align cInf_le' cinfₛ_le'
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) a)
+Case conversion may be inaccurate. Consider using '#align cInf_le' csInf_le'ₓ'. -/
+theorem csInf_le' {s : Set α} {a : α} (h : a ∈ s) : sInf s ≤ a :=
+  csInf_le ⟨⊥, fun a _ => bot_le⟩ h
+#align cInf_le' csInf_le'
 
-/- warning: cinfi_le' -> cinfᵢ_le' is a dubious translation:
+/- warning: cinfi_le' -> ciInf_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (f i)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α) (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iInf.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (f i)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (infᵢ.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι f) (f i)
-Case conversion may be inaccurate. Consider using '#align cinfi_le' cinfᵢ_le'ₓ'. -/
-theorem cinfᵢ_le' (f : ι → α) (i : ι) : infᵢ f ≤ f i :=
-  cinfᵢ_le ⟨⊥, fun a _ => bot_le⟩ _
-#align cinfi_le' cinfᵢ_le'
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α) (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iInf.{u2, u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι f) (f i)
+Case conversion may be inaccurate. Consider using '#align cinfi_le' ciInf_le'ₓ'. -/
+theorem ciInf_le' (f : ι → α) (i : ι) : iInf f ≤ f i :=
+  ciInf_le ⟨⊥, fun a _ => bot_le⟩ _
+#align cinfi_le' ciInf_le'
 
-/- warning: exists_lt_of_lt_cSup' -> exists_lt_of_lt_csupₛ' is a dubious translation:
+/- warning: exists_lt_of_lt_cSup' -> exists_lt_of_lt_csSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
-Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup' exists_lt_of_lt_csupₛ'ₓ'. -/
-theorem exists_lt_of_lt_csupₛ' {s : Set α} {a : α} (h : a < supₛ s) : ∃ b ∈ s, a < b :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) -> (Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a b)))
+Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'ₓ'. -/
+theorem exists_lt_of_lt_csSup' {s : Set α} {a : α} (h : a < sSup s) : ∃ b ∈ s, a < b :=
   by
   contrapose! h
-  exact csupₛ_le' h
-#align exists_lt_of_lt_cSup' exists_lt_of_lt_csupₛ'
+  exact csSup_le' h
+#align exists_lt_of_lt_cSup' exists_lt_of_lt_csSup'
 
-/- warning: csupr_le_iff' -> csupᵢ_le_iff' is a dubious translation:
+/- warning: csupr_le_iff' -> ciSup_le_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f)) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f)) -> (forall {a : α}, Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a) (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f)) -> (forall {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i)) a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) a))
-Case conversion may be inaccurate. Consider using '#align csupr_le_iff' csupᵢ_le_iff'ₓ'. -/
-theorem csupᵢ_le_iff' {f : ι → α} (h : BddAbove (range f)) {a : α} :
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f)) -> (forall {a : α}, Iff (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i)) a) (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) a))
+Case conversion may be inaccurate. Consider using '#align csupr_le_iff' ciSup_le_iff'ₓ'. -/
+theorem ciSup_le_iff' {f : ι → α} (h : BddAbove (range f)) {a : α} :
     (⨆ i, f i) ≤ a ↔ ∀ i, f i ≤ a :=
-  (csupₛ_le_iff' h).trans forall_range_iff
-#align csupr_le_iff' csupᵢ_le_iff'
+  (csSup_le_iff' h).trans forall_range_iff
+#align csupr_le_iff' ciSup_le_iff'
 
-/- warning: csupr_le' -> csupᵢ_le' is a dubious translation:
+/- warning: csupr_le' -> ciSup_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) a) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i)) a)
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i)) a)
-Case conversion may be inaccurate. Consider using '#align csupr_le' csupᵢ_le'ₓ'. -/
-theorem csupᵢ_le' {f : ι → α} {a : α} (h : ∀ i, f i ≤ a) : (⨆ i, f i) ≤ a :=
-  csupₛ_le' <| forall_range_iff.2 h
-#align csupr_le' csupᵢ_le'
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α} {a : α}, (forall (i : ι), LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) a) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i)) a)
+Case conversion may be inaccurate. Consider using '#align csupr_le' ciSup_le'ₓ'. -/
+theorem ciSup_le' {f : ι → α} {a : α} (h : ∀ i, f i ≤ a) : (⨆ i, f i) ≤ a :=
+  csSup_le' <| forall_range_iff.2 h
+#align csupr_le' ciSup_le'
 
-/- warning: exists_lt_of_lt_csupr' -> exists_lt_of_lt_csupᵢ' is a dubious translation:
+/- warning: exists_lt_of_lt_csupr' -> exists_lt_of_lt_ciSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i)))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {f : ι -> α} {a : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u2} ι (fun (i : ι) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) a (f i)))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α} {a : α}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (f i)))
-Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr' exists_lt_of_lt_csupᵢ'ₓ'. -/
-theorem exists_lt_of_lt_csupᵢ' {f : ι → α} {a : α} (h : a < ⨆ i, f i) : ∃ i, a < f i :=
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {f : ι -> α} {a : α}, (LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι (fun (i : ι) => f i))) -> (Exists.{u1} ι (fun (i : ι) => LT.lt.{u2} α (Preorder.toLT.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) a (f i)))
+Case conversion may be inaccurate. Consider using '#align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'ₓ'. -/
+theorem exists_lt_of_lt_ciSup' {f : ι → α} {a : α} (h : a < ⨆ i, f i) : ∃ i, a < f i :=
   by
   contrapose! h
-  exact csupᵢ_le' h
-#align exists_lt_of_lt_csupr' exists_lt_of_lt_csupᵢ'
+  exact ciSup_le' h
+#align exists_lt_of_lt_csupr' exists_lt_of_lt_ciSup'
 
-/- warning: csupr_mono' -> csupᵢ_mono' is a dubious translation:
+/- warning: csupr_mono' -> ciSup_mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (supᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι' g))
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (iSup.{u1, u2} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι f) (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) ι' g))
 but is expected to have type
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (supᵢ.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι f) (supᵢ.{u2, u3} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι' g))
-Case conversion may be inaccurate. Consider using '#align csupr_mono' csupᵢ_mono'ₓ'. -/
-theorem csupᵢ_mono' {ι'} {f : ι → α} {g : ι' → α} (hg : BddAbove (range g))
-    (h : ∀ i, ∃ i', f i ≤ g i') : supᵢ f ≤ supᵢ g :=
-  csupᵢ_le' fun i => Exists.elim (h i) (le_csupᵢ_of_le hg)
-#align csupr_mono' csupᵢ_mono'
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] {ι' : Sort.{u3}} {f : ι -> α} {g : ι' -> α}, (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u3} α ι' g)) -> (forall (i : ι), Exists.{u3} ι' (fun (i' : ι') => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (f i) (g i'))) -> (LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))))))) (iSup.{u2, u1} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι f) (iSup.{u2, u3} α (ConditionallyCompleteLattice.toSupSet.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1))) ι' g))
+Case conversion may be inaccurate. Consider using '#align csupr_mono' ciSup_mono'ₓ'. -/
+theorem ciSup_mono' {ι'} {f : ι → α} {g : ι' → α} (hg : BddAbove (range g))
+    (h : ∀ i, ∃ i', f i ≤ g i') : iSup f ≤ iSup g :=
+  ciSup_le' fun i => Exists.elim (h i) (le_ciSup_of_le hg)
+#align csupr_mono' ciSup_mono'
 
-/- warning: cInf_le_cInf' -> cinfₛ_le_cinfₛ' is a dubious translation:
+/- warning: cInf_le_cInf' -> csInf_le_csInf' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
-Case conversion may be inaccurate. Consider using '#align cInf_le_cInf' cinfₛ_le_cinfₛ'ₓ'. -/
-theorem cinfₛ_le_cinfₛ' {s t : Set α} (h₁ : t.Nonempty) (h₂ : t ⊆ s) : infₛ s ≤ infₛ t :=
-  cinfₛ_le_cinfₛ (OrderBot.bddBelow s) h₁ h₂
-#align cInf_le_cInf' cinfₛ_le_cinfₛ'
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) t))
+Case conversion may be inaccurate. Consider using '#align cInf_le_cInf' csInf_le_csInf'ₓ'. -/
+theorem csInf_le_csInf' {s t : Set α} (h₁ : t.Nonempty) (h₂ : t ⊆ s) : sInf s ≤ sInf t :=
+  csInf_le_csInf (OrderBot.bddBelow s) h₁ h₂
+#align cInf_le_cInf' csInf_le_csInf'
 
 end ConditionallyCompleteLinearOrderBot
 
@@ -1869,16 +1869,16 @@ open Classical
 
 variable [ConditionallyCompleteLinearOrderBot α]
 
-/- warning: with_top.is_lub_Sup' -> WithTop.isLUB_supₛ' is a dubious translation:
+/- warning: with_top.is_lub_Sup' -> WithTop.isLUB_sSup' is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (Set.Nonempty.{u1} (WithTop.{u1} β) s) -> (IsLUB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (SupSet.supₛ.{u1} (WithTop.{u1} β) (WithTop.hasSup.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (ConditionallyCompleteLattice.toHasSup.{u1} β _inst_2)) s))
+  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (Set.Nonempty.{u1} (WithTop.{u1} β) s) -> (IsLUB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (SupSet.sSup.{u1} (WithTop.{u1} β) (WithTop.hasSup.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (ConditionallyCompleteLattice.toHasSup.{u1} β _inst_2)) s))
 but is expected to have type
-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (Set.Nonempty.{u1} (WithTop.{u1} β) s) -> (IsLUB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (SupSet.supₛ.{u1} (WithTop.{u1} β) (instSupSetWithTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align with_top.is_lub_Sup' WithTop.isLUB_supₛ'ₓ'. -/
+  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (Set.Nonempty.{u1} (WithTop.{u1} β) s) -> (IsLUB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (SupSet.sSup.{u1} (WithTop.{u1} β) (instSupSetWithTop.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2)) s))
+Case conversion may be inaccurate. Consider using '#align with_top.is_lub_Sup' WithTop.isLUB_sSup'ₓ'. -/
 /-- The Sup of a non-empty set is its least upper bound for a conditionally
 complete lattice with a top. -/
-theorem isLUB_supₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
-    (hs : s.Nonempty) : IsLUB s (supₛ s) := by
+theorem isLUB_sSup' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
+    (hs : s.Nonempty) : IsLUB s (sSup s) := by
   constructor
   · show ite _ _ _ ∈ _
     split_ifs
@@ -1887,7 +1887,7 @@ theorem isLUB_supₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (
     · rintro (⟨⟩ | a) ha
       · contradiction
       apply some_le_some.2
-      exact le_csupₛ h_1 ha
+      exact le_csSup h_1 ha
     · intro _ _
       exact le_top
   · show ite _ _ _ ∈ _
@@ -1897,7 +1897,7 @@ theorem isLUB_supₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (
       · exact False.elim (not_top_le_coe a (ha h))
     · rintro (⟨⟩ | b) hb
       · exact le_top
-      refine' some_le_some.2 (csupₛ_le _ _)
+      refine' some_le_some.2 (csSup_le _ _)
       · rcases hs with ⟨⟨⟩ | b, hb⟩
         · exact absurd hb h
         · exact ⟨b, hb⟩
@@ -1910,40 +1910,40 @@ theorem isLUB_supₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (
         use b
         intro a ha
         exact some_le_some.1 (hb ha)
-#align with_top.is_lub_Sup' WithTop.isLUB_supₛ'
+#align with_top.is_lub_Sup' WithTop.isLUB_sSup'
 
-/- warning: with_top.is_lub_Sup -> WithTop.isLUB_supₛ is a dubious translation:
+/- warning: with_top.is_lub_Sup -> WithTop.isLUB_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsLUB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (SupSet.supₛ.{u1} (WithTop.{u1} α) (WithTop.hasSup.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsLUB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (SupSet.sSup.{u1} (WithTop.{u1} α) (WithTop.hasSup.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsLUB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (SupSet.supₛ.{u1} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
-Case conversion may be inaccurate. Consider using '#align with_top.is_lub_Sup WithTop.isLUB_supₛₓ'. -/
-theorem isLUB_supₛ (s : Set (WithTop α)) : IsLUB s (supₛ s) :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsLUB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (SupSet.sSup.{u1} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
+Case conversion may be inaccurate. Consider using '#align with_top.is_lub_Sup WithTop.isLUB_sSupₓ'. -/
+theorem isLUB_sSup (s : Set (WithTop α)) : IsLUB s (sSup s) :=
   by
   cases' s.eq_empty_or_nonempty with hs hs
   · rw [hs]
     show IsLUB ∅ (ite _ _ _)
     split_ifs
     · cases h
-    · rw [preimage_empty, csupₛ_empty]
+    · rw [preimage_empty, csSup_empty]
       exact isLUB_empty
     · exfalso
       apply h_1
       use ⊥
       rintro a ⟨⟩
   exact is_lub_Sup' hs
-#align with_top.is_lub_Sup WithTop.isLUB_supₛ
+#align with_top.is_lub_Sup WithTop.isLUB_sSup
 
-/- warning: with_top.is_glb_Inf' -> WithTop.isGLB_infₛ' is a dubious translation:
+/- warning: with_top.is_glb_Inf' -> WithTop.isGLB_sInf' is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (BddBelow.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s) -> (IsGLB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (InfSet.infₛ.{u1} (WithTop.{u1} β) (WithTop.hasInf.{u1} β (ConditionallyCompleteLattice.toHasInf.{u1} β _inst_2)) s))
+  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (BddBelow.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s) -> (IsGLB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (InfSet.sInf.{u1} (WithTop.{u1} β) (WithTop.hasInf.{u1} β (ConditionallyCompleteLattice.toHasInf.{u1} β _inst_2)) s))
 but is expected to have type
-  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (BddBelow.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s) -> (IsGLB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (InfSet.infₛ.{u1} (WithTop.{u1} β) (instInfSetWithTop.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2)) s))
-Case conversion may be inaccurate. Consider using '#align with_top.is_glb_Inf' WithTop.isGLB_infₛ'ₓ'. -/
+  forall {β : Type.{u1}} [_inst_2 : ConditionallyCompleteLattice.{u1} β] {s : Set.{u1} (WithTop.{u1} β)}, (BddBelow.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s) -> (IsGLB.{u1} (WithTop.{u1} β) (WithTop.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) s (InfSet.sInf.{u1} (WithTop.{u1} β) (instInfSetWithTop.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2)) s))
+Case conversion may be inaccurate. Consider using '#align with_top.is_glb_Inf' WithTop.isGLB_sInf'ₓ'. -/
 /-- The Inf of a bounded-below set is its greatest lower bound for a conditionally
 complete lattice with a top. -/
-theorem isGLB_infₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
-    (hs : BddBelow s) : IsGLB s (infₛ s) := by
+theorem isGLB_sInf' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (WithTop β)}
+    (hs : BddBelow s) : IsGLB s (sInf s) := by
   constructor
   · show ite _ _ _ ∈ _
     split_ifs
@@ -1951,7 +1951,7 @@ theorem isGLB_infₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (
       exact top_le_iff.2 (Set.mem_singleton_iff.1 (h ha))
     · rintro (⟨⟩ | a) ha
       · exact le_top
-      refine' some_le_some.2 (cinfₛ_le _ ha)
+      refine' some_le_some.2 (csInf_le _ ha)
       rcases hs with ⟨⟨⟩ | b, hb⟩
       · exfalso
         apply h
@@ -1970,7 +1970,7 @@ theorem isGLB_infₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (
         apply h
         intro b hb
         exact Set.mem_singleton_iff.2 (top_le_iff.1 (ha hb))
-      · refine' some_le_some.2 (le_cinfₛ _ _)
+      · refine' some_le_some.2 (le_csInf _ _)
         ·
           classical
             contrapose! h
@@ -1980,15 +1980,15 @@ theorem isGLB_infₛ' {β : Type _} [ConditionallyCompleteLattice β] {s : Set (
         · intro b hb
           rw [← some_le_some]
           exact ha hb
-#align with_top.is_glb_Inf' WithTop.isGLB_infₛ'
+#align with_top.is_glb_Inf' WithTop.isGLB_sInf'
 
-/- warning: with_top.is_glb_Inf -> WithTop.isGLB_infₛ is a dubious translation:
+/- warning: with_top.is_glb_Inf -> WithTop.isGLB_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsGLB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (InfSet.infₛ.{u1} (WithTop.{u1} α) (WithTop.hasInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsGLB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (InfSet.sInf.{u1} (WithTop.{u1} α) (WithTop.hasInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsGLB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (InfSet.infₛ.{u1} (WithTop.{u1} α) (instInfSetWithTop.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
-Case conversion may be inaccurate. Consider using '#align with_top.is_glb_Inf WithTop.isGLB_infₛₓ'. -/
-theorem isGLB_infₛ (s : Set (WithTop α)) : IsGLB s (infₛ s) :=
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (s : Set.{u1} (WithTop.{u1} α)), IsGLB.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))))))) s (InfSet.sInf.{u1} (WithTop.{u1} α) (instInfSetWithTop.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) s)
+Case conversion may be inaccurate. Consider using '#align with_top.is_glb_Inf WithTop.isGLB_sInfₓ'. -/
+theorem isGLB_sInf (s : Set (WithTop α)) : IsGLB s (sInf s) :=
   by
   by_cases hs : BddBelow s
   · exact is_glb_Inf' hs
@@ -1997,41 +1997,41 @@ theorem isGLB_infₛ (s : Set (WithTop α)) : IsGLB s (infₛ s) :=
     use ⊥
     intro _ _
     exact bot_le
-#align with_top.is_glb_Inf WithTop.isGLB_infₛ
+#align with_top.is_glb_Inf WithTop.isGLB_sInf
 
 noncomputable instance : CompleteLinearOrder (WithTop α) :=
   { WithTop.linearOrder, WithTop.lattice, WithTop.orderTop,
     WithTop.orderBot with
-    supₛ := supₛ
-    le_sup := fun s => (isLUB_supₛ s).1
-    sup_le := fun s => (isLUB_supₛ s).2
-    infₛ := infₛ
-    le_inf := fun s => (isGLB_infₛ s).2
-    inf_le := fun s => (isGLB_infₛ s).1 }
+    sSup := sSup
+    le_sup := fun s => (isLUB_sSup s).1
+    sup_le := fun s => (isLUB_sSup s).2
+    sInf := sInf
+    le_inf := fun s => (isGLB_sInf s).2
+    inf_le := fun s => (isGLB_sInf s).1 }
 
-/- warning: with_top.coe_Sup -> WithTop.coe_supₛ is a dubious translation:
+/- warning: with_top.coe_Sup -> WithTop.coe_sSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Eq.{succ u1} (WithTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (supᵢ.{u1, succ u1} (WithTop.{u1} α) (WithTop.hasSup.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => supᵢ.{u1, 0} (WithTop.{u1} α) (WithTop.hasSup.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) a))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Eq.{succ u1} (WithTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (iSup.{u1, succ u1} (WithTop.{u1} α) (WithTop.hasSup.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => iSup.{u1, 0} (WithTop.{u1} α) (WithTop.hasSup.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) a))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Eq.{succ u1} (WithTop.{u1} α) (WithTop.some.{u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (supᵢ.{u1, succ u1} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => supᵢ.{u1, 0} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => WithTop.some.{u1} α a))))
-Case conversion may be inaccurate. Consider using '#align with_top.coe_Sup WithTop.coe_supₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) s) -> (Eq.{succ u1} (WithTop.{u1} α) (WithTop.some.{u1} α (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (iSup.{u1, succ u1} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => iSup.{u1, 0} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => WithTop.some.{u1} α a))))
+Case conversion may be inaccurate. Consider using '#align with_top.coe_Sup WithTop.coe_sSupₓ'. -/
 /-- A version of `with_top.coe_Sup'` with a more convenient but less general statement. -/
 @[norm_cast]
-theorem coe_supₛ {s : Set α} (hb : BddAbove s) : ↑(supₛ s) = (⨆ a ∈ s, ↑a : WithTop α) := by
-  rw [coe_Sup' hb, supₛ_image]
-#align with_top.coe_Sup WithTop.coe_supₛ
+theorem coe_sSup {s : Set α} (hb : BddAbove s) : ↑(sSup s) = (⨆ a ∈ s, ↑a : WithTop α) := by
+  rw [coe_Sup' hb, sSup_image]
+#align with_top.coe_Sup WithTop.coe_sSup
 
-/- warning: with_top.coe_Inf -> WithTop.coe_infₛ is a dubious translation:
+/- warning: with_top.coe_Inf -> WithTop.coe_sInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (infᵢ.{u1, succ u1} (WithTop.{u1} α) (WithTop.hasInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => infᵢ.{u1, 0} (WithTop.{u1} α) (WithTop.hasInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) a))))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithTop.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (iInf.{u1, succ u1} (WithTop.{u1} α) (WithTop.hasInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => iInf.{u1, 0} (WithTop.{u1} α) (WithTop.hasInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithTop.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithTop.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithTop.{u1} α) (WithTop.hasCoeT.{u1} α))) a))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithTop.{u1} α) (WithTop.some.{u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (infᵢ.{u1, succ u1} (WithTop.{u1} α) (instInfSetWithTop.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => infᵢ.{u1, 0} (WithTop.{u1} α) (instInfSetWithTop.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => WithTop.some.{u1} α a))))
-Case conversion may be inaccurate. Consider using '#align with_top.coe_Inf WithTop.coe_infₛₓ'. -/
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} (WithTop.{u1} α) (WithTop.some.{u1} α (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1))) s)) (iInf.{u1, succ u1} (WithTop.{u1} α) (instInfSetWithTop.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) α (fun (a : α) => iInf.{u1, 0} (WithTop.{u1} α) (instInfSetWithTop.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) => WithTop.some.{u1} α a))))
+Case conversion may be inaccurate. Consider using '#align with_top.coe_Inf WithTop.coe_sInfₓ'. -/
 /-- A version of `with_top.coe_Inf'` with a more convenient but less general statement. -/
 @[norm_cast]
-theorem coe_infₛ {s : Set α} (hs : s.Nonempty) : ↑(infₛ s) = (⨅ a ∈ s, ↑a : WithTop α) := by
-  rw [coe_Inf' hs, infₛ_image]
-#align with_top.coe_Inf WithTop.coe_infₛ
+theorem coe_sInf {s : Set α} (hs : s.Nonempty) : ↑(sInf s) = (⨅ a ∈ s, ↑a : WithTop α) := by
+  rw [coe_Inf' hs, sInf_image]
+#align with_top.coe_Inf WithTop.coe_sInf
 
 end WithTop
 
@@ -2043,49 +2043,49 @@ variable [Preorder α] [ConditionallyCompleteLattice β] {f : α → β} (h_mono
 `Sup` and `Inf`. -/
 
 
-/- warning: monotone.le_cSup_image -> Monotone.le_csupₛ_image is a dubious translation:
+/- warning: monotone.le_cSup_image -> Monotone.le_csSup_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddAbove.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f c) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddAbove.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f c) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α} {c : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c s) -> (BddAbove.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (f c) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s))))
-Case conversion may be inaccurate. Consider using '#align monotone.le_cSup_image Monotone.le_csupₛ_imageₓ'. -/
-theorem le_csupₛ_image {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddAbove s) :
-    f c ≤ supₛ (f '' s) :=
-  le_csupₛ (map_bddAbove h_mono h_bdd) (mem_image_of_mem f hcs)
-#align monotone.le_cSup_image Monotone.le_csupₛ_image
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α} {c : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c s) -> (BddAbove.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (f c) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s))))
+Case conversion may be inaccurate. Consider using '#align monotone.le_cSup_image Monotone.le_csSup_imageₓ'. -/
+theorem le_csSup_image {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddAbove s) :
+    f c ≤ sSup (f '' s) :=
+  le_csSup (map_bddAbove h_mono h_bdd) (mem_image_of_mem f hcs)
+#align monotone.le_cSup_image Monotone.le_csSup_image
 
-/- warning: monotone.cSup_image_le -> Monotone.csupₛ_image_le is a dubious translation:
+/- warning: monotone.cSup_image_le -> Monotone.csSup_image_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (upperBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f B))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (upperBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f B))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (forall {B : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) B (upperBounds.{u2} α _inst_1 s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)) (f B))))
-Case conversion may be inaccurate. Consider using '#align monotone.cSup_image_le Monotone.csupₛ_image_leₓ'. -/
-theorem csupₛ_image_le {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ upperBounds s) :
-    supₛ (f '' s) ≤ f B :=
-  csupₛ_le (Nonempty.image f hs) (h_mono.mem_upperBounds_image hB)
-#align monotone.cSup_image_le Monotone.csupₛ_image_le
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (forall {B : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) B (upperBounds.{u2} α _inst_1 s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)) (f B))))
+Case conversion may be inaccurate. Consider using '#align monotone.cSup_image_le Monotone.csSup_image_leₓ'. -/
+theorem csSup_image_le {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ upperBounds s) :
+    sSup (f '' s) ≤ f B :=
+  csSup_le (Nonempty.image f hs) (h_mono.mem_upperBounds_image hB)
+#align monotone.cSup_image_le Monotone.csSup_image_le
 
-/- warning: monotone.cInf_image_le -> Monotone.cinfₛ_image_le is a dubious translation:
+/- warning: monotone.cInf_image_le -> Monotone.csInf_image_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddBelow.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f c)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α} {c : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) c s) -> (BddBelow.{u1} α _inst_1 s) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)) (f c)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α} {c : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c s) -> (BddBelow.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)) (f c)))
-Case conversion may be inaccurate. Consider using '#align monotone.cInf_image_le Monotone.cinfₛ_image_leₓ'. -/
-theorem cinfₛ_image_le {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddBelow s) :
-    infₛ (f '' s) ≤ f c :=
-  @le_csupₛ_image αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ _ hcs h_bdd
-#align monotone.cInf_image_le Monotone.cinfₛ_image_le
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α} {c : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) c s) -> (BddBelow.{u2} α _inst_1 s) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)) (f c)))
+Case conversion may be inaccurate. Consider using '#align monotone.cInf_image_le Monotone.csInf_image_leₓ'. -/
+theorem csInf_image_le {s : Set α} {c : α} (hcs : c ∈ s) (h_bdd : BddBelow s) :
+    sInf (f '' s) ≤ f c :=
+  @le_csSup_image αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ _ hcs h_bdd
+#align monotone.cInf_image_le Monotone.csInf_image_le
 
-/- warning: monotone.le_cInf_image -> Monotone.le_cinfₛ_image is a dubious translation:
+/- warning: monotone.le_cInf_image -> Monotone.le_csInf_image is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (lowerBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f B) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Preorder.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β _inst_1 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) f) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (forall {B : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) B (lowerBounds.{u1} α _inst_1 s)) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (f B) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β f s)))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (forall {B : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) B (lowerBounds.{u2} α _inst_1 s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (f B) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)))))
-Case conversion may be inaccurate. Consider using '#align monotone.le_cInf_image Monotone.le_cinfₛ_imageₓ'. -/
-theorem le_cinfₛ_image {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ lowerBounds s) :
-    f B ≤ infₛ (f '' s) :=
-  @csupₛ_image_le αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ hs _ hB
-#align monotone.le_cInf_image Monotone.le_cinfₛ_image
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Preorder.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {f : α -> β}, (Monotone.{u2, u1} α β _inst_1 (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) f) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (forall {B : α}, (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) B (lowerBounds.{u2} α _inst_1 s)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (f B) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β f s)))))
+Case conversion may be inaccurate. Consider using '#align monotone.le_cInf_image Monotone.le_csInf_imageₓ'. -/
+theorem le_csInf_image {s : Set α} (hs : s.Nonempty) {B : α} (hB : B ∈ lowerBounds s) :
+    f B ≤ sInf (f '' s) :=
+  @csSup_image_le αᵒᵈ βᵒᵈ _ _ _ (fun x y hxy => h_mono hxy) _ hs _ hB
+#align monotone.le_cInf_image Monotone.le_csInf_image
 
 end Monotone
 
@@ -2094,94 +2094,94 @@ namespace GaloisConnection
 variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [Nonempty ι] {l : α → β}
   {u : β → α}
 
-/- warning: galois_connection.l_cSup -> GaloisConnection.l_csupₛ is a dubious translation:
+/- warning: galois_connection.l_cSup -> GaloisConnection.l_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (l (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (supᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => l ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (l (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => l ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (l (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (supᵢ.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => l (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.l_cSup GaloisConnection.l_csupₛₓ'. -/
-theorem l_csupₛ (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
-    l (supₛ s) = ⨆ x : s, l x :=
-  Eq.symm <| IsLUB.csupᵢ_set_eq (gc.isLUB_l_image <| isLUB_csupₛ hne hbdd) hne
-#align galois_connection.l_cSup GaloisConnection.l_csupₛ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (l (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (iSup.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => l (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.l_cSup GaloisConnection.l_csSupₓ'. -/
+theorem l_csSup (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
+    l (sSup s) = ⨆ x : s, l x :=
+  Eq.symm <| IsLUB.ciSup_set_eq (gc.isLUB_l_image <| isLUB_csSup hne hbdd) hne
+#align galois_connection.l_cSup GaloisConnection.l_csSup
 
-/- warning: galois_connection.l_cSup' -> GaloisConnection.l_csupₛ' is a dubious translation:
+/- warning: galois_connection.l_cSup' -> GaloisConnection.l_csSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (l (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β l s))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (l (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β l s))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (l (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β l s))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.l_cSup' GaloisConnection.l_csupₛ'ₓ'. -/
-theorem l_csupₛ' (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
-    l (supₛ s) = supₛ (l '' s) := by rw [gc.l_cSup hne hbdd, supₛ_image']
-#align galois_connection.l_cSup' GaloisConnection.l_csupₛ'
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (l (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β l s))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.l_cSup' GaloisConnection.l_csSup'ₓ'. -/
+theorem l_csSup' (gc : GaloisConnection l u) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
+    l (sSup s) = sSup (l '' s) := by rw [gc.l_cSup hne hbdd, sSup_image']
+#align galois_connection.l_cSup' GaloisConnection.l_csSup'
 
-/- warning: galois_connection.l_csupr -> GaloisConnection.l_csupᵢ is a dubious translation:
+/- warning: galois_connection.l_csupr -> GaloisConnection.l_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (l (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => l (f i)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (l (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => l (f i)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (l (supᵢ.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => l (f i)))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.l_csupr GaloisConnection.l_csupᵢₓ'. -/
-theorem l_csupᵢ (gc : GaloisConnection l u) {f : ι → α} (hf : BddAbove (range f)) :
-    l (⨆ i, f i) = ⨆ i, l (f i) := by rw [supᵢ, gc.l_cSup (range_nonempty _) hf, supᵢ_range']
-#align galois_connection.l_csupr GaloisConnection.l_csupᵢ
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (l (iSup.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => l (f i)))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.l_csupr GaloisConnection.l_ciSupₓ'. -/
+theorem l_ciSup (gc : GaloisConnection l u) {f : ι → α} (hf : BddAbove (range f)) :
+    l (⨆ i, f i) = ⨆ i, l (f i) := by rw [iSup, gc.l_cSup (range_nonempty _) hf, iSup_range']
+#align galois_connection.l_csupr GaloisConnection.l_ciSup
 
-/- warning: galois_connection.l_csupr_set -> GaloisConnection.l_csupᵢ_set is a dubious translation:
+/- warning: galois_connection.l_csupr_set -> GaloisConnection.l_ciSup_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u3} γ} {f : γ -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (l (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => l (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u3} γ} {f : γ -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (l (iSup.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => l (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i))))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (l (supᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (supᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => l (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i))))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.l_csupr_set GaloisConnection.l_csupᵢ_setₓ'. -/
-theorem l_csupᵢ_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (l (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => l (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i))))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.l_csupr_set GaloisConnection.l_ciSup_setₓ'. -/
+theorem l_ciSup_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : l (⨆ i : s, f i) = ⨆ i : s, l (f i) :=
   by
   haveI := hne.to_subtype
   rw [image_eq_range] at hf
   exact gc.l_csupr hf
-#align galois_connection.l_csupr_set GaloisConnection.l_csupᵢ_set
+#align galois_connection.l_csupr_set GaloisConnection.l_ciSup_set
 
-/- warning: galois_connection.u_cInf -> GaloisConnection.u_cinfₛ is a dubious translation:
+/- warning: galois_connection.u_cInf -> GaloisConnection.u_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u2} β}, (Set.Nonempty.{u2} β s) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) s) -> (Eq.{succ u1} α (u (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) s)) (infᵢ.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => u ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) x)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u2} β}, (Set.Nonempty.{u2} β s) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) s) -> (Eq.{succ u1} α (u (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) s)) (iInf.{u1, succ u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) (fun (x : coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) => u ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) s) β (coeSubtype.{succ u2} β (fun (x : β) => Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s))))) x)))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u1} β}, (Set.Nonempty.{u1} β s) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) s) -> (Eq.{succ u2} α (u (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) s)) (infᵢ.{u2, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (Set.Elem.{u1} β s) (fun (x : Set.Elem.{u1} β s) => u (Subtype.val.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x s) x)))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.u_cInf GaloisConnection.u_cinfₛₓ'. -/
-theorem u_cinfₛ (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
-    u (infₛ s) = ⨅ x : s, u x :=
-  gc.dual.l_csupₛ hne hbdd
-#align galois_connection.u_cInf GaloisConnection.u_cinfₛ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u1} β}, (Set.Nonempty.{u1} β s) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) s) -> (Eq.{succ u2} α (u (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) s)) (iInf.{u2, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (Set.Elem.{u1} β s) (fun (x : Set.Elem.{u1} β s) => u (Subtype.val.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x s) x)))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.u_cInf GaloisConnection.u_csInfₓ'. -/
+theorem u_csInf (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
+    u (sInf s) = ⨅ x : s, u x :=
+  gc.dual.l_csSup hne hbdd
+#align galois_connection.u_cInf GaloisConnection.u_csInf
 
-/- warning: galois_connection.u_cInf' -> GaloisConnection.u_cinfₛ' is a dubious translation:
+/- warning: galois_connection.u_cInf' -> GaloisConnection.u_csInf' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u2} β}, (Set.Nonempty.{u2} β s) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) s) -> (Eq.{succ u1} α (u (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) s)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.image.{u2, u1} β α u s))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u2} β}, (Set.Nonempty.{u2} β s) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) s) -> (Eq.{succ u1} α (u (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) s)) (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Set.image.{u2, u1} β α u s))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u1} β}, (Set.Nonempty.{u1} β s) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) s) -> (Eq.{succ u2} α (u (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) s)) (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (Set.image.{u1, u2} β α u s))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.u_cInf' GaloisConnection.u_cinfₛ'ₓ'. -/
-theorem u_cinfₛ' (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
-    u (infₛ s) = infₛ (u '' s) :=
-  gc.dual.l_csupₛ' hne hbdd
-#align galois_connection.u_cInf' GaloisConnection.u_cinfₛ'
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) l u) -> (forall {s : Set.{u1} β}, (Set.Nonempty.{u1} β s) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) s) -> (Eq.{succ u2} α (u (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) s)) (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) (Set.image.{u1, u2} β α u s))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.u_cInf' GaloisConnection.u_csInf'ₓ'. -/
+theorem u_csInf' (gc : GaloisConnection l u) {s : Set β} (hne : s.Nonempty) (hbdd : BddBelow s) :
+    u (sInf s) = sInf (u '' s) :=
+  gc.dual.l_csSup' hne hbdd
+#align galois_connection.u_cInf' GaloisConnection.u_csInf'
 
-/- warning: galois_connection.u_cinfi -> GaloisConnection.u_cinfᵢ is a dubious translation:
+/- warning: galois_connection.u_cinfi -> GaloisConnection.u_ciInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.range.{u2, u3} β ι f)) -> (Eq.{succ u1} α (u (infᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) ι (fun (i : ι) => f i))) (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => u (f i)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.range.{u2, u3} β ι f)) -> (Eq.{succ u1} α (u (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) ι (fun (i : ι) => f i))) (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => u (f i)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.range.{u2, u1} β ι f)) -> (Eq.{succ u3} α (u (infᵢ.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => f i))) (infᵢ.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => u (f i)))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.u_cinfi GaloisConnection.u_cinfᵢₓ'. -/
-theorem u_cinfᵢ (gc : GaloisConnection l u) {f : ι → β} (hf : BddBelow (range f)) :
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {f : ι -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.range.{u2, u1} β ι f)) -> (Eq.{succ u3} α (u (iInf.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => f i))) (iInf.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => u (f i)))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.u_cinfi GaloisConnection.u_ciInfₓ'. -/
+theorem u_ciInf (gc : GaloisConnection l u) {f : ι → β} (hf : BddBelow (range f)) :
     u (⨅ i, f i) = ⨅ i, u (f i) :=
-  gc.dual.l_csupᵢ hf
-#align galois_connection.u_cinfi GaloisConnection.u_cinfᵢ
+  gc.dual.l_ciSup hf
+#align galois_connection.u_cinfi GaloisConnection.u_ciInf
 
-/- warning: galois_connection.u_cinfi_set -> GaloisConnection.u_cinfᵢ_set is a dubious translation:
+/- warning: galois_connection.u_cinfi_set -> GaloisConnection.u_ciInf_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u3} γ} {f : γ -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.image.{u3, u2} γ β f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u1} α (u (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => u (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u3} γ} {f : γ -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.image.{u3, u2} γ β f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u1} α (u (iInf.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => u (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i))))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} γ} {f : γ -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.image.{u1, u2} γ β f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u3} α (u (infᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (infᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => u (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i))))))
-Case conversion may be inaccurate. Consider using '#align galois_connection.u_cinfi_set GaloisConnection.u_cinfᵢ_setₓ'. -/
-theorem u_cinfᵢ_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → β} (hf : BddBelow (f '' s))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] {l : α -> β} {u : β -> α}, (GaloisConnection.{u3, u2} α β (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) l u) -> (forall {s : Set.{u1} γ} {f : γ -> β}, (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (Set.image.{u1, u2} γ β f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u3} α (u (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iInf.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => u (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i))))))
+Case conversion may be inaccurate. Consider using '#align galois_connection.u_cinfi_set GaloisConnection.u_ciInf_setₓ'. -/
+theorem u_ciInf_set (gc : GaloisConnection l u) {s : Set γ} {f : γ → β} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : u (⨅ i : s, f i) = ⨅ i : s, u (f i) :=
-  gc.dual.l_csupᵢ_set hf hne
-#align galois_connection.u_cinfi_set GaloisConnection.u_cinfᵢ_set
+  gc.dual.l_ciSup_set hf hne
+#align galois_connection.u_cinfi_set GaloisConnection.u_ciInf_set
 
 end GaloisConnection
 
@@ -2189,93 +2189,93 @@ namespace OrderIso
 
 variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [Nonempty ι]
 
-/- warning: order_iso.map_cSup -> OrderIso.map_csupₛ is a dubious translation:
+/- warning: order_iso.map_cSup -> OrderIso.map_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (supᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (supᵢ.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup OrderIso.map_csupₛₓ'. -/
-theorem map_csupₛ (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
-    e (supₛ s) = ⨆ x : s, e x :=
-  e.to_galoisConnection.l_csupₛ hne hbdd
-#align order_iso.map_cSup OrderIso.map_csupₛ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (iSup.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup OrderIso.map_csSupₓ'. -/
+theorem map_csSup (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
+    e (sSup s) = ⨆ x : s, e x :=
+  e.to_galoisConnection.l_csSup hne hbdd
+#align order_iso.map_cSup OrderIso.map_csSup
 
-/- warning: order_iso.map_cSup' -> OrderIso.map_csupₛ' is a dubious translation:
+/- warning: order_iso.map_cSup' -> OrderIso.map_csSup' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup' OrderIso.map_csupₛ'ₓ'. -/
-theorem map_csupₛ' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
-    e (supₛ s) = supₛ (e '' s) :=
-  e.to_galoisConnection.l_csupₛ' hne hbdd
-#align order_iso.map_cSup' OrderIso.map_csupₛ'
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup' OrderIso.map_csSup'ₓ'. -/
+theorem map_csSup' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
+    e (sSup s) = sSup (e '' s) :=
+  e.to_galoisConnection.l_csSup' hne hbdd
+#align order_iso.map_cSup' OrderIso.map_csSup'
 
-/- warning: order_iso.map_csupr -> OrderIso.map_csupᵢ is a dubious translation:
+/- warning: order_iso.map_csupr -> OrderIso.map_ciSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iSup.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (supᵢ.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr OrderIso.map_csupᵢₓ'. -/
-theorem map_csupᵢ (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => 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x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iSup.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iSup.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β 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(Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr OrderIso.map_ciSupₓ'. -/
+theorem map_ciSup (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
     e (⨆ i, f i) = ⨆ i, e (f i) :=
-  e.to_galoisConnection.l_csupᵢ hf
-#align order_iso.map_csupr OrderIso.map_csupᵢ
+  e.to_galoisConnection.l_ciSup hf
+#align order_iso.map_csupr OrderIso.map_ciSup
 
-/- warning: order_iso.map_csupr_set -> OrderIso.map_csupᵢ_set is a dubious translation:
+/- warning: order_iso.map_csupr_set -> OrderIso.map_ciSup_set is a dubious translation:
 lean 3 declaration is
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s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (iSup.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (supᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (supᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr_set OrderIso.map_csupᵢ_setₓ'. -/
-theorem map_csupᵢ_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iSup.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iSup.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr_set OrderIso.map_ciSup_setₓ'. -/
+theorem map_ciSup_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : e (⨆ i : s, f i) = ⨆ i : s, e (f i) :=
-  e.to_galoisConnection.l_csupᵢ_set hf hne
-#align order_iso.map_csupr_set OrderIso.map_csupᵢ_set
+  e.to_galoisConnection.l_ciSup_set hf hne
+#align order_iso.map_csupr_set OrderIso.map_ciSup_set
 
-/- warning: order_iso.map_cInf -> OrderIso.map_cinfₛ is a dubious translation:
+/- warning: order_iso.map_cInf -> OrderIso.map_csInf is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
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(SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (infᵢ.{u1, succ u2} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf OrderIso.map_cinfₛₓ'. -/
-theorem map_cinfₛ (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
-    e (infₛ s) = ⨅ x : s, e x :=
-  e.dual.map_csupₛ hne hbdd
-#align order_iso.map_cInf OrderIso.map_cinfₛ
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (iInf.{u1, succ u2} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf OrderIso.map_csInfₓ'. -/
+theorem map_csInf (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
+    e (sInf s) = ⨅ x : s, e x :=
+  e.dual.map_csSup hne hbdd
+#align order_iso.map_cInf OrderIso.map_csInf
 
-/- warning: order_iso.map_cInf' -> OrderIso.map_cinfₛ' is a dubious translation:
+/- warning: order_iso.map_cInf' -> OrderIso.map_csInf' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf' OrderIso.map_cinfₛ'ₓ'. -/
-theorem map_cinfₛ' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
-    e (infₛ s) = infₛ (e '' s) :=
-  e.dual.map_csupₛ' hne hbdd
-#align order_iso.map_cInf' OrderIso.map_cinfₛ'
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf' OrderIso.map_csInf'ₓ'. -/
+theorem map_csInf' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
+    e (sInf s) = sInf (e '' s) :=
+  e.dual.map_csSup' hne hbdd
+#align order_iso.map_cInf' OrderIso.map_csInf'
 
-/- warning: order_iso.map_cinfi -> OrderIso.map_cinfᵢ is a dubious translation:
+/- warning: order_iso.map_cinfi -> OrderIso.map_ciInf is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iInf.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
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LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (infᵢ.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi OrderIso.map_cinfᵢₓ'. -/
-theorem map_cinfᵢ (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iInf.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (iInf.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi OrderIso.map_ciInfₓ'. -/
+theorem map_ciInf (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
     e (⨅ i, f i) = ⨅ i, e (f i) :=
-  e.dual.map_csupᵢ hf
-#align order_iso.map_cinfi OrderIso.map_cinfᵢ
+  e.dual.map_ciSup hf
+#align order_iso.map_cinfi OrderIso.map_ciInf
 
-/- warning: order_iso.map_cinfi_set -> OrderIso.map_cinfᵢ_set is a dubious translation:
+/- warning: order_iso.map_cinfi_set -> OrderIso.map_ciInf_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u3} γ} {f : γ -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) 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+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u3} γ} {f : γ -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α 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(LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (iInf.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) 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 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) 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(Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) 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(SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
-Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi_set OrderIso.map_cinfᵢ_setₓ'. -/
-theorem map_cinfᵢ_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddBelow (f '' s))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (iInf.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (iInf.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
+Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi_set OrderIso.map_ciInf_setₓ'. -/
+theorem map_ciInf_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : e (⨅ i : s, f i) = ⨅ i : s, e (f i) :=
-  e.dual.map_csupᵢ_set hf hne
-#align order_iso.map_cinfi_set OrderIso.map_cinfᵢ_set
+  e.dual.map_ciSup_set hf hne
+#align order_iso.map_cinfi_set OrderIso.map_ciInf_set
 
 end OrderIso
 
@@ -2294,107 +2294,107 @@ variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β]
 
 variable {l u : α → β → γ} {l₁ u₁ : β → γ → α} {l₂ u₂ : α → γ → β}
 
-/- warning: cSup_image2_eq_cSup_cSup -> csupₛ_image2_eq_csupₛ_csupₛ is a dubious translation:
+/- warning: cSup_image2_eq_cSup_cSup -> csSup_image2_eq_csSup_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} α γ (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.supₛ.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} α γ (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.sSup.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.supₛ.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cSup_cSup csupₛ_image2_eq_csupₛ_csupₛₓ'. -/
-theorem csupₛ_image2_eq_csupₛ_csupₛ (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.sSup.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cSup_cSup csSup_image2_eq_csSup_csSupₓ'. -/
+theorem csSup_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) (hs₀ : s.Nonempty) (hs₁ : BddAbove s)
-    (ht₀ : t.Nonempty) (ht₁ : BddAbove t) : supₛ (image2 l s t) = l (supₛ s) (supₛ t) :=
+    (ht₀ : t.Nonempty) (ht₁ : BddAbove t) : sSup (image2 l s t) = l (sSup s) (sSup t) :=
   by
   refine' eq_of_forall_ge_iff fun c => _
-  rw [csupₛ_le_iff (hs₁.image2 (fun _ => (h₁ _).monotone_l) (fun _ => (h₂ _).monotone_l) ht₁)
+  rw [csSup_le_iff (hs₁.image2 (fun _ => (h₁ _).monotone_l) (fun _ => (h₂ _).monotone_l) ht₁)
       (hs₀.image2 ht₀),
-    forall_image2_iff, forall₂_swap, (h₂ _).le_iff_le, csupₛ_le_iff ht₁ ht₀]
-  simp_rw [← (h₂ _).le_iff_le, (h₁ _).le_iff_le, csupₛ_le_iff hs₁ hs₀]
-#align cSup_image2_eq_cSup_cSup csupₛ_image2_eq_csupₛ_csupₛ
+    forall_image2_iff, forall₂_swap, (h₂ _).le_iff_le, csSup_le_iff ht₁ ht₀]
+  simp_rw [← (h₂ _).le_iff_le, (h₁ _).le_iff_le, csSup_le_iff hs₁ hs₀]
+#align cSup_image2_eq_cSup_cSup csSup_image2_eq_csSup_csSup
 
-/- warning: cSup_image2_eq_cSup_cInf -> csupₛ_image2_eq_csupₛ_cinfₛ is a dubious translation:
+/- warning: cSup_image2_eq_cSup_cInf -> csSup_image2_eq_csSup_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} α γ (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.supₛ.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} α γ (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.sSup.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.supₛ.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cSup_cInf csupₛ_image2_eq_csupₛ_cinfₛₓ'. -/
-theorem csupₛ_image2_eq_csupₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.sSup.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cSup_cInf csSup_image2_eq_csSup_csInfₓ'. -/
+theorem csSup_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
-    s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → supₛ (image2 l s t) = l (supₛ s) (infₛ t) :=
-  @csupₛ_image2_eq_csupₛ_csupₛ _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
-#align cSup_image2_eq_cSup_cInf csupₛ_image2_eq_csupₛ_cinfₛ
+    s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → sSup (image2 l s t) = l (sSup s) (sInf t) :=
+  @csSup_image2_eq_csSup_csSup _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
+#align cSup_image2_eq_cSup_cInf csSup_image2_eq_csSup_csInf
 
-/- warning: cSup_image2_eq_cInf_cSup -> csupₛ_image2_eq_cinfₛ_csupₛ is a dubious translation:
+/- warning: cSup_image2_eq_cInf_cSup -> csSup_image2_eq_csInf_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.supₛ.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.sSup.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.infₛ.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cSup csupₛ_image2_eq_cinfₛ_csupₛₓ'. -/
-theorem csupₛ_image2_eq_cinfₛ_csupₛ (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.sInf.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cSup csSup_image2_eq_csInf_csSupₓ'. -/
+theorem csSup_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) :
-    s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → supₛ (image2 l s t) = l (infₛ s) (supₛ t) :=
-  @csupₛ_image2_eq_csupₛ_csupₛ αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
-#align cSup_image2_eq_cInf_cSup csupₛ_image2_eq_cinfₛ_csupₛ
+    s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → sSup (image2 l s t) = l (sInf s) (sSup t) :=
+  @csSup_image2_eq_csSup_csSup αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
+#align cSup_image2_eq_cInf_cSup csSup_image2_eq_csInf_csSup
 
-/- warning: cSup_image2_eq_cInf_cInf -> csupₛ_image2_eq_cinfₛ_cinfₛ is a dubious translation:
+/- warning: cSup_image2_eq_cInf_cInf -> csSup_image2_eq_csInf_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.supₛ.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.sSup.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.infₛ.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cInf csupₛ_image2_eq_cinfₛ_cinfₛₓ'. -/
-theorem csupₛ_image2_eq_cinfₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.sSup.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.sInf.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cInf csSup_image2_eq_csInf_csInfₓ'. -/
+theorem csSup_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
-    s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → supₛ (image2 l s t) = l (infₛ s) (infₛ t) :=
-  @csupₛ_image2_eq_csupₛ_csupₛ αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
-#align cSup_image2_eq_cInf_cInf csupₛ_image2_eq_cinfₛ_cinfₛ
+    s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → sSup (image2 l s t) = l (sInf s) (sInf t) :=
+  @csSup_image2_eq_csSup_csSup αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
+#align cSup_image2_eq_cInf_cInf csSup_image2_eq_csInf_csInf
 
-/- warning: cInf_image2_eq_cInf_cInf -> cinfₛ_image2_eq_cinfₛ_cinfₛ is a dubious translation:
+/- warning: cInf_image2_eq_cInf_cInf -> csInf_image2_eq_csInf_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (l₁ b) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u2} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (l₁ b) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u2} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cInf_cInf cinfₛ_image2_eq_cinfₛ_cinfₛₓ'. -/
-theorem cinfₛ_image2_eq_cinfₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cInf_cInf csInf_image2_eq_csInf_csInfₓ'. -/
+theorem csInf_image2_eq_csInf_csInf (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
-    s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → infₛ (image2 u s t) = u (infₛ s) (infₛ t) :=
-  @csupₛ_image2_eq_csupₛ_csupₛ αᵒᵈ βᵒᵈ γᵒᵈ _ _ _ _ _ _ l₁ l₂ (fun _ => (h₁ _).dual) fun _ =>
+    s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → sInf (image2 u s t) = u (sInf s) (sInf t) :=
+  @csSup_image2_eq_csSup_csSup αᵒᵈ βᵒᵈ γᵒᵈ _ _ _ _ _ _ l₁ l₂ (fun _ => (h₁ _).dual) fun _ =>
     (h₂ _).dual
-#align cInf_image2_eq_cInf_cInf cinfₛ_image2_eq_cinfₛ_cinfₛ
+#align cInf_image2_eq_cInf_cInf csInf_image2_eq_csInf_csInf
 
-/- warning: cInf_image2_eq_cInf_cSup -> cinfₛ_image2_eq_cinfₛ_csupₛ is a dubious translation:
+/- warning: cInf_image2_eq_cInf_cSup -> csInf_image2_eq_csInf_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (l₁ b) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (l₁ b) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (InfSet.sInf.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cInf_cSup cinfₛ_image2_eq_cinfₛ_csupₛₓ'. -/
-theorem cinfₛ_image2_eq_cinfₛ_csupₛ (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.sInf.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cInf_cSup csInf_image2_eq_csInf_csSupₓ'. -/
+theorem csInf_image2_eq_csInf_csSup (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
-    s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → infₛ (image2 u s t) = u (infₛ s) (supₛ t) :=
-  @cinfₛ_image2_eq_cinfₛ_cinfₛ _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
-#align cInf_image2_eq_cInf_cSup cinfₛ_image2_eq_cinfₛ_csupₛ
+    s.Nonempty → BddBelow s → t.Nonempty → BddAbove t → sInf (image2 u s t) = u (sInf s) (sSup t) :=
+  @csInf_image2_eq_csInf_csInf _ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
+#align cInf_image2_eq_cInf_cSup csInf_image2_eq_csInf_csSup
 
-/- warning: cInf_image2_eq_cSup_cInf -> cinfₛ_image2_eq_csupₛ_cinfₛ is a dubious translation:
+/- warning: cInf_image2_eq_cSup_cInf -> csInf_image2_eq_csSup_csInf is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cInf cinfₛ_image2_eq_csupₛ_cinfₛₓ'. -/
-theorem cinfₛ_image2_eq_csupₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cInf csInf_image2_eq_csSup_csInfₓ'. -/
+theorem csInf_image2_eq_csSup_csInf (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
-    s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → infₛ (image2 u s t) = u (supₛ s) (infₛ t) :=
-  @cinfₛ_image2_eq_cinfₛ_cinfₛ αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
-#align cInf_image2_eq_cSup_cInf cinfₛ_image2_eq_csupₛ_cinfₛ
+    s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → sInf (image2 u s t) = u (sSup s) (sInf t) :=
+  @csInf_image2_eq_csInf_csInf αᵒᵈ _ _ _ _ _ _ _ _ _ _ h₁ h₂
+#align cInf_image2_eq_cSup_cInf csInf_image2_eq_csSup_csInf
 
-/- warning: cInf_image2_eq_cSup_cSup -> cinfₛ_image2_eq_csupₛ_csupₛ is a dubious translation:
+/- warning: cInf_image2_eq_cSup_cSup -> csInf_image2_eq_csSup_csSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.sSup.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
-Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cSup cinfₛ_image2_eq_csupₛ_csupₛₓ'. -/
-theorem cinfₛ_image2_eq_csupₛ_csupₛ (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.sInf.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.sSup.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cSup csInf_image2_eq_csSup_csSupₓ'. -/
+theorem csInf_image2_eq_csSup_csSup (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
-    s.Nonempty → BddAbove s → t.Nonempty → BddAbove t → infₛ (image2 u s t) = u (supₛ s) (supₛ t) :=
-  @cinfₛ_image2_eq_cinfₛ_cinfₛ αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
-#align cInf_image2_eq_cSup_cSup cinfₛ_image2_eq_csupₛ_csupₛ
+    s.Nonempty → BddAbove s → t.Nonempty → BddAbove t → sInf (image2 u s t) = u (sSup s) (sSup t) :=
+  @csInf_image2_eq_csInf_csInf αᵒᵈ βᵒᵈ _ _ _ _ _ _ _ _ _ h₁ h₂
+#align cInf_image2_eq_cSup_cSup csInf_image2_eq_csSup_csSup
 
 end
 
@@ -2424,10 +2424,10 @@ noncomputable instance WithTop.conditionallyCompleteLattice {α : Type _}
     [ConditionallyCompleteLattice α] : ConditionallyCompleteLattice (WithTop α) :=
   { WithTop.lattice, WithTop.hasSup,
     WithTop.hasInf with
-    le_cSup := fun S a hS haS => (WithTop.isLUB_supₛ' ⟨a, haS⟩).1 haS
-    cSup_le := fun S a hS haS => (WithTop.isLUB_supₛ' hS).2 haS
-    cInf_le := fun S a hS haS => (WithTop.isGLB_infₛ' hS).1 haS
-    le_cInf := fun S a hS haS => (WithTop.isGLB_infₛ' ⟨a, haS⟩).2 haS }
+    le_cSup := fun S a hS haS => (WithTop.isLUB_sSup' ⟨a, haS⟩).1 haS
+    cSup_le := fun S a hS haS => (WithTop.isLUB_sSup' hS).2 haS
+    cInf_le := fun S a hS haS => (WithTop.isGLB_sInf' hS).1 haS
+    le_cInf := fun S a hS haS => (WithTop.isGLB_sInf' ⟨a, haS⟩).2 haS }
 #align with_top.conditionally_complete_lattice WithTop.conditionallyCompleteLattice
 -/
 
@@ -2450,7 +2450,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
     [ConditionallyCompleteLattice α] : CompleteLattice (WithTop (WithBot α)) :=
   { WithTop.hasInf, WithTop.hasSup, WithTop.boundedOrder,
     WithTop.lattice with
-    le_sup := fun S a haS => (WithTop.isLUB_supₛ' ⟨a, haS⟩).1 haS
+    le_sup := fun S a haS => (WithTop.isLUB_sSup' ⟨a, haS⟩).1 haS
     sup_le := fun S a ha => by
       cases' S.eq_empty_or_nonempty with h
       · show ite _ _ _ ≤ a
@@ -2458,7 +2458,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
         · rw [h] at h_1
           cases h_1
         · convert bot_le
-          convert WithBot.csupₛ_empty
+          convert WithBot.csSup_empty
           rw [h]
           rfl
         · exfalso
@@ -2466,7 +2466,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
           use ⊥
           rw [h]
           rintro b ⟨⟩
-      · refine' (WithTop.isLUB_supₛ' h).2 ha
+      · refine' (WithTop.isLUB_sSup' h).2 ha
     inf_le := fun S a haS =>
       show ite _ _ _ ≤ a by
         split_ifs
@@ -2476,11 +2476,11 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
         · cases a
           · exact le_top
           · apply WithTop.some_le_some.2
-            refine' cinfₛ_le _ haS
+            refine' csInf_le _ haS
             use ⊥
             intro b hb
             exact bot_le
-    le_inf := fun S a haS => (WithTop.isGLB_infₛ' ⟨a, haS⟩).2 haS }
+    le_inf := fun S a haS => (WithTop.isGLB_sInf' ⟨a, haS⟩).2 haS }
 #align with_top.with_bot.complete_lattice WithTop.WithBot.completeLattice
 -/
 
@@ -2510,33 +2510,33 @@ noncomputable instance WithBot.WithTop.completeLinearOrder {α : Type _}
 #align with_bot.with_top.complete_linear_order WithBot.WithTop.completeLinearOrder
 -/
 
-/- warning: with_top.supr_coe_eq_top -> WithTop.supᵢ_coe_eq_top is a dubious translation:
+/- warning: with_top.supr_coe_eq_top -> WithTop.iSup_coe_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} (WithTop.{u2} α) (supᵢ.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (Not (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f)))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} (WithTop.{u2} α) (iSup.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (Not (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f)))
 but is expected to have type
-  forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} (WithTop.{u1} α) (supᵢ.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f)))
-Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_eq_top WithTop.supᵢ_coe_eq_topₓ'. -/
-theorem WithTop.supᵢ_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
+  forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} (WithTop.{u1} α) (iSup.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f)))
+Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_eq_top WithTop.iSup_coe_eq_topₓ'. -/
+theorem WithTop.iSup_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) = ⊤ ↔ ¬BddAbove (Set.range f) :=
   by
-  rw [supᵢ_eq_top, not_bddAbove_iff]
+  rw [iSup_eq_top, not_bddAbove_iff]
   refine' ⟨fun hf r => _, fun hf a ha => _⟩
   · rcases hf r (WithTop.coe_lt_top r) with ⟨i, hi⟩
     exact ⟨f i, ⟨i, rfl⟩, with_top.coe_lt_coe.mp hi⟩
   · rcases hf (a.untop ha.ne) with ⟨-, ⟨i, rfl⟩, hi⟩
     exact ⟨i, by simpa only [WithTop.coe_untop _ ha.ne] using with_top.coe_lt_coe.mpr hi⟩
-#align with_top.supr_coe_eq_top WithTop.supᵢ_coe_eq_top
+#align with_top.supr_coe_eq_top WithTop.iSup_coe_eq_top
 
-/- warning: with_top.supr_coe_lt_top -> WithTop.supᵢ_coe_lt_top is a dubious translation:
+/- warning: with_top.supr_coe_lt_top -> WithTop.iSup_coe_lt_top is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (LT.lt.{u2} (WithTop.{u2} α) (Preorder.toLT.{u2} (WithTop.{u2} α) (WithTop.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))))) (supᵢ.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f))
+  forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (LT.lt.{u2} (WithTop.{u2} α) (Preorder.toLT.{u2} (WithTop.{u2} α) (WithTop.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))))) (iSup.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f))
 but is expected to have type
-  forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (LT.lt.{u1} (WithTop.{u1} α) (Preorder.toLT.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))))) (supᵢ.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f))
-Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_lt_top WithTop.supᵢ_coe_lt_topₓ'. -/
-theorem WithTop.supᵢ_coe_lt_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
+  forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (LT.lt.{u1} (WithTop.{u1} α) (Preorder.toLT.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))))) (iSup.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f))
+Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_lt_top WithTop.iSup_coe_lt_topₓ'. -/
+theorem WithTop.iSup_coe_lt_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) < ⊤ ↔ BddAbove (Set.range f) :=
-  lt_top_iff_ne_top.trans <| (WithTop.supᵢ_coe_eq_top f).Not.trans Classical.not_not
-#align with_top.supr_coe_lt_top WithTop.supᵢ_coe_lt_top
+  lt_top_iff_ne_top.trans <| (WithTop.iSup_coe_eq_top f).Not.trans Classical.not_not
+#align with_top.supr_coe_lt_top WithTop.iSup_coe_lt_top
 
 end WithTopBot
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/403190b5419b3f03f1a2893ad9352ca7f7d8bff6

@@ -156,28 +156,28 @@ theorem WithTop.coe_supᵢ [Preorder α] [SupSet α] (f : ι → α) (h : BddAbo
     ↑(⨆ i, f i) = (⨆ i, f i : WithTop α) := by rw [supᵢ, supᵢ, WithTop.coe_supₛ' h, range_comp]
 #align with_top.coe_supr WithTop.coe_supᵢ
 
-/- warning: with_bot.cSup_empty -> WithBot.supₛ_empty is a dubious translation:
+/- warning: with_bot.cSup_empty -> WithBot.csupₛ_empty is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α], Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.hasEmptyc.{u1} (WithBot.{u1} α)))) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α], Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.instEmptyCollectionSet.{u1} (WithBot.{u1} α)))) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α))
-Case conversion may be inaccurate. Consider using '#align with_bot.cSup_empty WithBot.supₛ_emptyₓ'. -/
+Case conversion may be inaccurate. Consider using '#align with_bot.cSup_empty WithBot.csupₛ_emptyₓ'. -/
 @[simp]
-theorem WithBot.supₛ_empty {α : Type _} [SupSet α] : supₛ (∅ : Set (WithBot α)) = ⊥ :=
+theorem WithBot.csupₛ_empty {α : Type _} [SupSet α] : supₛ (∅ : Set (WithBot α)) = ⊥ :=
   if_pos <| Set.empty_subset _
-#align with_bot.cSup_empty WithBot.supₛ_empty
+#align with_bot.cSup_empty WithBot.csupₛ_empty
 
-/- warning: with_bot.csupr_empty -> WithBot.supᵢ_empty is a dubious translation:
+/- warning: with_bot.csupr_empty -> WithBot.csupᵢ_empty is a dubious translation:
 lean 3 declaration is
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : IsEmpty.{u1} ι] [_inst_2 : SupSet.{u2} α] (f : ι -> (WithBot.{u2} α)), Eq.{succ u2} (WithBot.{u2} α) (supᵢ.{u2, u1} (WithBot.{u2} α) (WithBot.hasSup.{u2} α _inst_2) ι (fun (i : ι) => f i)) (Bot.bot.{u2} (WithBot.{u2} α) (WithBot.hasBot.{u2} α))
 but is expected to have type
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : IsEmpty.{u1} ι] [_inst_2 : SupSet.{u2} α] (f : ι -> (WithBot.{u2} α)), Eq.{succ u2} (WithBot.{u2} α) (supᵢ.{u2, u1} (WithBot.{u2} α) (instSupSetWithBot.{u2} α _inst_2) ι (fun (i : ι) => f i)) (Bot.bot.{u2} (WithBot.{u2} α) (WithBot.bot.{u2} α))
-Case conversion may be inaccurate. Consider using '#align with_bot.csupr_empty WithBot.supᵢ_emptyₓ'. -/
+Case conversion may be inaccurate. Consider using '#align with_bot.csupr_empty WithBot.csupᵢ_emptyₓ'. -/
 @[simp]
-theorem WithBot.supᵢ_empty {α : Type _} [IsEmpty ι] [SupSet α] (f : ι → WithBot α) :
+theorem WithBot.csupᵢ_empty {α : Type _} [IsEmpty ι] [SupSet α] (f : ι → WithBot α) :
     (⨆ i, f i) = ⊥ :=
   @WithTop.infᵢ_empty _ αᵒᵈ _ _ _
-#align with_bot.csupr_empty WithBot.supᵢ_empty
+#align with_bot.csupr_empty WithBot.csupᵢ_empty
 
 /- warning: with_bot.coe_Sup' -> WithBot.coe_supₛ' is a dubious translation:
 lean 3 declaration is
@@ -276,7 +276,7 @@ boundedness.-/
 class ConditionallyCompleteLinearOrderBot (α : Type _) extends ConditionallyCompleteLinearOrder α,
   Bot α where
   bot_le : ∀ x : α, ⊥ ≤ x
-  supₛ_empty : Sup ∅ = ⊥
+  csupₛ_empty : Sup ∅ = ⊥
 #align conditionally_complete_linear_order_bot ConditionallyCompleteLinearOrderBot
 -/
 
@@ -309,7 +309,7 @@ instance (priority := 100) CompleteLattice.toConditionallyCompleteLattice [Compl
 instance (priority := 100) CompleteLinearOrder.toConditionallyCompleteLinearOrderBot {α : Type _}
     [CompleteLinearOrder α] : ConditionallyCompleteLinearOrderBot α :=
   { CompleteLattice.toConditionallyCompleteLattice, ‹CompleteLinearOrder α› with
-    supₛ_empty := supₛ_empty }
+    csupₛ_empty := supₛ_empty }
 #align complete_linear_order.to_conditionally_complete_linear_order_bot CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
 -/
 
@@ -342,7 +342,7 @@ noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type _)
       have h's : (upperBounds s).Nonempty := ⟨a, has⟩
       simp only [h's, dif_pos]
       simpa using h.wf.not_lt_min _ h's has
-    supₛ_empty := by simpa using eq_bot_iff.2 (not_lt.1 <| h.wf.not_lt_min _ _ <| mem_univ ⊥) }
+    csupₛ_empty := by simpa using eq_bot_iff.2 (not_lt.1 <| h.wf.not_lt_min _ _ <| mem_univ ⊥) }
 #align is_well_order.conditionally_complete_linear_order_bot IsWellOrder.conditionallyCompleteLinearOrderBot
 -/
 
@@ -2458,7 +2458,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type _}
         · rw [h] at h_1
           cases h_1
         · convert bot_le
-          convert WithBot.supₛ_empty
+          convert WithBot.csupₛ_empty
           rw [h]
           rfl
         · exfalso
@@ -2510,13 +2510,13 @@ noncomputable instance WithBot.WithTop.completeLinearOrder {α : Type _}
 #align with_bot.with_top.complete_linear_order WithBot.WithTop.completeLinearOrder
 -/
 
-/- warning: with_top.supr_coe_eq_top -> WithTop.supr_coe_eq_top is a dubious translation:
+/- warning: with_top.supr_coe_eq_top -> WithTop.supᵢ_coe_eq_top is a dubious translation:
 lean 3 declaration is
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (Eq.{succ u2} (WithTop.{u2} α) (supᵢ.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (Not (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f)))
 but is expected to have type
   forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (Eq.{succ u1} (WithTop.{u1} α) (supᵢ.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (Not (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f)))
-Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_eq_top WithTop.supr_coe_eq_topₓ'. -/
-theorem WithTop.supr_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
+Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_eq_top WithTop.supᵢ_coe_eq_topₓ'. -/
+theorem WithTop.supᵢ_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) = ⊤ ↔ ¬BddAbove (Set.range f) :=
   by
   rw [supᵢ_eq_top, not_bddAbove_iff]
@@ -2525,18 +2525,18 @@ theorem WithTop.supr_coe_eq_top {ι : Sort _} {α : Type _} [ConditionallyComple
     exact ⟨f i, ⟨i, rfl⟩, with_top.coe_lt_coe.mp hi⟩
   · rcases hf (a.untop ha.ne) with ⟨-, ⟨i, rfl⟩, hi⟩
     exact ⟨i, by simpa only [WithTop.coe_untop _ ha.ne] using with_top.coe_lt_coe.mpr hi⟩
-#align with_top.supr_coe_eq_top WithTop.supr_coe_eq_top
+#align with_top.supr_coe_eq_top WithTop.supᵢ_coe_eq_top
 
-/- warning: with_top.supr_coe_lt_top -> WithTop.supr_coe_lt_top is a dubious translation:
+/- warning: with_top.supr_coe_lt_top -> WithTop.supᵢ_coe_lt_top is a dubious translation:
 lean 3 declaration is
   forall {ι : Sort.{u1}} {α : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u2} α] (f : ι -> α), Iff (LT.lt.{u2} (WithTop.{u2} α) (Preorder.toLT.{u2} (WithTop.{u2} α) (WithTop.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))))) (supᵢ.{u2, u1} (WithTop.{u2} α) (WithTop.hasSup.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (ConditionallyCompleteLattice.toHasSup.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))) ι (fun (x : ι) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) α (WithTop.{u2} α) (HasLiftT.mk.{succ u2, succ u2} α (WithTop.{u2} α) (CoeTCₓ.coe.{succ u2, succ u2} α (WithTop.{u2} α) (WithTop.hasCoeT.{u2} α))) (f x))) (Top.top.{u2} (WithTop.{u2} α) (WithTop.hasTop.{u2} α))) (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u2} α _inst_1)))))) (Set.range.{u2, u1} α ι f))
 but is expected to have type
   forall {ι : Sort.{u2}} {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrderBot.{u1} α] (f : ι -> α), Iff (LT.lt.{u1} (WithTop.{u1} α) (Preorder.toLT.{u1} (WithTop.{u1} α) (WithTop.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))))) (supᵢ.{u1, u2} (WithTop.{u1} α) (instSupSetWithTop.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (ConditionallyCompleteLattice.toSupSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))) ι (fun (x : ι) => WithTop.some.{u1} α (f x))) (Top.top.{u1} (WithTop.{u1} α) (WithTop.top.{u1} α))) (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{u1} α _inst_1)))))) (Set.range.{u1, u2} α ι f))
-Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_lt_top WithTop.supr_coe_lt_topₓ'. -/
-theorem WithTop.supr_coe_lt_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
+Case conversion may be inaccurate. Consider using '#align with_top.supr_coe_lt_top WithTop.supᵢ_coe_lt_topₓ'. -/
+theorem WithTop.supᵢ_coe_lt_top {ι : Sort _} {α : Type _} [ConditionallyCompleteLinearOrderBot α]
     (f : ι → α) : (⨆ x, (f x : WithTop α)) < ⊤ ↔ BddAbove (Set.range f) :=
-  lt_top_iff_ne_top.trans <| (WithTop.supr_coe_eq_top f).Not.trans Classical.not_not
-#align with_top.supr_coe_lt_top WithTop.supr_coe_lt_top
+  lt_top_iff_ne_top.trans <| (WithTop.supᵢ_coe_eq_top f).Not.trans Classical.not_not
+#align with_top.supr_coe_lt_top WithTop.supᵢ_coe_lt_top
 
 end WithTopBot
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -249,7 +249,7 @@ class ConditionallyCompleteLattice (α : Type _) extends Lattice α, SupSet α,
 -/
 
 #print ConditionallyCompleteLinearOrder /-
-/- ./././Mathport/Syntax/Translate/Command.lean:417:11: unsupported: advanced extends in structure -/
+/- ./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure -/
 /-- A conditionally complete linear order is a linear order in which
 every nonempty subset which is bounded above has a supremum, and
 every nonempty subset which is bounded below has an infimum.
@@ -260,7 +260,7 @@ complete linear orders, we prefix Inf and Sup by a c everywhere. The same statem
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
 boundedness.-/
 class ConditionallyCompleteLinearOrder (α : Type _) extends ConditionallyCompleteLattice α,
-  "./././Mathport/Syntax/Translate/Command.lean:417:11: unsupported: advanced extends in structure"
+  "./././Mathport/Syntax/Translate/Command.lean:422:11: unsupported: advanced extends in structure"
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -2193,7 +2193,7 @@ variable [ConditionallyCompleteLattice α] [ConditionallyCompleteLattice β] [No
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (supᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (supᵢ.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (supᵢ.{u1, succ u2} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup OrderIso.map_csupₛₓ'. -/
 theorem map_csupₛ (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (supₛ s) = ⨆ x : s, e x :=
@@ -2204,7 +2204,7 @@ theorem map_csupₛ (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : Bdd
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e))) s)))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s)) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cSup' OrderIso.map_csupₛ'ₓ'. -/
 theorem map_csupₛ' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddAbove s) :
     e (supₛ s) = supₛ (e '' s) :=
@@ -2215,7 +2215,7 @@ theorem map_csupₛ' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : Bd
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (supᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (supᵢ.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (supᵢ.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (f i))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (supᵢ.{u3, u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (supᵢ.{u2, u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr OrderIso.map_csupᵢₓ'. -/
 theorem map_csupᵢ (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
     e (⨆ i, f i) = ⨆ i, e (f i) :=
@@ -2226,7 +2226,7 @@ theorem map_csupᵢ (e : α ≃o β) {f : ι → α} (hf : BddAbove (range f)) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u3} γ} {f : γ -> α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α 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(LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (supᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (supᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (supᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (supᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (supᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (supᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (supᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toSupSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_csupr_set OrderIso.map_csupᵢ_setₓ'. -/
 theorem map_csupᵢ_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddAbove (f '' s))
     (hne : s.Nonempty) : e (⨆ i : s, f i) = ⨆ i : s, e (f i) :=
@@ -2237,7 +2237,7 @@ theorem map_csupᵢ_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddA
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (infᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (fun (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (infᵢ.{u1, succ u2} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (infᵢ.{u1, succ u2} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.Elem.{u2} α s) (fun (x : Set.Elem.{u2} α s) => FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf OrderIso.map_cinfₛₓ'. -/
 theorem map_cinfₛ (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (infₛ s) = ⨅ x : s, e x :=
@@ -2248,7 +2248,7 @@ theorem map_cinfₛ (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : Bdd
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} α}, (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (Set.image.{u1, u2} α β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e) s)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} α β)) (RelEmbedding.toEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e))) s)))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] (e : OrderIso.{u2, u1} α β (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))))) {s : Set.{u2} α}, (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Eq.{succ u1} β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s)) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) (Set.image.{u2, u1} α β (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u2 u1, u2, u1} (RelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u2, u1} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u2} α (Preorder.toLE.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e) s)))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cInf' OrderIso.map_cinfₛ'ₓ'. -/
 theorem map_cinfₛ' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : BddBelow s) :
     e (infₛ s) = infₛ (e '' s) :=
@@ -2259,7 +2259,7 @@ theorem map_cinfₛ' (e : α ≃o β) {s : Set α} (hne : s.Nonempty) (hbdd : Bd
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {ι : Sort.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u3} ι] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.range.{u1, u3} α ι f)) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (infᵢ.{u1, u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) ι (fun (i : ι) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f i))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (infᵢ.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (infᵢ.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (f i))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : Nonempty.{u1} ι] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {f : ι -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.range.{u3, u1} α ι f)) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (infᵢ.{u3, u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) ι (fun (i : ι) => f i))) (infᵢ.{u2, u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) ι (fun (i : ι) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f i))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi OrderIso.map_cinfᵢₓ'. -/
 theorem map_cinfᵢ (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
     e (⨅ i, f i) = ⨅ i, e (f i) :=
@@ -2270,7 +2270,7 @@ theorem map_cinfᵢ (e : α ≃o β) {f : ι → α} (hf : BddBelow (range f)) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u3} γ} {f : γ -> α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (Set.image.{u3, u1} γ α f s)) -> (Set.Nonempty.{u3} γ s) -> (Eq.{succ u2} β (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (infᵢ.{u1, succ u3} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))) (infᵢ.{u2, succ u3} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) (fun (i : coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) => coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (OrderIso.{u1, u2} α β (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) (fun (_x : RelIso.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) => α -> β) (RelIso.hasCoeToFun.{u1, u2} α β (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))))) (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))))) e (f ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (HasLiftT.mk.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (CoeTCₓ.coe.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeBase.{succ u3, succ u3} (coeSort.{succ u3, succ (succ u3)} (Set.{u3} γ) Type.{u3} (Set.hasCoeToSort.{u3} γ) s) γ (coeSubtype.{succ u3} γ (fun (x : γ) => Membership.Mem.{u3, u3} γ (Set.{u3} γ) (Set.hasMem.{u3} γ) x s))))) i)))))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (infᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (infᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (infᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u3) (succ u2), succ u3, succ u2} (Function.Embedding.{succ u3, succ u2} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u3, succ u2} α β)) (RelEmbedding.toEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.toRelEmbedding.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) e)) (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] (e : OrderIso.{u3, u2} α β (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))))) {s : Set.{u1} γ} {f : γ -> α}, (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (Set.image.{u1, u3} γ α f s)) -> (Set.Nonempty.{u1} γ s) -> (Eq.{succ u2} β (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (infᵢ.{u3, succ u1} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))) (infᵢ.{u2, succ u1} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_2) (Set.Elem.{u1} γ s) (fun (i : Set.Elem.{u1} γ s) => FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α (fun (_x : α) => β) (RelHomClass.toFunLike.{max u3 u2, u3, u2} (RelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298)) α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298) (RelIso.instRelHomClassRelIso.{u3, u2} α β (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1281 : α) (x._@.Mathlib.Order.Hom.Basic._hyg.1283 : α) => LE.le.{u3} α (Preorder.toLE.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) x._@.Mathlib.Order.Hom.Basic._hyg.1281 x._@.Mathlib.Order.Hom.Basic._hyg.1283) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1296 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1298 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) x._@.Mathlib.Order.Hom.Basic._hyg.1296 x._@.Mathlib.Order.Hom.Basic._hyg.1298))) e (f (Subtype.val.{succ u1} γ (fun (x : γ) => Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) i)))))
 Case conversion may be inaccurate. Consider using '#align order_iso.map_cinfi_set OrderIso.map_cinfᵢ_setₓ'. -/
 theorem map_cinfᵢ_set (e : α ≃o β) {s : Set γ} {f : γ → α} (hf : BddBelow (f '' s))
     (hne : s.Nonempty) : e (⨅ i : s, f i) = ⨅ i : s, e (f i) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

@@ -63,21 +63,37 @@ noncomputable instance {α : Type _} [SupSet α] : SupSet (WithBot α) :=
 noncomputable instance {α : Type _} [Preorder α] [InfSet α] : InfSet (WithBot α) :=
   ⟨(@WithTop.hasSup αᵒᵈ _ _).supₛ⟩
 
+#print WithTop.supₛ_eq /-
 theorem WithTop.supₛ_eq [Preorder α] [SupSet α] {s : Set (WithTop α)} (hs : ⊤ ∉ s)
     (hs' : BddAbove (coe ⁻¹' s : Set α)) : supₛ s = ↑(supₛ (coe ⁻¹' s) : α) :=
   (if_neg hs).trans <| if_pos hs'
 #align with_top.Sup_eq WithTop.supₛ_eq
+-/
 
+#print WithTop.infₛ_eq /-
 theorem WithTop.infₛ_eq [InfSet α] {s : Set (WithTop α)} (hs : ¬s ⊆ {⊤}) :
     infₛ s = ↑(infₛ (coe ⁻¹' s) : α) :=
   if_neg hs
 #align with_top.Inf_eq WithTop.infₛ_eq
+-/
 
+/- warning: with_bot.Inf_eq -> WithBot.infₛ_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (Membership.Mem.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.hasMem.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α)) s)) -> (BddBelow.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s)) -> (Eq.{succ u1} (WithBot.{u1} α) (InfSet.infₛ.{u1} (WithBot.{u1} α) (WithBot.hasInf.{u1} α _inst_1 _inst_2) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (InfSet.infₛ.{u1} α _inst_2 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : Preorder.{u1} α] [_inst_2 : InfSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (Membership.mem.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.instMembershipSet.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α)) s)) -> (BddBelow.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s)) -> (Eq.{succ u1} (WithBot.{u1} α) (InfSet.infₛ.{u1} (WithBot.{u1} α) (instInfSetWithBot.{u1} α _inst_1 _inst_2) s) (WithBot.some.{u1} α (InfSet.infₛ.{u1} α _inst_2 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s))))
+Case conversion may be inaccurate. Consider using '#align with_bot.Inf_eq WithBot.infₛ_eqₓ'. -/
 theorem WithBot.infₛ_eq [Preorder α] [InfSet α] {s : Set (WithBot α)} (hs : ⊥ ∉ s)
     (hs' : BddBelow (coe ⁻¹' s : Set α)) : infₛ s = ↑(infₛ (coe ⁻¹' s) : α) :=
   (if_neg hs).trans <| if_pos hs'
 #align with_bot.Inf_eq WithBot.infₛ_eq
 
+/- warning: with_bot.Sup_eq -> WithBot.supₛ_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (HasSubset.Subset.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.hasSubset.{u1} (WithBot.{u1} α)) s (Singleton.singleton.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.hasSingleton.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.hasBot.{u1} α))))) -> (Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (WithBot.hasSup.{u1} α _inst_1) s) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α))) (SupSet.supₛ.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) α (WithBot.{u1} α) (HasLiftT.mk.{succ u1, succ u1} α (WithBot.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} α (WithBot.{u1} α) (WithBot.hasCoeT.{u1} α)))) s))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : SupSet.{u1} α] {s : Set.{u1} (WithBot.{u1} α)}, (Not (HasSubset.Subset.{u1} (Set.{u1} (WithBot.{u1} α)) (Set.instHasSubsetSet.{u1} (WithBot.{u1} α)) s (Singleton.singleton.{u1, u1} (WithBot.{u1} α) (Set.{u1} (WithBot.{u1} α)) (Set.instSingletonSet.{u1} (WithBot.{u1} α)) (Bot.bot.{u1} (WithBot.{u1} α) (WithBot.bot.{u1} α))))) -> (Eq.{succ u1} (WithBot.{u1} α) (SupSet.supₛ.{u1} (WithBot.{u1} α) (instSupSetWithBot.{u1} α _inst_1) s) (WithBot.some.{u1} α (SupSet.supₛ.{u1} α _inst_1 (Set.preimage.{u1, u1} α (WithBot.{u1} α) (WithBot.some.{u1} α) s))))
+Case conversion may be inaccurate. Consider using '#align with_bot.Sup_eq WithBot.supₛ_eqₓ'. -/
 theorem WithBot.supₛ_eq [SupSet α] {s : Set (WithBot α)} (hs : ¬s ⊆ {⊥}) :
     supₛ s = ↑(supₛ (coe ⁻¹' s) : α) :=
   if_neg hs
@@ -1556,7 +1572,7 @@ variable [IsWellOrder α (· < ·)]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (IsWellOrder.to_isWellFounded.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) _inst_2)) s hs)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8966 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8968 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8966 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8968)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995) _inst_2)) s hs)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9222 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9224)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251) _inst_2)) s hs)
 Case conversion may be inaccurate. Consider using '#align Inf_eq_argmin_on infₛ_eq_argmin_onₓ'. -/
 theorem infₛ_eq_argmin_on (hs : s.Nonempty) :
     infₛ s = argminOn id (@IsWellFounded.wf α (· < ·) _) s hs :=
@@ -1567,7 +1583,7 @@ theorem infₛ_eq_argmin_on (hs : s.Nonempty) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9046 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9048 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9046 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9048)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9302 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9304)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_cinfₛₓ'. -/
 theorem isLeast_cinfₛ (hs : s.Nonempty) : IsLeast s (infₛ s) :=
   by
@@ -1579,7 +1595,7 @@ theorem isLeast_cinfₛ (hs : s.Nonempty) : IsLeast s (infₛ s) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9136 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9138 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9136 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9138)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9392 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9394)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_iff' le_cinfₛ_iff'ₓ'. -/
 theorem le_cinfₛ_iff' (hs : s.Nonempty) : b ≤ infₛ s ↔ b ∈ lowerBounds s :=
   le_isGLB_iff (isLeast_cinfₛ hs).IsGLB
@@ -1589,7 +1605,7 @@ theorem le_cinfₛ_iff' (hs : s.Nonempty) : b ≤ infₛ s ↔ b ∈ lowerBounds
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9191 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9193 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9191 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9193)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9447 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9449)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 Case conversion may be inaccurate. Consider using '#align Inf_mem cinfₛ_memₓ'. -/
 theorem cinfₛ_mem (hs : s.Nonempty) : infₛ s ∈ s :=
   (isLeast_cinfₛ hs).1
@@ -1599,7 +1615,7 @@ theorem cinfₛ_mem (hs : s.Nonempty) : infₛ s ∈ s :=
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9236 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9238 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9236 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9238)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9492 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9494)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 Case conversion may be inaccurate. Consider using '#align infi_mem cinfᵢ_memₓ'. -/
 theorem cinfᵢ_mem [Nonempty ι] (f : ι → α) : infᵢ f ∈ range f :=
   cinfₛ_mem (range_nonempty f)
@@ -1609,7 +1625,7 @@ theorem cinfᵢ_mem [Nonempty ι] (f : ι → α) : infᵢ f ∈ range f :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9290 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9292 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9290 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9292)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9546 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9548)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone_on.map_Inf MonotoneOn.map_cinfₛₓ'. -/
 theorem MonotoneOn.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : MonotoneOn f s) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=
@@ -1620,7 +1636,7 @@ theorem MonotoneOn.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9362 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9364 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9362 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9364)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9618 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9620)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone.map_Inf Monotone.map_cinfₛₓ'. -/
 theorem Monotone.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : Monotone f) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

@@ -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 order.conditionally_complete_lattice.basic
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
+! leanprover-community/mathlib commit 29cb56a7b35f72758b05a30490e1f10bd62c35c1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -63,6 +63,26 @@ noncomputable instance {α : Type _} [SupSet α] : SupSet (WithBot α) :=
 noncomputable instance {α : Type _} [Preorder α] [InfSet α] : InfSet (WithBot α) :=
   ⟨(@WithTop.hasSup αᵒᵈ _ _).supₛ⟩
 
+theorem WithTop.supₛ_eq [Preorder α] [SupSet α] {s : Set (WithTop α)} (hs : ⊤ ∉ s)
+    (hs' : BddAbove (coe ⁻¹' s : Set α)) : supₛ s = ↑(supₛ (coe ⁻¹' s) : α) :=
+  (if_neg hs).trans <| if_pos hs'
+#align with_top.Sup_eq WithTop.supₛ_eq
+
+theorem WithTop.infₛ_eq [InfSet α] {s : Set (WithTop α)} (hs : ¬s ⊆ {⊤}) :
+    infₛ s = ↑(infₛ (coe ⁻¹' s) : α) :=
+  if_neg hs
+#align with_top.Inf_eq WithTop.infₛ_eq
+
+theorem WithBot.infₛ_eq [Preorder α] [InfSet α] {s : Set (WithBot α)} (hs : ⊥ ∉ s)
+    (hs' : BddBelow (coe ⁻¹' s : Set α)) : infₛ s = ↑(infₛ (coe ⁻¹' s) : α) :=
+  (if_neg hs).trans <| if_pos hs'
+#align with_bot.Inf_eq WithBot.infₛ_eq
+
+theorem WithBot.supₛ_eq [SupSet α] {s : Set (WithBot α)} (hs : ¬s ⊆ {⊥}) :
+    supₛ s = ↑(supₛ (coe ⁻¹' s) : α) :=
+  if_neg hs
+#align with_bot.Sup_eq WithBot.supₛ_eq
+
 #print WithTop.infₛ_empty /-
 @[simp]
 theorem WithTop.infₛ_empty {α : Type _} [InfSet α] : infₛ (∅ : Set (WithTop α)) = ⊤ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

@@ -1536,7 +1536,7 @@ variable [IsWellOrder α (· < ·)]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (IsWellOrder.to_isWellFounded.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) _inst_2)) s hs)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8925 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8927 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8925 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8927)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954) _inst_2)) s hs)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8966 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8968 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8966 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8968)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8993 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8995) _inst_2)) s hs)
 Case conversion may be inaccurate. Consider using '#align Inf_eq_argmin_on infₛ_eq_argmin_onₓ'. -/
 theorem infₛ_eq_argmin_on (hs : s.Nonempty) :
     infₛ s = argminOn id (@IsWellFounded.wf α (· < ·) _) s hs :=
@@ -1547,7 +1547,7 @@ theorem infₛ_eq_argmin_on (hs : s.Nonempty) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9005 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9007 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9005 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9007)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9046 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9048 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9046 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9048)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_cinfₛₓ'. -/
 theorem isLeast_cinfₛ (hs : s.Nonempty) : IsLeast s (infₛ s) :=
   by
@@ -1559,7 +1559,7 @@ theorem isLeast_cinfₛ (hs : s.Nonempty) : IsLeast s (infₛ s) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9095 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9097 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9095 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9097)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9136 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9138 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9136 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9138)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_iff' le_cinfₛ_iff'ₓ'. -/
 theorem le_cinfₛ_iff' (hs : s.Nonempty) : b ≤ infₛ s ↔ b ∈ lowerBounds s :=
   le_isGLB_iff (isLeast_cinfₛ hs).IsGLB
@@ -1569,7 +1569,7 @@ theorem le_cinfₛ_iff' (hs : s.Nonempty) : b ≤ infₛ s ↔ b ∈ lowerBounds
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9150 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9152 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9150 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9152)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9191 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9193 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9191 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9193)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 Case conversion may be inaccurate. Consider using '#align Inf_mem cinfₛ_memₓ'. -/
 theorem cinfₛ_mem (hs : s.Nonempty) : infₛ s ∈ s :=
   (isLeast_cinfₛ hs).1
@@ -1579,7 +1579,7 @@ theorem cinfₛ_mem (hs : s.Nonempty) : infₛ s ∈ s :=
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9195 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9197 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9195 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9197)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9236 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9238 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9236 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9238)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 Case conversion may be inaccurate. Consider using '#align infi_mem cinfᵢ_memₓ'. -/
 theorem cinfᵢ_mem [Nonempty ι] (f : ι → α) : infᵢ f ∈ range f :=
   cinfₛ_mem (range_nonempty f)
@@ -1589,7 +1589,7 @@ theorem cinfᵢ_mem [Nonempty ι] (f : ι → α) : infᵢ f ∈ range f :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9290 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9292 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9290 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9292)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone_on.map_Inf MonotoneOn.map_cinfₛₓ'. -/
 theorem MonotoneOn.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : MonotoneOn f s) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=
@@ -1600,7 +1600,7 @@ theorem MonotoneOn.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9321 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9323 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9321 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9323)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9362 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9364 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9362 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9364)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone.map_Inf Monotone.map_cinfₛₓ'. -/
 theorem Monotone.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : Monotone f) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

@@ -1536,7 +1536,7 @@ variable [IsWellOrder α (· < ·)]
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) (IsWellOrder.to_isWellFounded.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))))) _inst_2)) s hs)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8927 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8929 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8927 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8929)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8956 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8956) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8956 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8956) _inst_2)) s hs)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8925 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8927 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8925 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8927)] (hs : Set.Nonempty.{u1} α s), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) (Function.argminOn.{u1, u1} α α (id.{succ u1} α) (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) (IsWellFounded.wf.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954) (IsWellOrder.toIsWellFounded.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8952 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.8954) _inst_2)) s hs)
 Case conversion may be inaccurate. Consider using '#align Inf_eq_argmin_on infₛ_eq_argmin_onₓ'. -/
 theorem infₛ_eq_argmin_on (hs : s.Nonempty) :
     infₛ s = argminOn id (@IsWellFounded.wf α (· < ·) _) s hs :=
@@ -1547,7 +1547,7 @@ theorem infₛ_eq_argmin_on (hs : s.Nonempty) :
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9007 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9009 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9007 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9009)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9005 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9007 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9005 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9007)], (Set.Nonempty.{u1} α s) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s))
 Case conversion may be inaccurate. Consider using '#align is_least_Inf isLeast_cinfₛₓ'. -/
 theorem isLeast_cinfₛ (hs : s.Nonempty) : IsLeast s (infₛ s) :=
   by
@@ -1559,7 +1559,7 @@ theorem isLeast_cinfₛ (hs : s.Nonempty) : IsLeast s (infₛ s) :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9097 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9099 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9097 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9099)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} {b : α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9095 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9097 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9095 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9097)], (Set.Nonempty.{u1} α s) -> (Iff (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) b (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (lowerBounds.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) s)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_iff' le_cinfₛ_iff'ₓ'. -/
 theorem le_cinfₛ_iff' (hs : s.Nonempty) : b ≤ infₛ s ↔ b ∈ lowerBounds s :=
   le_isGLB_iff (isLeast_cinfₛ hs).IsGLB
@@ -1569,7 +1569,7 @@ theorem le_cinfₛ_iff' (hs : s.Nonempty) : b ≤ infₛ s ↔ b ∈ lowerBounds
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))], (Set.Nonempty.{u1} α s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9152 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9154 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9152 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9154)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9150 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9152 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9150 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9152)], (Set.Nonempty.{u1} α s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s) s)
 Case conversion may be inaccurate. Consider using '#align Inf_mem cinfₛ_memₓ'. -/
 theorem cinfₛ_mem (hs : s.Nonempty) : infₛ s ∈ s :=
   (isLeast_cinfₛ hs).1
@@ -1579,7 +1579,7 @@ theorem cinfₛ_mem (hs : s.Nonempty) : infₛ s ∈ s :=
 lean 3 declaration is
   forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9197 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9199 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9197 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9199)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9195 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9197 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9195 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9197)] [_inst_3 : Nonempty.{u2} ι] (f : ι -> α), Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (infᵢ.{u1, u2} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) ι f) (Set.range.{u1, u2} α ι f)
 Case conversion may be inaccurate. Consider using '#align infi_mem cinfᵢ_memₓ'. -/
 theorem cinfᵢ_mem [Nonempty ι] (f : ι → α) : infᵢ f ∈ range f :=
   cinfₛ_mem (range_nonempty f)
@@ -1589,7 +1589,7 @@ theorem cinfᵢ_mem [Nonempty ι] (f : ι → α) : infᵢ f ∈ range f :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9253 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9253)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9249 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9251)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone_on.map_Inf MonotoneOn.map_cinfₛₓ'. -/
 theorem MonotoneOn.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : MonotoneOn f s) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=
@@ -1600,7 +1600,7 @@ theorem MonotoneOn.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))))] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9323 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9325 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9323 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9325)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} α] {s : Set.{u1} α} [_inst_2 : IsWellOrder.{u1} α (fun (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9321 : α) (x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9323 : α) => LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)))))) x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9321 x._@.Mathlib.Order.ConditionallyCompleteLattice.Basic._hyg.9323)] {β : Type.{u2}} [_inst_3 : ConditionallyCompleteLattice.{u2} β] {f : α -> β}, (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_3)))) f) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u2} β (f (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} α _inst_1)) s)) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toInfSet.{u2} β _inst_3) (Set.image.{u1, u2} α β f s)))
 Case conversion may be inaccurate. Consider using '#align monotone.map_Inf Monotone.map_cinfₛₓ'. -/
 theorem Monotone.map_cinfₛ {β : Type _} [ConditionallyCompleteLattice β] {f : α → β}
     (hf : Monotone f) (hs : s.Nonempty) : f (infₛ s) = infₛ (f '' s) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -2279,7 +2279,7 @@ theorem csupₛ_image2_eq_csupₛ_csupₛ (h₁ : ∀ b, GaloisConnection (swap
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} α γ (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.supₛ.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.supₛ.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} α γ (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (u₁ b)) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddAbove.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (SupSet.supₛ.{u3} α (ConditionallyCompleteLattice.toSupSet.{u3} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cSup_cInf csupₛ_image2_eq_csupₛ_cinfₛₓ'. -/
 theorem csupₛ_image2_eq_csupₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (swap l b) (u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
@@ -2291,7 +2291,7 @@ theorem csupₛ_image2_eq_csupₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (swap
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} β γ (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.supₛ.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.infₛ.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} β γ (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (l a) (u₂ a)) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.infₛ.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cSup csupₛ_image2_eq_cinfₛ_csupₛₓ'. -/
 theorem csupₛ_image2_eq_cinfₛ_csupₛ (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a) (u₂ a)) :
@@ -2303,7 +2303,7 @@ theorem csupₛ_image2_eq_cinfₛ_csupₛ (h₁ : ∀ b, GaloisConnection (swap
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u1, u3} (OrderDual.{u1} α) γ (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u2, u3} (OrderDual.{u2} β) γ (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (l a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (u₂ a))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (SupSet.supₛ.{u3} γ (ConditionallyCompleteLattice.toHasSup.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ l s t)) (l (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.infₛ.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} [_inst_1 : ConditionallyCompleteLattice.{u3} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u2} γ] {s : Set.{u3} α} {t : Set.{u1} β} {l : α -> β -> γ} {u₁ : β -> γ -> α} {u₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} (OrderDual.{u3} α) γ (OrderDual.preorder.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} α) α γ (Function.swap.{succ u3, succ u1, succ u2} α β (fun (ᾰ : α) (ᾰ : β) => γ) l b) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.{u3} α) (fun (_x : OrderDual.{u3} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u3} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} (OrderDual.{u3} α) α) (OrderDual.ofDual.{u3} α))) (Function.comp.{succ u2, succ u3, succ u3} γ α (OrderDual.{u3} α) (FunLike.coe.{succ u3, succ u3, succ u3} (Equiv.{succ u3, succ u3} α (OrderDual.{u3} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u3} α) _x) (Equiv.instFunLikeEquiv.{succ u3, succ u3} α (OrderDual.{u3} α)) (OrderDual.toDual.{u3} α)) (u₁ b))) -> (forall (a : α), GaloisConnection.{u1, u2} (OrderDual.{u1} β) γ (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (PartialOrder.toPreorder.{u2} γ (SemilatticeInf.toPartialOrder.{u2} γ (Lattice.toSemilatticeInf.{u2} γ (ConditionallyCompleteLattice.toLattice.{u2} γ _inst_3)))) (Function.comp.{succ u1, succ u1, succ u2} (OrderDual.{u1} β) β γ (l a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β))) (Function.comp.{succ u2, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (u₂ a))) -> (Set.Nonempty.{u3} α s) -> (BddBelow.{u3} α (PartialOrder.toPreorder.{u3} α (SemilatticeInf.toPartialOrder.{u3} α (Lattice.toSemilatticeInf.{u3} α (ConditionallyCompleteLattice.toLattice.{u3} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u2} γ (SupSet.supₛ.{u2} γ (ConditionallyCompleteLattice.toSupSet.{u2} γ _inst_3) (Set.image2.{u3, u1, u2} α β γ l s t)) (l (InfSet.infₛ.{u3} α (ConditionallyCompleteLattice.toInfSet.{u3} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_image2_eq_cInf_cInf csupₛ_image2_eq_cinfₛ_cinfₛₓ'. -/
 theorem csupₛ_image2_eq_cinfₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (swap l b ∘ ofDual) (toDual ∘ u₁ b))
     (h₂ : ∀ a, GaloisConnection (l a ∘ ofDual) (toDual ∘ u₂ a)) :
@@ -2328,7 +2328,7 @@ theorem cinfₛ_image2_eq_cinfₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (l₁
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) (l₁ b) (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ α (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) (l₁ b) (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b)) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddBelow.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (InfSet.infₛ.{u2} α (ConditionallyCompleteLattice.toInfSet.{u2} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cInf_cSup cinfₛ_image2_eq_cinfₛ_csupₛₓ'. -/
 theorem cinfₛ_image2_eq_cinfₛ_csupₛ (h₁ : ∀ b, GaloisConnection (l₁ b) (swap u b))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :
@@ -2340,7 +2340,7 @@ theorem cinfₛ_image2_eq_cinfₛ_csupₛ (h₁ : ∀ b, GaloisConnection (l₁
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (InfSet.infₛ.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ β (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) (l₂ a) (u a)) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (InfSet.infₛ.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cInf cinfₛ_image2_eq_csupₛ_cinfₛₓ'. -/
 theorem cinfₛ_image2_eq_csupₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (l₂ a) (u a)) :
@@ -2352,7 +2352,7 @@ theorem cinfₛ_image2_eq_csupₛ_cinfₛ (h₁ : ∀ b, GaloisConnection (toDua
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] [_inst_2 : ConditionallyCompleteLattice.{u2} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u1} α} {t : Set.{u2} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u1} γ (OrderDual.{u1} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Function.comp.{succ u3, succ u1, succ u1} γ α (OrderDual.{u1} α) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} α (OrderDual.{u1} α)) => α -> (OrderDual.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} α (OrderDual.{u1} α)) (OrderDual.toDual.{u1} α)) (l₁ b)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} α) α γ (Function.swap.{succ u1, succ u2, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) (fun (_x : Equiv.{succ u1, succ u1} (OrderDual.{u1} α) α) => (OrderDual.{u1} α) -> α) (Equiv.hasCoeToFun.{succ u1, succ u1} (OrderDual.{u1} α) α) (OrderDual.ofDual.{u1} α)))) -> (forall (a : α), GaloisConnection.{u3, u2} γ (OrderDual.{u2} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2))))) (Function.comp.{succ u3, succ u2, succ u2} γ β (OrderDual.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} β (OrderDual.{u2} β)) => β -> (OrderDual.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} β (OrderDual.{u2} β)) (OrderDual.toDual.{u2} β)) (l₂ a)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} β) β γ (u a) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) (fun (_x : Equiv.{succ u2, succ u2} (OrderDual.{u2} β) β) => (OrderDual.{u2} β) -> β) (Equiv.hasCoeToFun.{succ u2, succ u2} (OrderDual.{u2} β) β) (OrderDual.ofDual.{u2} β)))) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u2} β t) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toHasInf.{u3} γ _inst_3) (Set.image2.{u1, u2, u3} α β γ u s t)) (u (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β _inst_2) t)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {γ : Type.{u3}} [_inst_1 : ConditionallyCompleteLattice.{u2} α] [_inst_2 : ConditionallyCompleteLattice.{u1} β] [_inst_3 : ConditionallyCompleteLattice.{u3} γ] {s : Set.{u2} α} {t : Set.{u1} β} {u : α -> β -> γ} {l₁ : β -> γ -> α} {l₂ : α -> γ -> β}, (forall (b : β), GaloisConnection.{u3, u2} γ (OrderDual.{u2} α) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1))))) (Function.comp.{succ u3, succ u2, succ u2} γ α (OrderDual.{u2} α) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} α (OrderDual.{u2} α)) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => OrderDual.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} α (OrderDual.{u2} α)) (OrderDual.toDual.{u2} α)) (l₁ b)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} α) α γ (Function.swap.{succ u2, succ u1, succ u3} α β (fun (ᾰ : α) (ᾰ : β) => γ) u b) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.{u2} α) (fun (_x : OrderDual.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} α) => α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} α) α) (OrderDual.ofDual.{u2} α)))) -> (forall (a : α), GaloisConnection.{u3, u1} γ (OrderDual.{u1} β) (PartialOrder.toPreorder.{u3} γ (SemilatticeInf.toPartialOrder.{u3} γ (Lattice.toSemilatticeInf.{u3} γ (ConditionallyCompleteLattice.toLattice.{u3} γ _inst_3)))) (OrderDual.preorder.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2))))) (Function.comp.{succ u3, succ u1, succ u1} γ β (OrderDual.{u1} β) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} β (OrderDual.{u1} β)) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => OrderDual.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} β (OrderDual.{u1} β)) (OrderDual.toDual.{u1} β)) (l₂ a)) (Function.comp.{succ u1, succ u1, succ u3} (OrderDual.{u1} β) β γ (u a) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.{u1} β) (fun (_x : OrderDual.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u1} β) => β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (OrderDual.{u1} β) β) (OrderDual.ofDual.{u1} β)))) -> (Set.Nonempty.{u2} α s) -> (BddAbove.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (ConditionallyCompleteLattice.toLattice.{u2} α _inst_1)))) s) -> (Set.Nonempty.{u1} β t) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β _inst_2)))) t) -> (Eq.{succ u3} γ (InfSet.infₛ.{u3} γ (ConditionallyCompleteLattice.toInfSet.{u3} γ _inst_3) (Set.image2.{u2, u1, u3} α β γ u s t)) (u (SupSet.supₛ.{u2} α (ConditionallyCompleteLattice.toSupSet.{u2} α _inst_1) s) (SupSet.supₛ.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β _inst_2) t)))
 Case conversion may be inaccurate. Consider using '#align cInf_image2_eq_cSup_cSup cinfₛ_image2_eq_csupₛ_csupₛₓ'. -/
 theorem cinfₛ_image2_eq_csupₛ_csupₛ (h₁ : ∀ b, GaloisConnection (toDual ∘ l₁ b) (swap u b ∘ ofDual))
     (h₂ : ∀ a, GaloisConnection (toDual ∘ l₂ a) (u a ∘ ofDual)) :

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

@@ -953,9 +953,9 @@ theorem cinfₛ_singleton (a : α) : infₛ {a} = a :=
 
 /- warning: cSup_pair -> csupₛ_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
 Case conversion may be inaccurate. Consider using '#align cSup_pair csupₛ_pairₓ'. -/
 @[simp]
 theorem csupₛ_pair (a b : α) : supₛ {a, b} = a ⊔ b :=
@@ -964,9 +964,9 @@ theorem csupₛ_pair (a b : α) : supₛ {a, b} = a ⊔ b :=
 
 /- warning: cInf_pair -> cinfₛ_pair is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) b))) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a b)
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a b)
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] (a : α) (b : α), Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) b))) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a b)
 Case conversion may be inaccurate. Consider using '#align cInf_pair cinfₛ_pairₓ'. -/
 @[simp]
 theorem cinfₛ_pair (a b : α) : infₛ {a, b} = a ⊓ b :=
@@ -987,9 +987,9 @@ theorem cinfₛ_le_csupₛ (hb : BddBelow s) (ha : BddAbove s) (ne : s.Nonempty)
 
 /- warning: cSup_union -> csupₛ_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_union csupₛ_unionₓ'. -/
 /-- The sup of a union of two sets is the max of the suprema of each subset, under the assumptions
 that all sets are bounded above and nonempty.-/
@@ -1000,9 +1000,9 @@ theorem csupₛ_union (hs : BddAbove s) (sne : s.Nonempty) (ht : BddAbove t) (tn
 
 /- warning: cInf_union -> cinfₛ_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α t) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)))
 Case conversion may be inaccurate. Consider using '#align cInf_union cinfₛ_unionₓ'. -/
 /-- The inf of a union of two sets is the min of the infima of each subset, under the assumptions
 that all sets are bounded below and nonempty.-/
@@ -1013,9 +1013,9 @@ theorem cinfₛ_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tn
 
 /- warning: cSup_inter_le -> csupₛ_inter_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s) (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) t)))
 Case conversion may be inaccurate. Consider using '#align cSup_inter_le csupₛ_inter_leₓ'. -/
 /-- The supremum of an intersection of two sets is bounded by the minimum of the suprema of each
 set, if all sets are bounded above and nonempty.-/
@@ -1026,9 +1026,9 @@ theorem csupₛ_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).No
 
 /- warning: le_cInf_inter -> le_cinfₛ_inter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) t) -> (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{u1} α (Preorder.toLE.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))))) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) t)) (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)))
 Case conversion may be inaccurate. Consider using '#align le_cInf_inter le_cinfₛ_interₓ'. -/
 /-- The infimum of an intersection of two sets is bounded below by the maximum of the
 infima of each set, if all sets are bounded below and nonempty.-/
@@ -1039,9 +1039,9 @@ theorem le_cinfₛ_inter :
 
 /- warning: cSup_insert -> csupₛ_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toHasSup.{u1} α _inst_1) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (HasSup.sup.{u1} α (SemilatticeSup.toHasSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddAbove.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Sup.sup.{u1} α (SemilatticeSup.toSup.{u1} α (Lattice.toSemilatticeSup.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (SupSet.supₛ.{u1} α (ConditionallyCompleteLattice.toSupSet.{u1} α _inst_1) s)))
 Case conversion may be inaccurate. Consider using '#align cSup_insert csupₛ_insertₓ'. -/
 /-- The supremum of insert a s is the maximum of a and the supremum of s, if s is
 nonempty and bounded above.-/
@@ -1051,9 +1051,9 @@ theorem csupₛ_insert (hs : BddAbove s) (sne : s.Nonempty) : supₛ (insert a s
 
 /- warning: cInf_insert -> cinfₛ_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (HasInf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) a s)) (Inf.inf.{u1} α (SemilatticeInf.toHasInf.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1))) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toHasInf.{u1} α _inst_1) s)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (HasInf.inf.{u1} α (Lattice.toHasInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)))
+  forall {α : Type.{u1}} [_inst_1 : ConditionallyCompleteLattice.{u1} α] {s : Set.{u1} α} {a : α}, (BddBelow.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)))) s) -> (Set.Nonempty.{u1} α s) -> (Eq.{succ u1} α (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) a s)) (Inf.inf.{u1} α (Lattice.toInf.{u1} α (ConditionallyCompleteLattice.toLattice.{u1} α _inst_1)) a (InfSet.infₛ.{u1} α (ConditionallyCompleteLattice.toInfSet.{u1} α _inst_1) s)))
 Case conversion may be inaccurate. Consider using '#align cInf_insert cinfₛ_insertₓ'. -/
 /-- The infimum of insert a s is the minimum of a and the infimum of s, if s is
 nonempty and bounded below.-/

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

A PR accompanying #12339.

Zulip discussion

@@ -1670,7 +1670,7 @@ noncomputable instance WithTop.WithBot.completeLattice {α : Type*}
       show ite _ _ _ ≤ a by
         split_ifs with h₁
         · cases' a with a
-          exact le_rfl
+          · exact le_rfl
           cases h₁ haS
         · cases a
           · exact le_top

Move Set.Ixx, Finset.Ixx, Multiset.Ixx together under two different folders:

• Order.Interval for their definition and basic properties
• Algebra.Order.Interval for their algebraic properties

Move the definitions of Multiset.Ixx to what is now Order.Interval.Multiset. I believe we could just delete this file in a later PR as nothing uses it (and I already had doubts when defining Multiset.Ixx three years ago).

Move the algebraic results out of what is now Order.Interval.Finset.Basic to a new file Algebra.Order.Interval.Finset.Basic.

@@ -6,7 +6,7 @@ Authors: Sébastien Gouëzel
 import Mathlib.Order.Bounds.Basic
 import Mathlib.Order.WellFounded
 import Mathlib.Data.Set.Image
-import Mathlib.Data.Set.Intervals.Basic
+import Mathlib.Order.Interval.Set.Basic
 import Mathlib.Data.Set.Lattice
 
 #align_import order.conditionally_complete_lattice.basic from "leanprover-community/mathlib"@"29cb56a7b35f72758b05a30490e1f10bd62c35c1"

Fix a few names and deduplicate the AddCommGroup ℤ instance

@@ -208,7 +208,8 @@ class ConditionallyCompleteLinearOrder (α : Type*) extends ConditionallyComplet
   csInf_of_not_bddBelow : ∀ s, ¬BddBelow s → sInf s = sInf (∅ : Set α)
 #align conditionally_complete_linear_order ConditionallyCompleteLinearOrder
 
-instance (α : Type*) [ConditionallyCompleteLinearOrder α] : LinearOrder α :=
+instance ConditionallyCompleteLinearOrder.toLinearOrder [ConditionallyCompleteLinearOrder α] :
+    LinearOrder α :=
   { ‹ConditionallyCompleteLinearOrder α› with
     max := Sup.sup, min := Inf.inf,
     min_def := fun a b ↦ by

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

@@ -170,7 +170,7 @@ Typical examples are real numbers or natural numbers.
 To differentiate the statements from the corresponding statements in (unconditional)
 complete lattices, we prefix sInf and subₛ by a c everywhere. The same statements should
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
-boundedness.-/
+boundedness. -/
 class ConditionallyCompleteLattice (α : Type*) extends Lattice α, SupSet α, InfSet α where
   /-- `a ≤ sSup s` for all `a ∈ s`. -/
   le_csSup : ∀ s a, BddAbove s → a ∈ s → a ≤ sSup s
@@ -191,7 +191,7 @@ Typical examples are real numbers or natural numbers.
 To differentiate the statements from the corresponding statements in (unconditional)
 complete linear orders, we prefix sInf and sSup by a c everywhere. The same statements should
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
-boundedness.-/
+boundedness. -/
 class ConditionallyCompleteLinearOrder (α : Type*) extends ConditionallyCompleteLattice α where
   /-- A `ConditionallyCompleteLinearOrder` is total. -/
   le_total (a b : α) : a ≤ b ∨ b ≤ a
@@ -231,7 +231,7 @@ bounded below) has an infimum.  A typical example is the natural numbers.
 To differentiate the statements from the corresponding statements in (unconditional)
 complete linear orders, we prefix `sInf` and `sSup` by a c everywhere. The same statements should
 hold in both worlds, sometimes with additional assumptions of nonemptiness or
-boundedness.-/
+boundedness. -/
 class ConditionallyCompleteLinearOrderBot (α : Type*) extends ConditionallyCompleteLinearOrder α,
   Bot α where
   /-- `⊥` is the least element -/
@@ -248,7 +248,7 @@ instance (priority := 100) ConditionallyCompleteLinearOrderBot.toOrderBot
 
 -- see Note [lower instance priority]
 /-- A complete lattice is a conditionally complete lattice, as there are no restrictions
-on the properties of sInf and sSup in a complete lattice.-/
+on the properties of sInf and sSup in a complete lattice. -/
 instance (priority := 100) CompleteLattice.toConditionallyCompleteLattice [CompleteLattice α] :
     ConditionallyCompleteLattice α :=
   { ‹CompleteLattice α› with
@@ -641,7 +641,7 @@ theorem csInf_eq_of_forall_ge_of_forall_gt_exists_lt :
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness above for one direction, nonemptiness and linear
 order for the other one), so we formulate separately the two implications, contrary to
-the `CompleteLattice` case.-/
+the `CompleteLattice` case. -/
 theorem lt_csSup_of_lt (hs : BddAbove s) (ha : a ∈ s) (h : b < a) : b < sSup s :=
   lt_of_lt_of_le h (le_csSup hs ha)
 #align lt_cSup_of_lt lt_csSup_of_lt
@@ -650,7 +650,7 @@ theorem lt_csSup_of_lt (hs : BddAbove s) (ha : a ∈ s) (h : b < a) : b < sSup s
 This is essentially an iff, except that the assumptions for the two implications are
 slightly different (one needs boundedness below for one direction, nonemptiness and linear
 order for the other one), so we formulate separately the two implications, contrary to
-the `CompleteLattice` case.-/
+the `CompleteLattice` case. -/
 theorem csInf_lt_of_lt : BddBelow s → a ∈ s → a < b → sInf s < b :=
   lt_csSup_of_lt (α := αᵒᵈ)
 #align cInf_lt_of_lt csInf_lt_of_lt
@@ -685,47 +685,47 @@ theorem csInf_pair (a b : α) : sInf {a, b} = a ⊓ b :=
 #align cInf_pair csInf_pair
 
 /-- If a set is bounded below and above, and nonempty, its infimum is less than or equal to
-its supremum.-/
+its supremum. -/
 theorem csInf_le_csSup (hb : BddBelow s) (ha : BddAbove s) (ne : s.Nonempty) : sInf s ≤ sSup s :=
   isGLB_le_isLUB (isGLB_csInf ne hb) (isLUB_csSup ne ha) ne
 #align cInf_le_cSup csInf_le_csSup
 
 /-- The `sSup` of a union of two sets is the max of the suprema of each subset, under the
-assumptions that all sets are bounded above and nonempty.-/
+assumptions that all sets are bounded above and nonempty. -/
 theorem csSup_union (hs : BddAbove s) (sne : s.Nonempty) (ht : BddAbove t) (tne : t.Nonempty) :
     sSup (s ∪ t) = sSup s ⊔ sSup t :=
   ((isLUB_csSup sne hs).union (isLUB_csSup tne ht)).csSup_eq sne.inl
 #align cSup_union csSup_union
 
 /-- The `sInf` of a union of two sets is the min of the infima of each subset, under the assumptions
-that all sets are bounded below and nonempty.-/
+that all sets are bounded below and nonempty. -/
 theorem csInf_union (hs : BddBelow s) (sne : s.Nonempty) (ht : BddBelow t) (tne : t.Nonempty) :
     sInf (s ∪ t) = sInf s ⊓ sInf t :=
   csSup_union (α := αᵒᵈ) hs sne ht tne
 #align cInf_union csInf_union
 
 /-- The supremum of an intersection of two sets is bounded by the minimum of the suprema of each
-set, if all sets are bounded above and nonempty.-/
+set, if all sets are bounded above and nonempty. -/
 theorem csSup_inter_le (hs : BddAbove s) (ht : BddAbove t) (hst : (s ∩ t).Nonempty) :
     sSup (s ∩ t) ≤ sSup s ⊓ sSup t :=
   (csSup_le hst) fun _ hx => le_inf (le_csSup hs hx.1) (le_csSup ht hx.2)
 #align cSup_inter_le csSup_inter_le
 
 /-- The infimum of an intersection of two sets is bounded below by the maximum of the
-infima of each set, if all sets are bounded below and nonempty.-/
+infima of each set, if all sets are bounded below and nonempty. -/
 theorem le_csInf_inter :
     BddBelow s → BddBelow t → (s ∩ t).Nonempty → sInf s ⊔ sInf t ≤ sInf (s ∩ t) :=
   csSup_inter_le (α := αᵒᵈ)
 #align le_cInf_inter le_csInf_inter
 
 /-- The supremum of `insert a s` is the maximum of `a` and the supremum of `s`, if `s` is
-nonempty and bounded above.-/
+nonempty and bounded above. -/
 theorem csSup_insert (hs : BddAbove s) (sne : s.Nonempty) : sSup (insert a s) = a ⊔ sSup s :=
   ((isLUB_csSup sne hs).insert a).csSup_eq (insert_nonempty a s)
 #align cSup_insert csSup_insert
 
 /-- The infimum of `insert a s` is the minimum of `a` and the infimum of `s`, if `s` is
-nonempty and bounded below.-/
+nonempty and bounded below. -/
 theorem csInf_insert (hs : BddBelow s) (sne : s.Nonempty) : sInf (insert a s) = a ⊓ sInf s :=
   csSup_insert (α := αᵒᵈ) hs sne
 #align cInf_insert csInf_insert
@@ -955,7 +955,7 @@ theorem ciSup_mem_iInter_Icc_of_antitone_Icc [SemilatticeSup β] {f g : β → 
 
 /-- Introduction rule to prove that `b` is the supremum of `s`: it suffices to check that
 1) `b` is an upper bound
-2) every other upper bound `b'` satisfies `b ≤ b'`.-/
+2) every other upper bound `b'` satisfies `b ≤ b'`. -/
 theorem csSup_eq_of_is_forall_le_of_forall_le_imp_ge (hs : s.Nonempty) (h_is_ub : ∀ a ∈ s, a ≤ b)
     (h_b_le_ub : ∀ ub, (∀ a ∈ s, a ≤ ub) → b ≤ ub) : sSup s = b :=
   (csSup_le hs h_is_ub).antisymm ((h_b_le_ub _) fun _ => le_csSup ⟨b, h_is_ub⟩)
@@ -1011,7 +1011,7 @@ theorem exists_lt_of_lt_ciSup [Nonempty ι] {f : ι → α} (h : b < iSup f) : 
 #align exists_lt_of_lt_csupr exists_lt_of_lt_ciSup
 
 /-- When `sInf s < b`, there is an element `a` in `s` with `a < b`, if `s` is nonempty and the order
-is a linear order.-/
+is a linear order. -/
 theorem exists_lt_of_csInf_lt (hs : s.Nonempty) (hb : sInf s < b) : ∃ a ∈ s, a < b :=
   exists_lt_of_lt_csSup (α := αᵒᵈ) hs hb
 #align exists_lt_of_cInf_lt exists_lt_of_csInf_lt

fix comment calling a supremum infimum

@@ -1071,7 +1071,7 @@ theorem csSup_eq_csSup_of_forall_exists_le {s t : Set α}
   · simp [csSup_of_not_bddAbove, (not_or.1 B).1, (not_or.1 B).2]
 
 /-- When every element of a set `s` is bounded by an element of a set `t`, and conversely, then
-`s` and `t` have the same supremum. This holds even when the sets may be empty or unbounded. -/
+`s` and `t` have the same infimum. This holds even when the sets may be empty or unbounded. -/
 theorem csInf_eq_csInf_of_forall_exists_le {s t : Set α}
     (hs : ∀ x ∈ s, ∃ y ∈ t, y ≤ x) (ht : ∀ y ∈ t, ∃ x ∈ s, x ≤ y) :
     sInf s = sInf t :=

@@ -1719,7 +1719,7 @@ lemma iSup_coe_lt_top : ⨆ x, (f x : WithTop α) < ⊤ ↔ BddAbove (range f) :
 lemma iInf_coe_eq_top : ⨅ x, (f x : WithTop α) = ⊤ ↔ IsEmpty ι := by simp [isEmpty_iff]
 
 lemma iInf_coe_lt_top : ⨅ i, (f i : WithTop α) < ⊤ ↔ Nonempty ι := by
-  rw [lt_top_iff_ne_top, Ne.def, iInf_coe_eq_top, not_isEmpty_iff]
+  rw [lt_top_iff_ne_top, Ne, iInf_coe_eq_top, not_isEmpty_iff]
 
 end WithTop
 end WithTopBot

This is not exhaustive; it largely does not rename instances that relate to algebra, and only focuses on the "core" order files.

@@ -304,18 +304,18 @@ noncomputable def IsWellOrder.conditionallyCompleteLinearOrderBot (α : Type*)
 
 end
 
-section OrderDual
+namespace OrderDual
 
-instance instConditionallyCompleteLatticeOrderDual (α : Type*) [ConditionallyCompleteLattice α] :
+instance instConditionallyCompleteLattice (α : Type*) [ConditionallyCompleteLattice α] :
     ConditionallyCompleteLattice αᵒᵈ :=
-  { instInfOrderDual α, instSupOrderDual α, OrderDual.lattice α with
+  { OrderDual.instInf α, OrderDual.instSup α, OrderDual.instLattice α with
     le_csSup := ConditionallyCompleteLattice.csInf_le (α := α)
     csSup_le := ConditionallyCompleteLattice.le_csInf (α := α)
     le_csInf := ConditionallyCompleteLattice.csSup_le (α := α)
     csInf_le := ConditionallyCompleteLattice.le_csSup (α := α) }
 
 instance (α : Type*) [ConditionallyCompleteLinearOrder α] : ConditionallyCompleteLinearOrder αᵒᵈ :=
-  { instConditionallyCompleteLatticeOrderDual α, OrderDual.instLinearOrder α with
+  { OrderDual.instConditionallyCompleteLattice α, OrderDual.instLinearOrder α with
     csSup_of_not_bddAbove := ConditionallyCompleteLinearOrder.csInf_of_not_bddBelow (α := α)
     csInf_of_not_bddBelow := ConditionallyCompleteLinearOrder.csSup_of_not_bddAbove (α := α) }
 
@@ -978,7 +978,7 @@ end ConditionallyCompleteLattice
 
 instance Pi.conditionallyCompleteLattice {ι : Type*} {α : ι → Type*}
     [∀ i, ConditionallyCompleteLattice (α i)] : ConditionallyCompleteLattice (∀ i, α i) :=
-  { Pi.lattice, Pi.supSet, Pi.infSet with
+  { Pi.instLattice, Pi.supSet, Pi.infSet with
     le_csSup := fun s f ⟨g, hg⟩ hf i =>
       le_csSup ⟨g i, Set.forall_mem_range.2 fun ⟨f', hf'⟩ => hg hf' i⟩ ⟨⟨f, hf⟩, rfl⟩
     csSup_le := fun s f hs hf i =>

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

• "new lemma"
• "added lemma"

@@ -864,11 +864,11 @@ theorem ciInf_unique [Unique ι] {s : ι → α} : ⨅ i, s i = s default :=
   ciSup_unique (α := αᵒᵈ)
 #align infi_unique ciInf_unique
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem ciSup_subsingleton [Subsingleton ι] (i : ι) (s : ι → α) : ⨆ i, s i = s i :=
   @ciSup_unique α ι _ ⟨⟨i⟩, fun j => Subsingleton.elim j i⟩ _
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem ciInf_subsingleton [Subsingleton ι] (i : ι) (s : ι → α) : ⨅ i, s i = s i :=
   @ciInf_unique α ι _ ⟨⟨i⟩, fun j => Subsingleton.elim j i⟩ _